# Comparing PLI, wPLI, and dPLI#

This example demonstrates the different connectivity information captured by the phase lag index (PLI) [1], weighted phase lag index (wPLI) [2], and directed phase lag index (dPLI) [3] on simulated data.

# Authors: Kenji Marshall <kenji.marshall99@gmail.com>
#          Charlotte Maschke <charlotte.maschke@mail.mcgill.ca>
#          Stefanie Blain-Moraes <stefanie.blain-moraes@mcgill.ca>
#

import matplotlib.pyplot as plt
import mne
import numpy as np
from mne.datasets import sample

from mne_connectivity import spectral_connectivity_epochs


## Background#

The formulae for PLI, wPLI, and dPLI are given below. In these equations, $$X_{ij}$$ is the cross-spectral density (CSD) between two signals $$i, j$$. Importantly, the imaginary component of the CSD is maximal when the signals have a phase difference given by $$k\pi+\frac{\pi}{2}$$, and is $$0$$ when the phase difference is given by $$k\pi$$ (where $$k \in \mathbb{Z}$$). This property provides protection against recognizing volume conduction effects as connectivity, and is the backbone for these methods [2]. In the equations below, $$\mathcal{I}$$ refers to the imaginary component, $$\mathcal{H}$$ refers to the Heaviside step function, and $$sgn$$ refers to the sign function.

$$PLI = |E[sgn(\mathcal{I}(X_{ij}))]|$$ [1]

$$wPLI = \frac{|E[\mathcal{I}(X_{ij})]|}{E[|\mathcal{I}(X_{ij})|]}$$ [2]

$$dPLI = E[\mathcal{H}(\mathcal{I}(X_{ij}))]$$ [3]

All three of these metrics are bounded in the range $$[0, 1]$$.

• For PLI, $$0$$ means that signal $$i$$ leads and lags signal $$j$$ equally often, while a value greater than $$0$$ means that there is an imbalance in the likelihood for signal $$i$$ to be leading or lagging. A value of $$1$$ means that signal $$i$$ only leads or only lags signal $$j$$.

• For wPLI, $$0$$ means that the total weight (not the quantity) of all leading relationships equals the total weight of lagging relationships, while a value greater than $$0$$ means that there is an imbalance between these weights. A value of $$1$$, just as in PLI, means that signal $$i$$ only leads or only lags signal $$j$$.

• With dPLI, we gain the ability to distinguish whether signal $$i$$ is leading or lagging signal $$j$$, complementing the information provided by PLI or wPLI. A value of $$0.5$$ means that signal $$i$$ leads and lags signal $$j$$ equally often. A value in the range $$(0.5, 1.0]$$ means that signal $$i$$ leads signal $$j$$ more often than it lags, with a value of $$1$$ meaning that signal $$i$$ always leads signal $$j$$. A value in the range $$[0.0, 0.5)$$ means that signal $$i$$ lags signal $$j$$ more often than it leads, with a value of $$0$$ meaning that signal $$i$$ always lags signal $$j$$. The PLI can actually be extracted from the dPLI by the relationship $$PLI = 2|dPLI - 0.5|$$, but this relationship is not invertible (dPLI can not be estimated from the PLI).

Overall, these different approaches are closely related but have subtle differences, as will be demonstrated throughout the rest of this example.

## Capturing Leading/Lagging Phase Relationships with dPLI#

The main advantage of dPLI is that it’s directed, meaning it can differentiate between phase relationships which are leading or lagging. To illustrate this, we generate sinusoids with Gaussian noise. In particular, we generate signals with phase differences of $$[-\pi, -\frac{\pi}{2}, 0, \frac{\pi}{2}, \pi]$$ relative to a reference signal. A negative difference means that the reference signal is lagging the other signal.

fs = 250  # sampling rate (Hz)
n_e = 300  # number of epochs
T = 10  # length of epochs (s)
f = 10  # frequency of sinusoids (Hz)
t = np.arange(0, T, 1 / fs)
A = 1  # noise amplitude
sigma = 0.5  # Gaussian noise variance

data = []

phase_differences = [0, -np.pi, -np.pi / 2, 0, np.pi / 2, np.pi]
for ps in zip(phase_differences):
sig = []
for _ in range(n_e):
sig.append(
np.sin(2 * np.pi * f * t - ps)
+ A * np.random.normal(0, sigma, size=t.shape)
)
data.append(sig)

data = np.swapaxes(np.array(data), 0, 1)  # make epochs the first dimension


A snippet of this simulated data is shown below. The blue signal is the reference signal.

fig, ax = plt.subplots(1, 2, figsize=(12, 5), sharey=True)
ax[0].plot(t[:fs], data[0, 0, :fs], label="Reference")
ax[0].plot(t[:fs], data[0, 2, :fs])

ax[0].set_title(r"Phase Lagging ($-\pi/2$ Phase Difference)")
ax[0].set_xlabel("Time (s)")
ax[0].set_ylabel("Signal")
ax[0].legend()

ax[1].plot(t[:fs], data[0, 0, :fs], label="Reference")
ax[1].plot(t[:fs], data[0, 4, :fs])
ax[1].set_title(r"Phase Leading ($\pi/2$ Phase Difference)")
ax[1].set_xlabel("Time (s)")

plt.show()


We will now compute PLI, wPLI, and dPLI for each phase relationship.

conn = []
indices = ([0, 0, 0, 0, 0], [1, 2, 3, 4, 5])
for method in ["pli", "wpli", "dpli"]:
conn.append(
spectral_connectivity_epochs(
data,
method=method,
sfreq=fs,
indices=indices,
fmin=9,
fmax=11,
faverage=True,
).get_data()[:, 0]
)
conn = np.array(conn)

Connectivity computation...
computing connectivity for 5 connections
using t=0.000s..9.996s for estimation (2500 points)
frequencies: 9.0Hz..11.0Hz (21 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: PLI
computing cross-spectral density for epoch 1
computing cross-spectral density for epoch 2
computing cross-spectral density for epoch 3
computing cross-spectral density for epoch 4
computing cross-spectral density for epoch 5
computing cross-spectral density for epoch 6
computing cross-spectral density for epoch 7
computing cross-spectral density for epoch 8
computing cross-spectral density for epoch 9
computing cross-spectral density for epoch 10
computing cross-spectral density for epoch 11
computing cross-spectral density for epoch 12
computing cross-spectral density for epoch 13
computing cross-spectral density for epoch 14
computing cross-spectral density for epoch 15
computing cross-spectral density for epoch 16
computing cross-spectral density for epoch 17
computing cross-spectral density for epoch 18
computing cross-spectral density for epoch 19
computing cross-spectral density for epoch 20
computing cross-spectral density for epoch 21
computing cross-spectral density for epoch 22
computing cross-spectral density for epoch 23
computing cross-spectral density for epoch 24
computing cross-spectral density for epoch 25
computing cross-spectral density for epoch 26
computing cross-spectral density for epoch 27
computing cross-spectral density for epoch 28
computing cross-spectral density for epoch 29
computing cross-spectral density for epoch 30
computing cross-spectral density for epoch 31
computing cross-spectral density for epoch 32
computing cross-spectral density for epoch 33
computing cross-spectral density for epoch 34
computing cross-spectral density for epoch 35
computing cross-spectral density for epoch 36
computing cross-spectral density for epoch 37
computing cross-spectral density for epoch 38
computing cross-spectral density for epoch 39
computing cross-spectral density for epoch 40
computing cross-spectral density for epoch 41
computing cross-spectral density for epoch 42
computing cross-spectral density for epoch 43
computing cross-spectral density for epoch 44
computing cross-spectral density for epoch 45
computing cross-spectral density for epoch 46
computing cross-spectral density for epoch 47
computing cross-spectral density for epoch 48
computing cross-spectral density for epoch 49
computing cross-spectral density for epoch 50
computing cross-spectral density for epoch 51
computing cross-spectral density for epoch 52
computing cross-spectral density for epoch 53
computing cross-spectral density for epoch 54
computing cross-spectral density for epoch 55
computing cross-spectral density for epoch 56
computing cross-spectral density for epoch 57
computing cross-spectral density for epoch 58
computing cross-spectral density for epoch 59
computing cross-spectral density for epoch 60
computing cross-spectral density for epoch 61
computing cross-spectral density for epoch 62
computing cross-spectral density for epoch 63
computing cross-spectral density for epoch 64
computing cross-spectral density for epoch 65
computing cross-spectral density for epoch 66
computing cross-spectral density for epoch 67
computing cross-spectral density for epoch 68
computing cross-spectral density for epoch 69
computing cross-spectral density for epoch 70
computing cross-spectral density for epoch 71
computing cross-spectral density for epoch 72
computing cross-spectral density for epoch 73
computing cross-spectral density for epoch 74
computing cross-spectral density for epoch 75
computing cross-spectral density for epoch 76
computing cross-spectral density for epoch 77
computing cross-spectral density for epoch 78
computing cross-spectral density for epoch 79
computing cross-spectral density for epoch 80
computing cross-spectral density for epoch 81
computing cross-spectral density for epoch 82
computing cross-spectral density for epoch 83
computing cross-spectral density for epoch 84
computing cross-spectral density for epoch 85
computing cross-spectral density for epoch 86
computing cross-spectral density for epoch 87
computing cross-spectral density for epoch 88
computing cross-spectral density for epoch 89
computing cross-spectral density for epoch 90
computing cross-spectral density for epoch 91
computing cross-spectral density for epoch 92
computing cross-spectral density for epoch 93
computing cross-spectral density for epoch 94
computing cross-spectral density for epoch 95
computing cross-spectral density for epoch 96
computing cross-spectral density for epoch 97
computing cross-spectral density for epoch 98
computing cross-spectral density for epoch 99
computing cross-spectral density for epoch 100
computing cross-spectral density for epoch 101
computing cross-spectral density for epoch 102
computing cross-spectral density for epoch 103
computing cross-spectral density for epoch 104
computing cross-spectral density for epoch 105
computing cross-spectral density for epoch 106
computing cross-spectral density for epoch 107
computing cross-spectral density for epoch 108
computing cross-spectral density for epoch 109
computing cross-spectral density for epoch 110
computing cross-spectral density for epoch 111
computing cross-spectral density for epoch 112
computing cross-spectral density for epoch 113
computing cross-spectral density for epoch 114
computing cross-spectral density for epoch 115
computing cross-spectral density for epoch 116
computing cross-spectral density for epoch 117
computing cross-spectral density for epoch 118
computing cross-spectral density for epoch 119
computing cross-spectral density for epoch 120
computing cross-spectral density for epoch 121
computing cross-spectral density for epoch 122
computing cross-spectral density for epoch 123
computing cross-spectral density for epoch 124
computing cross-spectral density for epoch 125
computing cross-spectral density for epoch 126
computing cross-spectral density for epoch 127
computing cross-spectral density for epoch 128
computing cross-spectral density for epoch 129
computing cross-spectral density for epoch 130
computing cross-spectral density for epoch 131
computing cross-spectral density for epoch 132
computing cross-spectral density for epoch 133
computing cross-spectral density for epoch 134
computing cross-spectral density for epoch 135
computing cross-spectral density for epoch 136
computing cross-spectral density for epoch 137
computing cross-spectral density for epoch 138
computing cross-spectral density for epoch 139
computing cross-spectral density for epoch 140
computing cross-spectral density for epoch 141
computing cross-spectral density for epoch 142
computing cross-spectral density for epoch 143
computing cross-spectral density for epoch 144
computing cross-spectral density for epoch 145
computing cross-spectral density for epoch 146
computing cross-spectral density for epoch 147
computing cross-spectral density for epoch 148
computing cross-spectral density for epoch 149
computing cross-spectral density for epoch 150
computing cross-spectral density for epoch 151
computing cross-spectral density for epoch 152
computing cross-spectral density for epoch 153
computing cross-spectral density for epoch 154
computing cross-spectral density for epoch 155
computing cross-spectral density for epoch 156
computing cross-spectral density for epoch 157
computing cross-spectral density for epoch 158
computing cross-spectral density for epoch 159
computing cross-spectral density for epoch 160
computing cross-spectral density for epoch 161
computing cross-spectral density for epoch 162
computing cross-spectral density for epoch 163
computing cross-spectral density for epoch 164
computing cross-spectral density for epoch 165
computing cross-spectral density for epoch 166
computing cross-spectral density for epoch 167
computing cross-spectral density for epoch 168
computing cross-spectral density for epoch 169
computing cross-spectral density for epoch 170
computing cross-spectral density for epoch 171
computing cross-spectral density for epoch 172
computing cross-spectral density for epoch 173
computing cross-spectral density for epoch 174
computing cross-spectral density for epoch 175
computing cross-spectral density for epoch 176
computing cross-spectral density for epoch 177
computing cross-spectral density for epoch 178
computing cross-spectral density for epoch 179
computing cross-spectral density for epoch 180
computing cross-spectral density for epoch 181
computing cross-spectral density for epoch 182
computing cross-spectral density for epoch 183
computing cross-spectral density for epoch 184
computing cross-spectral density for epoch 185
computing cross-spectral density for epoch 186
computing cross-spectral density for epoch 187
computing cross-spectral density for epoch 188
computing cross-spectral density for epoch 189
computing cross-spectral density for epoch 190
computing cross-spectral density for epoch 191
computing cross-spectral density for epoch 192
computing cross-spectral density for epoch 193
computing cross-spectral density for epoch 194
computing cross-spectral density for epoch 195
computing cross-spectral density for epoch 196
computing cross-spectral density for epoch 197
computing cross-spectral density for epoch 198
computing cross-spectral density for epoch 199
computing cross-spectral density for epoch 200
computing cross-spectral density for epoch 201
computing cross-spectral density for epoch 202
computing cross-spectral density for epoch 203
computing cross-spectral density for epoch 204
computing cross-spectral density for epoch 205
computing cross-spectral density for epoch 206
computing cross-spectral density for epoch 207
computing cross-spectral density for epoch 208
computing cross-spectral density for epoch 209
computing cross-spectral density for epoch 210
computing cross-spectral density for epoch 211
computing cross-spectral density for epoch 212
computing cross-spectral density for epoch 213
computing cross-spectral density for epoch 214
computing cross-spectral density for epoch 215
computing cross-spectral density for epoch 216
computing cross-spectral density for epoch 217
computing cross-spectral density for epoch 218
computing cross-spectral density for epoch 219
computing cross-spectral density for epoch 220
computing cross-spectral density for epoch 221
computing cross-spectral density for epoch 222
computing cross-spectral density for epoch 223
computing cross-spectral density for epoch 224
computing cross-spectral density for epoch 225
computing cross-spectral density for epoch 226
computing cross-spectral density for epoch 227
computing cross-spectral density for epoch 228
computing cross-spectral density for epoch 229
computing cross-spectral density for epoch 230
computing cross-spectral density for epoch 231
computing cross-spectral density for epoch 232
computing cross-spectral density for epoch 233
computing cross-spectral density for epoch 234
computing cross-spectral density for epoch 235
computing cross-spectral density for epoch 236
computing cross-spectral density for epoch 237
computing cross-spectral density for epoch 238
computing cross-spectral density for epoch 239
computing cross-spectral density for epoch 240
computing cross-spectral density for epoch 241
computing cross-spectral density for epoch 242
computing cross-spectral density for epoch 243
computing cross-spectral density for epoch 244
computing cross-spectral density for epoch 245
computing cross-spectral density for epoch 246
computing cross-spectral density for epoch 247
computing cross-spectral density for epoch 248
computing cross-spectral density for epoch 249
computing cross-spectral density for epoch 250
computing cross-spectral density for epoch 251
computing cross-spectral density for epoch 252
computing cross-spectral density for epoch 253
computing cross-spectral density for epoch 254
computing cross-spectral density for epoch 255
computing cross-spectral density for epoch 256
computing cross-spectral density for epoch 257
computing cross-spectral density for epoch 258
computing cross-spectral density for epoch 259
computing cross-spectral density for epoch 260
computing cross-spectral density for epoch 261
computing cross-spectral density for epoch 262
computing cross-spectral density for epoch 263
computing cross-spectral density for epoch 264
computing cross-spectral density for epoch 265
computing cross-spectral density for epoch 266
computing cross-spectral density for epoch 267
computing cross-spectral density for epoch 268
computing cross-spectral density for epoch 269
computing cross-spectral density for epoch 270
computing cross-spectral density for epoch 271
computing cross-spectral density for epoch 272
computing cross-spectral density for epoch 273
computing cross-spectral density for epoch 274
computing cross-spectral density for epoch 275
computing cross-spectral density for epoch 276
computing cross-spectral density for epoch 277
computing cross-spectral density for epoch 278
computing cross-spectral density for epoch 279
computing cross-spectral density for epoch 280
computing cross-spectral density for epoch 281
computing cross-spectral density for epoch 282
computing cross-spectral density for epoch 283
computing cross-spectral density for epoch 284
computing cross-spectral density for epoch 285
computing cross-spectral density for epoch 286
computing cross-spectral density for epoch 287
computing cross-spectral density for epoch 288
computing cross-spectral density for epoch 289
computing cross-spectral density for epoch 290
computing cross-spectral density for epoch 291
computing cross-spectral density for epoch 292
computing cross-spectral density for epoch 293
computing cross-spectral density for epoch 294
computing cross-spectral density for epoch 295
computing cross-spectral density for epoch 296
computing cross-spectral density for epoch 297
computing cross-spectral density for epoch 298
computing cross-spectral density for epoch 299
computing cross-spectral density for epoch 300
[Connectivity computation done]
Connectivity computation...
computing connectivity for 5 connections
using t=0.000s..9.996s for estimation (2500 points)
frequencies: 9.0Hz..11.0Hz (21 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: WPLI
computing cross-spectral density for epoch 1
computing cross-spectral density for epoch 2
computing cross-spectral density for epoch 3
computing cross-spectral density for epoch 4
computing cross-spectral density for epoch 5
computing cross-spectral density for epoch 6
computing cross-spectral density for epoch 7
computing cross-spectral density for epoch 8
computing cross-spectral density for epoch 9
computing cross-spectral density for epoch 10
computing cross-spectral density for epoch 11
computing cross-spectral density for epoch 12
computing cross-spectral density for epoch 13
computing cross-spectral density for epoch 14
computing cross-spectral density for epoch 15
computing cross-spectral density for epoch 16
computing cross-spectral density for epoch 17
computing cross-spectral density for epoch 18
computing cross-spectral density for epoch 19
computing cross-spectral density for epoch 20
computing cross-spectral density for epoch 21
computing cross-spectral density for epoch 22
computing cross-spectral density for epoch 23
computing cross-spectral density for epoch 24
computing cross-spectral density for epoch 25
computing cross-spectral density for epoch 26
computing cross-spectral density for epoch 27
computing cross-spectral density for epoch 28
computing cross-spectral density for epoch 29
computing cross-spectral density for epoch 30
computing cross-spectral density for epoch 31
computing cross-spectral density for epoch 32
computing cross-spectral density for epoch 33
computing cross-spectral density for epoch 34
computing cross-spectral density for epoch 35
computing cross-spectral density for epoch 36
computing cross-spectral density for epoch 37
computing cross-spectral density for epoch 38
computing cross-spectral density for epoch 39
computing cross-spectral density for epoch 40
computing cross-spectral density for epoch 41
computing cross-spectral density for epoch 42
computing cross-spectral density for epoch 43
computing cross-spectral density for epoch 44
computing cross-spectral density for epoch 45
computing cross-spectral density for epoch 46
computing cross-spectral density for epoch 47
computing cross-spectral density for epoch 48
computing cross-spectral density for epoch 49
computing cross-spectral density for epoch 50
computing cross-spectral density for epoch 51
computing cross-spectral density for epoch 52
computing cross-spectral density for epoch 53
computing cross-spectral density for epoch 54
computing cross-spectral density for epoch 55
computing cross-spectral density for epoch 56
computing cross-spectral density for epoch 57
computing cross-spectral density for epoch 58
computing cross-spectral density for epoch 59
computing cross-spectral density for epoch 60
computing cross-spectral density for epoch 61
computing cross-spectral density for epoch 62
computing cross-spectral density for epoch 63
computing cross-spectral density for epoch 64
computing cross-spectral density for epoch 65
computing cross-spectral density for epoch 66
computing cross-spectral density for epoch 67
computing cross-spectral density for epoch 68
computing cross-spectral density for epoch 69
computing cross-spectral density for epoch 70
computing cross-spectral density for epoch 71
computing cross-spectral density for epoch 72
computing cross-spectral density for epoch 73
computing cross-spectral density for epoch 74
computing cross-spectral density for epoch 75
computing cross-spectral density for epoch 76
computing cross-spectral density for epoch 77
computing cross-spectral density for epoch 78
computing cross-spectral density for epoch 79
computing cross-spectral density for epoch 80
computing cross-spectral density for epoch 81
computing cross-spectral density for epoch 82
computing cross-spectral density for epoch 83
computing cross-spectral density for epoch 84
computing cross-spectral density for epoch 85
computing cross-spectral density for epoch 86
computing cross-spectral density for epoch 87
computing cross-spectral density for epoch 88
computing cross-spectral density for epoch 89
computing cross-spectral density for epoch 90
computing cross-spectral density for epoch 91
computing cross-spectral density for epoch 92
computing cross-spectral density for epoch 93
computing cross-spectral density for epoch 94
computing cross-spectral density for epoch 95
computing cross-spectral density for epoch 96
computing cross-spectral density for epoch 97
computing cross-spectral density for epoch 98
computing cross-spectral density for epoch 99
computing cross-spectral density for epoch 100
computing cross-spectral density for epoch 101
computing cross-spectral density for epoch 102
computing cross-spectral density for epoch 103
computing cross-spectral density for epoch 104
computing cross-spectral density for epoch 105
computing cross-spectral density for epoch 106
computing cross-spectral density for epoch 107
computing cross-spectral density for epoch 108
computing cross-spectral density for epoch 109
computing cross-spectral density for epoch 110
computing cross-spectral density for epoch 111
computing cross-spectral density for epoch 112
computing cross-spectral density for epoch 113
computing cross-spectral density for epoch 114
computing cross-spectral density for epoch 115
computing cross-spectral density for epoch 116
computing cross-spectral density for epoch 117
computing cross-spectral density for epoch 118
computing cross-spectral density for epoch 119
computing cross-spectral density for epoch 120
computing cross-spectral density for epoch 121
computing cross-spectral density for epoch 122
computing cross-spectral density for epoch 123
computing cross-spectral density for epoch 124
computing cross-spectral density for epoch 125
computing cross-spectral density for epoch 126
computing cross-spectral density for epoch 127
computing cross-spectral density for epoch 128
computing cross-spectral density for epoch 129
computing cross-spectral density for epoch 130
computing cross-spectral density for epoch 131
computing cross-spectral density for epoch 132
computing cross-spectral density for epoch 133
computing cross-spectral density for epoch 134
computing cross-spectral density for epoch 135
computing cross-spectral density for epoch 136
computing cross-spectral density for epoch 137
computing cross-spectral density for epoch 138
computing cross-spectral density for epoch 139
computing cross-spectral density for epoch 140
computing cross-spectral density for epoch 141
computing cross-spectral density for epoch 142
computing cross-spectral density for epoch 143
computing cross-spectral density for epoch 144
computing cross-spectral density for epoch 145
computing cross-spectral density for epoch 146
computing cross-spectral density for epoch 147
computing cross-spectral density for epoch 148
computing cross-spectral density for epoch 149
computing cross-spectral density for epoch 150
computing cross-spectral density for epoch 151
computing cross-spectral density for epoch 152
computing cross-spectral density for epoch 153
computing cross-spectral density for epoch 154
computing cross-spectral density for epoch 155
computing cross-spectral density for epoch 156
computing cross-spectral density for epoch 157
computing cross-spectral density for epoch 158
computing cross-spectral density for epoch 159
computing cross-spectral density for epoch 160
computing cross-spectral density for epoch 161
computing cross-spectral density for epoch 162
computing cross-spectral density for epoch 163
computing cross-spectral density for epoch 164
computing cross-spectral density for epoch 165
computing cross-spectral density for epoch 166
computing cross-spectral density for epoch 167
computing cross-spectral density for epoch 168
computing cross-spectral density for epoch 169
computing cross-spectral density for epoch 170
computing cross-spectral density for epoch 171
computing cross-spectral density for epoch 172
computing cross-spectral density for epoch 173
computing cross-spectral density for epoch 174
computing cross-spectral density for epoch 175
computing cross-spectral density for epoch 176
computing cross-spectral density for epoch 177
computing cross-spectral density for epoch 178
computing cross-spectral density for epoch 179
computing cross-spectral density for epoch 180
computing cross-spectral density for epoch 181
computing cross-spectral density for epoch 182
computing cross-spectral density for epoch 183
computing cross-spectral density for epoch 184
computing cross-spectral density for epoch 185
computing cross-spectral density for epoch 186
computing cross-spectral density for epoch 187
computing cross-spectral density for epoch 188
computing cross-spectral density for epoch 189
computing cross-spectral density for epoch 190
computing cross-spectral density for epoch 191
computing cross-spectral density for epoch 192
computing cross-spectral density for epoch 193
computing cross-spectral density for epoch 194
computing cross-spectral density for epoch 195
computing cross-spectral density for epoch 196
computing cross-spectral density for epoch 197
computing cross-spectral density for epoch 198
computing cross-spectral density for epoch 199
computing cross-spectral density for epoch 200
computing cross-spectral density for epoch 201
computing cross-spectral density for epoch 202
computing cross-spectral density for epoch 203
computing cross-spectral density for epoch 204
computing cross-spectral density for epoch 205
computing cross-spectral density for epoch 206
computing cross-spectral density for epoch 207
computing cross-spectral density for epoch 208
computing cross-spectral density for epoch 209
computing cross-spectral density for epoch 210
computing cross-spectral density for epoch 211
computing cross-spectral density for epoch 212
computing cross-spectral density for epoch 213
computing cross-spectral density for epoch 214
computing cross-spectral density for epoch 215
computing cross-spectral density for epoch 216
computing cross-spectral density for epoch 217
computing cross-spectral density for epoch 218
computing cross-spectral density for epoch 219
computing cross-spectral density for epoch 220
computing cross-spectral density for epoch 221
computing cross-spectral density for epoch 222
computing cross-spectral density for epoch 223
computing cross-spectral density for epoch 224
computing cross-spectral density for epoch 225
computing cross-spectral density for epoch 226
computing cross-spectral density for epoch 227
computing cross-spectral density for epoch 228
computing cross-spectral density for epoch 229
computing cross-spectral density for epoch 230
computing cross-spectral density for epoch 231
computing cross-spectral density for epoch 232
computing cross-spectral density for epoch 233
computing cross-spectral density for epoch 234
computing cross-spectral density for epoch 235
computing cross-spectral density for epoch 236
computing cross-spectral density for epoch 237
computing cross-spectral density for epoch 238
computing cross-spectral density for epoch 239
computing cross-spectral density for epoch 240
computing cross-spectral density for epoch 241
computing cross-spectral density for epoch 242
computing cross-spectral density for epoch 243
computing cross-spectral density for epoch 244
computing cross-spectral density for epoch 245
computing cross-spectral density for epoch 246
computing cross-spectral density for epoch 247
computing cross-spectral density for epoch 248
computing cross-spectral density for epoch 249
computing cross-spectral density for epoch 250
computing cross-spectral density for epoch 251
computing cross-spectral density for epoch 252
computing cross-spectral density for epoch 253
computing cross-spectral density for epoch 254
computing cross-spectral density for epoch 255
computing cross-spectral density for epoch 256
computing cross-spectral density for epoch 257
computing cross-spectral density for epoch 258
computing cross-spectral density for epoch 259
computing cross-spectral density for epoch 260
computing cross-spectral density for epoch 261
computing cross-spectral density for epoch 262
computing cross-spectral density for epoch 263
computing cross-spectral density for epoch 264
computing cross-spectral density for epoch 265
computing cross-spectral density for epoch 266
computing cross-spectral density for epoch 267
computing cross-spectral density for epoch 268
computing cross-spectral density for epoch 269
computing cross-spectral density for epoch 270
computing cross-spectral density for epoch 271
computing cross-spectral density for epoch 272
computing cross-spectral density for epoch 273
computing cross-spectral density for epoch 274
computing cross-spectral density for epoch 275
computing cross-spectral density for epoch 276
computing cross-spectral density for epoch 277
computing cross-spectral density for epoch 278
computing cross-spectral density for epoch 279
computing cross-spectral density for epoch 280
computing cross-spectral density for epoch 281
computing cross-spectral density for epoch 282
computing cross-spectral density for epoch 283
computing cross-spectral density for epoch 284
computing cross-spectral density for epoch 285
computing cross-spectral density for epoch 286
computing cross-spectral density for epoch 287
computing cross-spectral density for epoch 288
computing cross-spectral density for epoch 289
computing cross-spectral density for epoch 290
computing cross-spectral density for epoch 291
computing cross-spectral density for epoch 292
computing cross-spectral density for epoch 293
computing cross-spectral density for epoch 294
computing cross-spectral density for epoch 295
computing cross-spectral density for epoch 296
computing cross-spectral density for epoch 297
computing cross-spectral density for epoch 298
computing cross-spectral density for epoch 299
computing cross-spectral density for epoch 300
[Connectivity computation done]
Connectivity computation...
computing connectivity for 5 connections
using t=0.000s..9.996s for estimation (2500 points)
frequencies: 9.0Hz..11.0Hz (21 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: DPLI
computing cross-spectral density for epoch 1
computing cross-spectral density for epoch 2
computing cross-spectral density for epoch 3
computing cross-spectral density for epoch 4
computing cross-spectral density for epoch 5
computing cross-spectral density for epoch 6
computing cross-spectral density for epoch 7
computing cross-spectral density for epoch 8
computing cross-spectral density for epoch 9
computing cross-spectral density for epoch 10
computing cross-spectral density for epoch 11
computing cross-spectral density for epoch 12
computing cross-spectral density for epoch 13
computing cross-spectral density for epoch 14
computing cross-spectral density for epoch 15
computing cross-spectral density for epoch 16
computing cross-spectral density for epoch 17
computing cross-spectral density for epoch 18
computing cross-spectral density for epoch 19
computing cross-spectral density for epoch 20
computing cross-spectral density for epoch 21
computing cross-spectral density for epoch 22
computing cross-spectral density for epoch 23
computing cross-spectral density for epoch 24
computing cross-spectral density for epoch 25
computing cross-spectral density for epoch 26
computing cross-spectral density for epoch 27
computing cross-spectral density for epoch 28
computing cross-spectral density for epoch 29
computing cross-spectral density for epoch 30
computing cross-spectral density for epoch 31
computing cross-spectral density for epoch 32
computing cross-spectral density for epoch 33
computing cross-spectral density for epoch 34
computing cross-spectral density for epoch 35
computing cross-spectral density for epoch 36
computing cross-spectral density for epoch 37
computing cross-spectral density for epoch 38
computing cross-spectral density for epoch 39
computing cross-spectral density for epoch 40
computing cross-spectral density for epoch 41
computing cross-spectral density for epoch 42
computing cross-spectral density for epoch 43
computing cross-spectral density for epoch 44
computing cross-spectral density for epoch 45
computing cross-spectral density for epoch 46
computing cross-spectral density for epoch 47
computing cross-spectral density for epoch 48
computing cross-spectral density for epoch 49
computing cross-spectral density for epoch 50
computing cross-spectral density for epoch 51
computing cross-spectral density for epoch 52
computing cross-spectral density for epoch 53
computing cross-spectral density for epoch 54
computing cross-spectral density for epoch 55
computing cross-spectral density for epoch 56
computing cross-spectral density for epoch 57
computing cross-spectral density for epoch 58
computing cross-spectral density for epoch 59
computing cross-spectral density for epoch 60
computing cross-spectral density for epoch 61
computing cross-spectral density for epoch 62
computing cross-spectral density for epoch 63
computing cross-spectral density for epoch 64
computing cross-spectral density for epoch 65
computing cross-spectral density for epoch 66
computing cross-spectral density for epoch 67
computing cross-spectral density for epoch 68
computing cross-spectral density for epoch 69
computing cross-spectral density for epoch 70
computing cross-spectral density for epoch 71
computing cross-spectral density for epoch 72
computing cross-spectral density for epoch 73
computing cross-spectral density for epoch 74
computing cross-spectral density for epoch 75
computing cross-spectral density for epoch 76
computing cross-spectral density for epoch 77
computing cross-spectral density for epoch 78
computing cross-spectral density for epoch 79
computing cross-spectral density for epoch 80
computing cross-spectral density for epoch 81
computing cross-spectral density for epoch 82
computing cross-spectral density for epoch 83
computing cross-spectral density for epoch 84
computing cross-spectral density for epoch 85
computing cross-spectral density for epoch 86
computing cross-spectral density for epoch 87
computing cross-spectral density for epoch 88
computing cross-spectral density for epoch 89
computing cross-spectral density for epoch 90
computing cross-spectral density for epoch 91
computing cross-spectral density for epoch 92
computing cross-spectral density for epoch 93
computing cross-spectral density for epoch 94
computing cross-spectral density for epoch 95
computing cross-spectral density for epoch 96
computing cross-spectral density for epoch 97
computing cross-spectral density for epoch 98
computing cross-spectral density for epoch 99
computing cross-spectral density for epoch 100
computing cross-spectral density for epoch 101
computing cross-spectral density for epoch 102
computing cross-spectral density for epoch 103
computing cross-spectral density for epoch 104
computing cross-spectral density for epoch 105
computing cross-spectral density for epoch 106
computing cross-spectral density for epoch 107
computing cross-spectral density for epoch 108
computing cross-spectral density for epoch 109
computing cross-spectral density for epoch 110
computing cross-spectral density for epoch 111
computing cross-spectral density for epoch 112
computing cross-spectral density for epoch 113
computing cross-spectral density for epoch 114
computing cross-spectral density for epoch 115
computing cross-spectral density for epoch 116
computing cross-spectral density for epoch 117
computing cross-spectral density for epoch 118
computing cross-spectral density for epoch 119
computing cross-spectral density for epoch 120
computing cross-spectral density for epoch 121
computing cross-spectral density for epoch 122
computing cross-spectral density for epoch 123
computing cross-spectral density for epoch 124
computing cross-spectral density for epoch 125
computing cross-spectral density for epoch 126
computing cross-spectral density for epoch 127
computing cross-spectral density for epoch 128
computing cross-spectral density for epoch 129
computing cross-spectral density for epoch 130
computing cross-spectral density for epoch 131
computing cross-spectral density for epoch 132
computing cross-spectral density for epoch 133
computing cross-spectral density for epoch 134
computing cross-spectral density for epoch 135
computing cross-spectral density for epoch 136
computing cross-spectral density for epoch 137
computing cross-spectral density for epoch 138
computing cross-spectral density for epoch 139
computing cross-spectral density for epoch 140
computing cross-spectral density for epoch 141
computing cross-spectral density for epoch 142
computing cross-spectral density for epoch 143
computing cross-spectral density for epoch 144
computing cross-spectral density for epoch 145
computing cross-spectral density for epoch 146
computing cross-spectral density for epoch 147
computing cross-spectral density for epoch 148
computing cross-spectral density for epoch 149
computing cross-spectral density for epoch 150
computing cross-spectral density for epoch 151
computing cross-spectral density for epoch 152
computing cross-spectral density for epoch 153
computing cross-spectral density for epoch 154
computing cross-spectral density for epoch 155
computing cross-spectral density for epoch 156
computing cross-spectral density for epoch 157
computing cross-spectral density for epoch 158
computing cross-spectral density for epoch 159
computing cross-spectral density for epoch 160
computing cross-spectral density for epoch 161
computing cross-spectral density for epoch 162
computing cross-spectral density for epoch 163
computing cross-spectral density for epoch 164
computing cross-spectral density for epoch 165
computing cross-spectral density for epoch 166
computing cross-spectral density for epoch 167
computing cross-spectral density for epoch 168
computing cross-spectral density for epoch 169
computing cross-spectral density for epoch 170
computing cross-spectral density for epoch 171
computing cross-spectral density for epoch 172
computing cross-spectral density for epoch 173
computing cross-spectral density for epoch 174
computing cross-spectral density for epoch 175
computing cross-spectral density for epoch 176
computing cross-spectral density for epoch 177
computing cross-spectral density for epoch 178
computing cross-spectral density for epoch 179
computing cross-spectral density for epoch 180
computing cross-spectral density for epoch 181
computing cross-spectral density for epoch 182
computing cross-spectral density for epoch 183
computing cross-spectral density for epoch 184
computing cross-spectral density for epoch 185
computing cross-spectral density for epoch 186
computing cross-spectral density for epoch 187
computing cross-spectral density for epoch 188
computing cross-spectral density for epoch 189
computing cross-spectral density for epoch 190
computing cross-spectral density for epoch 191
computing cross-spectral density for epoch 192
computing cross-spectral density for epoch 193
computing cross-spectral density for epoch 194
computing cross-spectral density for epoch 195
computing cross-spectral density for epoch 196
computing cross-spectral density for epoch 197
computing cross-spectral density for epoch 198
computing cross-spectral density for epoch 199
computing cross-spectral density for epoch 200
computing cross-spectral density for epoch 201
computing cross-spectral density for epoch 202
computing cross-spectral density for epoch 203
computing cross-spectral density for epoch 204
computing cross-spectral density for epoch 205
computing cross-spectral density for epoch 206
computing cross-spectral density for epoch 207
computing cross-spectral density for epoch 208
computing cross-spectral density for epoch 209
computing cross-spectral density for epoch 210
computing cross-spectral density for epoch 211
computing cross-spectral density for epoch 212
computing cross-spectral density for epoch 213
computing cross-spectral density for epoch 214
computing cross-spectral density for epoch 215
computing cross-spectral density for epoch 216
computing cross-spectral density for epoch 217
computing cross-spectral density for epoch 218
computing cross-spectral density for epoch 219
computing cross-spectral density for epoch 220
computing cross-spectral density for epoch 221
computing cross-spectral density for epoch 222
computing cross-spectral density for epoch 223
computing cross-spectral density for epoch 224
computing cross-spectral density for epoch 225
computing cross-spectral density for epoch 226
computing cross-spectral density for epoch 227
computing cross-spectral density for epoch 228
computing cross-spectral density for epoch 229
computing cross-spectral density for epoch 230
computing cross-spectral density for epoch 231
computing cross-spectral density for epoch 232
computing cross-spectral density for epoch 233
computing cross-spectral density for epoch 234
computing cross-spectral density for epoch 235
computing cross-spectral density for epoch 236
computing cross-spectral density for epoch 237
computing cross-spectral density for epoch 238
computing cross-spectral density for epoch 239
computing cross-spectral density for epoch 240
computing cross-spectral density for epoch 241
computing cross-spectral density for epoch 242
computing cross-spectral density for epoch 243
computing cross-spectral density for epoch 244
computing cross-spectral density for epoch 245
computing cross-spectral density for epoch 246
computing cross-spectral density for epoch 247
computing cross-spectral density for epoch 248
computing cross-spectral density for epoch 249
computing cross-spectral density for epoch 250
computing cross-spectral density for epoch 251
computing cross-spectral density for epoch 252
computing cross-spectral density for epoch 253
computing cross-spectral density for epoch 254
computing cross-spectral density for epoch 255
computing cross-spectral density for epoch 256
computing cross-spectral density for epoch 257
computing cross-spectral density for epoch 258
computing cross-spectral density for epoch 259
computing cross-spectral density for epoch 260
computing cross-spectral density for epoch 261
computing cross-spectral density for epoch 262
computing cross-spectral density for epoch 263
computing cross-spectral density for epoch 264
computing cross-spectral density for epoch 265
computing cross-spectral density for epoch 266
computing cross-spectral density for epoch 267
computing cross-spectral density for epoch 268
computing cross-spectral density for epoch 269
computing cross-spectral density for epoch 270
computing cross-spectral density for epoch 271
computing cross-spectral density for epoch 272
computing cross-spectral density for epoch 273
computing cross-spectral density for epoch 274
computing cross-spectral density for epoch 275
computing cross-spectral density for epoch 276
computing cross-spectral density for epoch 277
computing cross-spectral density for epoch 278
computing cross-spectral density for epoch 279
computing cross-spectral density for epoch 280
computing cross-spectral density for epoch 281
computing cross-spectral density for epoch 282
computing cross-spectral density for epoch 283
computing cross-spectral density for epoch 284
computing cross-spectral density for epoch 285
computing cross-spectral density for epoch 286
computing cross-spectral density for epoch 287
computing cross-spectral density for epoch 288
computing cross-spectral density for epoch 289
computing cross-spectral density for epoch 290
computing cross-spectral density for epoch 291
computing cross-spectral density for epoch 292
computing cross-spectral density for epoch 293
computing cross-spectral density for epoch 294
computing cross-spectral density for epoch 295
computing cross-spectral density for epoch 296
computing cross-spectral density for epoch 297
computing cross-spectral density for epoch 298
computing cross-spectral density for epoch 299
computing cross-spectral density for epoch 300
[Connectivity computation done]


The estimated connectivites are shown in the figure below, which provides insight into the differences between PLI/wPLI, and dPLI.

Similarities Of All Measures

• Capture presence of connectivity in same situations (phase difference of $$\pm\frac{\pi}{2}$$)

• Do not predict connectivity when phase difference is a multiple of $$\pi$$

• Bounded between $$0$$ and $$1$$

How dPLI is Different Than PLI/wPLI

• Null connectivity is $$0$$ for PLI and wPLI, but $$0.5$$ for dPLI

• dPLI differentiates whether the reference signal is leading or lagging the other signal (lagging if $$0 <= dPlI < 0.5$$, leading if $$0.5 < dPLI <= 1.0$$)

x = np.arange(5)

plt.figure()
plt.bar(x - 0.2, conn[0], 0.2, align="center", label="PLI")
plt.bar(x, conn[1], 0.2, align="center", label="wPLI")
plt.bar(x + 0.2, conn[2], 0.2, align="center", label="dPLI")

plt.title("Connectivity Estimation Comparison")
plt.xticks(x, (r"$-\pi$", r"$-\pi/2$", r"$0$", r"$\pi/2$", r"$\pi$"))
plt.legend()
plt.xlabel("Phase Difference")
plt.ylabel("Estimated Connectivity")

plt.show()


## Robustness to Outliers and Noise with wPLI#

The previous experiment illustrated the advantages conferred by dPLI when differentiating leading and lagging phase relationships. This experiment will now focus on understanding the advantages of wPLI, and explore how it extends upon PLI.

The main difference between PLI and wPLI is in how different phase relationships are weighted. In PLI, phase differences are weighted as $$-1$$ or $$1$$ according to their sign. In wPLI, phase differences are weighted based on their value, meaning that phase differences closer to $$\pm\frac{\pi}{2}$$ are weighted more heavily than those close to $$0$$ or any other multiple of $$\pi$$.

This avoids a discontinuity at the transition between positive and negative phase, treating all phase differences near this transition in a similar way. This provides some robustness against outliers and noise when estimating connectivity. For instance, volume conduction can distort EEG/MEG recordings, wherein signals emanating from the same neural source will be picked up by multiple sensors on the scalp. This can effect connectivity estimations, bringing the relative phase differences between two signals close to $$0$$. wPLI minimizes the contribution of phase relationships that are small but non-zero (and may thus be attributed to volume conduciton), while PLI weighs these in the same way as phase relationships of $$\pm\frac{\pi}{2}$$.

To demonstrate this, we recreate a result from (Vinck et al, 2011) [2]. Two sinusoids are simulated, where the phase difference for half of the epochs is $$\frac{\pi}{2}$$, and is $$-\frac{\pi}{100}$$ for the others. We also explore the effect of applying uniform noise to this phase difference.

n_noise = 41  # amount of noise amplitude samples in [0, 4]
data = [[]]

# Generate reference
for _ in range(n_e):
data[0].append(np.sin(2 * np.pi * f * t))

A_list = np.linspace(0, 4, n_noise)

for A in A_list:
sig = []
# Generate other signal
for _ in range(int(n_e / 2)):  # phase difference -pi/100
sig.append(
np.sin(2 * np.pi * f * t + np.pi / 100 + A * np.random.uniform(-1, 1))
)
for _ in range(int(n_e / 2), n_e):  # phase difference pi/2
sig.append(np.sin(2 * np.pi * f * t - np.pi / 2 + A * np.random.uniform(-1, 1)))
data.append(sig)

data = np.swapaxes(np.array(data), 0, 1)

# Visualize the data
fig, ax = plt.subplots(1, 2, figsize=(12, 5), sharey=True)
ax[0].plot(t[:10], data[0, 0, :10], label="Reference")
ax[0].plot(t[:10], data[1, 1, :10])

ax[0].set_title(r"Phase Lagging ($-\pi/100$ Phase Difference)")
ax[0].set_xlabel("Time (s)")
ax[0].set_ylabel("Signal")
ax[0].legend()

ax[1].plot(t[:fs], data[0, 0, :fs], label="Reference")
ax[1].plot(t[:fs], data[-1, 1, :fs])
ax[1].set_title(r"Phase Leading ($\pi/2$ Phase Difference)")
ax[1].set_xlabel("Time (s)")

plt.show()


We can now compute PLI and wPLI

conn = []
indices = ([0] * n_noise, np.arange(1, n_noise + 1))
for method in ["pli", "wpli"]:
conn.append(
spectral_connectivity_epochs(
data,
method=method,
sfreq=fs,
indices=indices,
fmin=9,
fmax=11,
faverage=True,
).get_data()[:, 0]
)
conn = np.array(conn)

Connectivity computation...
computing connectivity for 41 connections
using t=0.000s..9.996s for estimation (2500 points)
frequencies: 9.0Hz..11.0Hz (21 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: PLI
computing cross-spectral density for epoch 1
computing cross-spectral density for epoch 2
computing cross-spectral density for epoch 3
computing cross-spectral density for epoch 4
computing cross-spectral density for epoch 5
computing cross-spectral density for epoch 6
computing cross-spectral density for epoch 7
computing cross-spectral density for epoch 8
computing cross-spectral density for epoch 9
computing cross-spectral density for epoch 10
computing cross-spectral density for epoch 11
computing cross-spectral density for epoch 12
computing cross-spectral density for epoch 13
computing cross-spectral density for epoch 14
computing cross-spectral density for epoch 15
computing cross-spectral density for epoch 16
computing cross-spectral density for epoch 17
computing cross-spectral density for epoch 18
computing cross-spectral density for epoch 19
computing cross-spectral density for epoch 20
computing cross-spectral density for epoch 21
computing cross-spectral density for epoch 22
computing cross-spectral density for epoch 23
computing cross-spectral density for epoch 24
computing cross-spectral density for epoch 25
computing cross-spectral density for epoch 26
computing cross-spectral density for epoch 27
computing cross-spectral density for epoch 28
computing cross-spectral density for epoch 29
computing cross-spectral density for epoch 30
computing cross-spectral density for epoch 31
computing cross-spectral density for epoch 32
computing cross-spectral density for epoch 33
computing cross-spectral density for epoch 34
computing cross-spectral density for epoch 35
computing cross-spectral density for epoch 36
computing cross-spectral density for epoch 37
computing cross-spectral density for epoch 38
computing cross-spectral density for epoch 39
computing cross-spectral density for epoch 40
computing cross-spectral density for epoch 41
computing cross-spectral density for epoch 42
computing cross-spectral density for epoch 43
computing cross-spectral density for epoch 44
computing cross-spectral density for epoch 45
computing cross-spectral density for epoch 46
computing cross-spectral density for epoch 47
computing cross-spectral density for epoch 48
computing cross-spectral density for epoch 49
computing cross-spectral density for epoch 50
computing cross-spectral density for epoch 51
computing cross-spectral density for epoch 52
computing cross-spectral density for epoch 53
computing cross-spectral density for epoch 54
computing cross-spectral density for epoch 55
computing cross-spectral density for epoch 56
computing cross-spectral density for epoch 57
computing cross-spectral density for epoch 58
computing cross-spectral density for epoch 59
computing cross-spectral density for epoch 60
computing cross-spectral density for epoch 61
computing cross-spectral density for epoch 62
computing cross-spectral density for epoch 63
computing cross-spectral density for epoch 64
computing cross-spectral density for epoch 65
computing cross-spectral density for epoch 66
computing cross-spectral density for epoch 67
computing cross-spectral density for epoch 68
computing cross-spectral density for epoch 69
computing cross-spectral density for epoch 70
computing cross-spectral density for epoch 71
computing cross-spectral density for epoch 72
computing cross-spectral density for epoch 73
computing cross-spectral density for epoch 74
computing cross-spectral density for epoch 75
computing cross-spectral density for epoch 76
computing cross-spectral density for epoch 77
computing cross-spectral density for epoch 78
computing cross-spectral density for epoch 79
computing cross-spectral density for epoch 80
computing cross-spectral density for epoch 81
computing cross-spectral density for epoch 82
computing cross-spectral density for epoch 83
computing cross-spectral density for epoch 84
computing cross-spectral density for epoch 85
computing cross-spectral density for epoch 86
computing cross-spectral density for epoch 87
computing cross-spectral density for epoch 88
computing cross-spectral density for epoch 89
computing cross-spectral density for epoch 90
computing cross-spectral density for epoch 91
computing cross-spectral density for epoch 92
computing cross-spectral density for epoch 93
computing cross-spectral density for epoch 94
computing cross-spectral density for epoch 95
computing cross-spectral density for epoch 96
computing cross-spectral density for epoch 97
computing cross-spectral density for epoch 98
computing cross-spectral density for epoch 99
computing cross-spectral density for epoch 100
computing cross-spectral density for epoch 101
computing cross-spectral density for epoch 102
computing cross-spectral density for epoch 103
computing cross-spectral density for epoch 104
computing cross-spectral density for epoch 105
computing cross-spectral density for epoch 106
computing cross-spectral density for epoch 107
computing cross-spectral density for epoch 108
computing cross-spectral density for epoch 109
computing cross-spectral density for epoch 110
computing cross-spectral density for epoch 111
computing cross-spectral density for epoch 112
computing cross-spectral density for epoch 113
computing cross-spectral density for epoch 114
computing cross-spectral density for epoch 115
computing cross-spectral density for epoch 116
computing cross-spectral density for epoch 117
computing cross-spectral density for epoch 118
computing cross-spectral density for epoch 119
computing cross-spectral density for epoch 120
computing cross-spectral density for epoch 121
computing cross-spectral density for epoch 122
computing cross-spectral density for epoch 123
computing cross-spectral density for epoch 124
computing cross-spectral density for epoch 125
computing cross-spectral density for epoch 126
computing cross-spectral density for epoch 127
computing cross-spectral density for epoch 128
computing cross-spectral density for epoch 129
computing cross-spectral density for epoch 130
computing cross-spectral density for epoch 131
computing cross-spectral density for epoch 132
computing cross-spectral density for epoch 133
computing cross-spectral density for epoch 134
computing cross-spectral density for epoch 135
computing cross-spectral density for epoch 136
computing cross-spectral density for epoch 137
computing cross-spectral density for epoch 138
computing cross-spectral density for epoch 139
computing cross-spectral density for epoch 140
computing cross-spectral density for epoch 141
computing cross-spectral density for epoch 142
computing cross-spectral density for epoch 143
computing cross-spectral density for epoch 144
computing cross-spectral density for epoch 145
computing cross-spectral density for epoch 146
computing cross-spectral density for epoch 147
computing cross-spectral density for epoch 148
computing cross-spectral density for epoch 149
computing cross-spectral density for epoch 150
computing cross-spectral density for epoch 151
computing cross-spectral density for epoch 152
computing cross-spectral density for epoch 153
computing cross-spectral density for epoch 154
computing cross-spectral density for epoch 155
computing cross-spectral density for epoch 156
computing cross-spectral density for epoch 157
computing cross-spectral density for epoch 158
computing cross-spectral density for epoch 159
computing cross-spectral density for epoch 160
computing cross-spectral density for epoch 161
computing cross-spectral density for epoch 162
computing cross-spectral density for epoch 163
computing cross-spectral density for epoch 164
computing cross-spectral density for epoch 165
computing cross-spectral density for epoch 166
computing cross-spectral density for epoch 167
computing cross-spectral density for epoch 168
computing cross-spectral density for epoch 169
computing cross-spectral density for epoch 170
computing cross-spectral density for epoch 171
computing cross-spectral density for epoch 172
computing cross-spectral density for epoch 173
computing cross-spectral density for epoch 174
computing cross-spectral density for epoch 175
computing cross-spectral density for epoch 176
computing cross-spectral density for epoch 177
computing cross-spectral density for epoch 178
computing cross-spectral density for epoch 179
computing cross-spectral density for epoch 180
computing cross-spectral density for epoch 181
computing cross-spectral density for epoch 182
computing cross-spectral density for epoch 183
computing cross-spectral density for epoch 184
computing cross-spectral density for epoch 185
computing cross-spectral density for epoch 186
computing cross-spectral density for epoch 187
computing cross-spectral density for epoch 188
computing cross-spectral density for epoch 189
computing cross-spectral density for epoch 190
computing cross-spectral density for epoch 191
computing cross-spectral density for epoch 192
computing cross-spectral density for epoch 193
computing cross-spectral density for epoch 194
computing cross-spectral density for epoch 195
computing cross-spectral density for epoch 196
computing cross-spectral density for epoch 197
computing cross-spectral density for epoch 198
computing cross-spectral density for epoch 199
computing cross-spectral density for epoch 200
computing cross-spectral density for epoch 201
computing cross-spectral density for epoch 202
computing cross-spectral density for epoch 203
computing cross-spectral density for epoch 204
computing cross-spectral density for epoch 205
computing cross-spectral density for epoch 206
computing cross-spectral density for epoch 207
computing cross-spectral density for epoch 208
computing cross-spectral density for epoch 209
computing cross-spectral density for epoch 210
computing cross-spectral density for epoch 211
computing cross-spectral density for epoch 212
computing cross-spectral density for epoch 213
computing cross-spectral density for epoch 214
computing cross-spectral density for epoch 215
computing cross-spectral density for epoch 216
computing cross-spectral density for epoch 217
computing cross-spectral density for epoch 218
computing cross-spectral density for epoch 219
computing cross-spectral density for epoch 220
computing cross-spectral density for epoch 221
computing cross-spectral density for epoch 222
computing cross-spectral density for epoch 223
computing cross-spectral density for epoch 224
computing cross-spectral density for epoch 225
computing cross-spectral density for epoch 226
computing cross-spectral density for epoch 227
computing cross-spectral density for epoch 228
computing cross-spectral density for epoch 229
computing cross-spectral density for epoch 230
computing cross-spectral density for epoch 231
computing cross-spectral density for epoch 232
computing cross-spectral density for epoch 233
computing cross-spectral density for epoch 234
computing cross-spectral density for epoch 235
computing cross-spectral density for epoch 236
computing cross-spectral density for epoch 237
computing cross-spectral density for epoch 238
computing cross-spectral density for epoch 239
computing cross-spectral density for epoch 240
computing cross-spectral density for epoch 241
computing cross-spectral density for epoch 242
computing cross-spectral density for epoch 243
computing cross-spectral density for epoch 244
computing cross-spectral density for epoch 245
computing cross-spectral density for epoch 246
computing cross-spectral density for epoch 247
computing cross-spectral density for epoch 248
computing cross-spectral density for epoch 249
computing cross-spectral density for epoch 250
computing cross-spectral density for epoch 251
computing cross-spectral density for epoch 252
computing cross-spectral density for epoch 253
computing cross-spectral density for epoch 254
computing cross-spectral density for epoch 255
computing cross-spectral density for epoch 256
computing cross-spectral density for epoch 257
computing cross-spectral density for epoch 258
computing cross-spectral density for epoch 259
computing cross-spectral density for epoch 260
computing cross-spectral density for epoch 261
computing cross-spectral density for epoch 262
computing cross-spectral density for epoch 263
computing cross-spectral density for epoch 264
computing cross-spectral density for epoch 265
computing cross-spectral density for epoch 266
computing cross-spectral density for epoch 267
computing cross-spectral density for epoch 268
computing cross-spectral density for epoch 269
computing cross-spectral density for epoch 270
computing cross-spectral density for epoch 271
computing cross-spectral density for epoch 272
computing cross-spectral density for epoch 273
computing cross-spectral density for epoch 274
computing cross-spectral density for epoch 275
computing cross-spectral density for epoch 276
computing cross-spectral density for epoch 277
computing cross-spectral density for epoch 278
computing cross-spectral density for epoch 279
computing cross-spectral density for epoch 280
computing cross-spectral density for epoch 281
computing cross-spectral density for epoch 282
computing cross-spectral density for epoch 283
computing cross-spectral density for epoch 284
computing cross-spectral density for epoch 285
computing cross-spectral density for epoch 286
computing cross-spectral density for epoch 287
computing cross-spectral density for epoch 288
computing cross-spectral density for epoch 289
computing cross-spectral density for epoch 290
computing cross-spectral density for epoch 291
computing cross-spectral density for epoch 292
computing cross-spectral density for epoch 293
computing cross-spectral density for epoch 294
computing cross-spectral density for epoch 295
computing cross-spectral density for epoch 296
computing cross-spectral density for epoch 297
computing cross-spectral density for epoch 298
computing cross-spectral density for epoch 299
computing cross-spectral density for epoch 300
[Connectivity computation done]
Connectivity computation...
computing connectivity for 41 connections
using t=0.000s..9.996s for estimation (2500 points)
frequencies: 9.0Hz..11.0Hz (21 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: WPLI
computing cross-spectral density for epoch 1
computing cross-spectral density for epoch 2
computing cross-spectral density for epoch 3
computing cross-spectral density for epoch 4
computing cross-spectral density for epoch 5
computing cross-spectral density for epoch 6
computing cross-spectral density for epoch 7
computing cross-spectral density for epoch 8
computing cross-spectral density for epoch 9
computing cross-spectral density for epoch 10
computing cross-spectral density for epoch 11
computing cross-spectral density for epoch 12
computing cross-spectral density for epoch 13
computing cross-spectral density for epoch 14
computing cross-spectral density for epoch 15
computing cross-spectral density for epoch 16
computing cross-spectral density for epoch 17
computing cross-spectral density for epoch 18
computing cross-spectral density for epoch 19
computing cross-spectral density for epoch 20
computing cross-spectral density for epoch 21
computing cross-spectral density for epoch 22
computing cross-spectral density for epoch 23
computing cross-spectral density for epoch 24
computing cross-spectral density for epoch 25
computing cross-spectral density for epoch 26
computing cross-spectral density for epoch 27
computing cross-spectral density for epoch 28
computing cross-spectral density for epoch 29
computing cross-spectral density for epoch 30
computing cross-spectral density for epoch 31
computing cross-spectral density for epoch 32
computing cross-spectral density for epoch 33
computing cross-spectral density for epoch 34
computing cross-spectral density for epoch 35
computing cross-spectral density for epoch 36
computing cross-spectral density for epoch 37
computing cross-spectral density for epoch 38
computing cross-spectral density for epoch 39
computing cross-spectral density for epoch 40
computing cross-spectral density for epoch 41
computing cross-spectral density for epoch 42
computing cross-spectral density for epoch 43
computing cross-spectral density for epoch 44
computing cross-spectral density for epoch 45
computing cross-spectral density for epoch 46
computing cross-spectral density for epoch 47
computing cross-spectral density for epoch 48
computing cross-spectral density for epoch 49
computing cross-spectral density for epoch 50
computing cross-spectral density for epoch 51
computing cross-spectral density for epoch 52
computing cross-spectral density for epoch 53
computing cross-spectral density for epoch 54
computing cross-spectral density for epoch 55
computing cross-spectral density for epoch 56
computing cross-spectral density for epoch 57
computing cross-spectral density for epoch 58
computing cross-spectral density for epoch 59
computing cross-spectral density for epoch 60
computing cross-spectral density for epoch 61
computing cross-spectral density for epoch 62
computing cross-spectral density for epoch 63
computing cross-spectral density for epoch 64
computing cross-spectral density for epoch 65
computing cross-spectral density for epoch 66
computing cross-spectral density for epoch 67
computing cross-spectral density for epoch 68
computing cross-spectral density for epoch 69
computing cross-spectral density for epoch 70
computing cross-spectral density for epoch 71
computing cross-spectral density for epoch 72
computing cross-spectral density for epoch 73
computing cross-spectral density for epoch 74
computing cross-spectral density for epoch 75
computing cross-spectral density for epoch 76
computing cross-spectral density for epoch 77
computing cross-spectral density for epoch 78
computing cross-spectral density for epoch 79
computing cross-spectral density for epoch 80
computing cross-spectral density for epoch 81
computing cross-spectral density for epoch 82
computing cross-spectral density for epoch 83
computing cross-spectral density for epoch 84
computing cross-spectral density for epoch 85
computing cross-spectral density for epoch 86
computing cross-spectral density for epoch 87
computing cross-spectral density for epoch 88
computing cross-spectral density for epoch 89
computing cross-spectral density for epoch 90
computing cross-spectral density for epoch 91
computing cross-spectral density for epoch 92
computing cross-spectral density for epoch 93
computing cross-spectral density for epoch 94
computing cross-spectral density for epoch 95
computing cross-spectral density for epoch 96
computing cross-spectral density for epoch 97
computing cross-spectral density for epoch 98
computing cross-spectral density for epoch 99
computing cross-spectral density for epoch 100
computing cross-spectral density for epoch 101
computing cross-spectral density for epoch 102
computing cross-spectral density for epoch 103
computing cross-spectral density for epoch 104
computing cross-spectral density for epoch 105
computing cross-spectral density for epoch 106
computing cross-spectral density for epoch 107
computing cross-spectral density for epoch 108
computing cross-spectral density for epoch 109
computing cross-spectral density for epoch 110
computing cross-spectral density for epoch 111
computing cross-spectral density for epoch 112
computing cross-spectral density for epoch 113
computing cross-spectral density for epoch 114
computing cross-spectral density for epoch 115
computing cross-spectral density for epoch 116
computing cross-spectral density for epoch 117
computing cross-spectral density for epoch 118
computing cross-spectral density for epoch 119
computing cross-spectral density for epoch 120
computing cross-spectral density for epoch 121
computing cross-spectral density for epoch 122
computing cross-spectral density for epoch 123
computing cross-spectral density for epoch 124
computing cross-spectral density for epoch 125
computing cross-spectral density for epoch 126
computing cross-spectral density for epoch 127
computing cross-spectral density for epoch 128
computing cross-spectral density for epoch 129
computing cross-spectral density for epoch 130
computing cross-spectral density for epoch 131
computing cross-spectral density for epoch 132
computing cross-spectral density for epoch 133
computing cross-spectral density for epoch 134
computing cross-spectral density for epoch 135
computing cross-spectral density for epoch 136
computing cross-spectral density for epoch 137
computing cross-spectral density for epoch 138
computing cross-spectral density for epoch 139
computing cross-spectral density for epoch 140
computing cross-spectral density for epoch 141
computing cross-spectral density for epoch 142
computing cross-spectral density for epoch 143
computing cross-spectral density for epoch 144
computing cross-spectral density for epoch 145
computing cross-spectral density for epoch 146
computing cross-spectral density for epoch 147
computing cross-spectral density for epoch 148
computing cross-spectral density for epoch 149
computing cross-spectral density for epoch 150
computing cross-spectral density for epoch 151
computing cross-spectral density for epoch 152
computing cross-spectral density for epoch 153
computing cross-spectral density for epoch 154
computing cross-spectral density for epoch 155
computing cross-spectral density for epoch 156
computing cross-spectral density for epoch 157
computing cross-spectral density for epoch 158
computing cross-spectral density for epoch 159
computing cross-spectral density for epoch 160
computing cross-spectral density for epoch 161
computing cross-spectral density for epoch 162
computing cross-spectral density for epoch 163
computing cross-spectral density for epoch 164
computing cross-spectral density for epoch 165
computing cross-spectral density for epoch 166
computing cross-spectral density for epoch 167
computing cross-spectral density for epoch 168
computing cross-spectral density for epoch 169
computing cross-spectral density for epoch 170
computing cross-spectral density for epoch 171
computing cross-spectral density for epoch 172
computing cross-spectral density for epoch 173
computing cross-spectral density for epoch 174
computing cross-spectral density for epoch 175
computing cross-spectral density for epoch 176
computing cross-spectral density for epoch 177
computing cross-spectral density for epoch 178
computing cross-spectral density for epoch 179
computing cross-spectral density for epoch 180
computing cross-spectral density for epoch 181
computing cross-spectral density for epoch 182
computing cross-spectral density for epoch 183
computing cross-spectral density for epoch 184
computing cross-spectral density for epoch 185
computing cross-spectral density for epoch 186
computing cross-spectral density for epoch 187
computing cross-spectral density for epoch 188
computing cross-spectral density for epoch 189
computing cross-spectral density for epoch 190
computing cross-spectral density for epoch 191
computing cross-spectral density for epoch 192
computing cross-spectral density for epoch 193
computing cross-spectral density for epoch 194
computing cross-spectral density for epoch 195
computing cross-spectral density for epoch 196
computing cross-spectral density for epoch 197
computing cross-spectral density for epoch 198
computing cross-spectral density for epoch 199
computing cross-spectral density for epoch 200
computing cross-spectral density for epoch 201
computing cross-spectral density for epoch 202
computing cross-spectral density for epoch 203
computing cross-spectral density for epoch 204
computing cross-spectral density for epoch 205
computing cross-spectral density for epoch 206
computing cross-spectral density for epoch 207
computing cross-spectral density for epoch 208
computing cross-spectral density for epoch 209
computing cross-spectral density for epoch 210
computing cross-spectral density for epoch 211
computing cross-spectral density for epoch 212
computing cross-spectral density for epoch 213
computing cross-spectral density for epoch 214
computing cross-spectral density for epoch 215
computing cross-spectral density for epoch 216
computing cross-spectral density for epoch 217
computing cross-spectral density for epoch 218
computing cross-spectral density for epoch 219
computing cross-spectral density for epoch 220
computing cross-spectral density for epoch 221
computing cross-spectral density for epoch 222
computing cross-spectral density for epoch 223
computing cross-spectral density for epoch 224
computing cross-spectral density for epoch 225
computing cross-spectral density for epoch 226
computing cross-spectral density for epoch 227
computing cross-spectral density for epoch 228
computing cross-spectral density for epoch 229
computing cross-spectral density for epoch 230
computing cross-spectral density for epoch 231
computing cross-spectral density for epoch 232
computing cross-spectral density for epoch 233
computing cross-spectral density for epoch 234
computing cross-spectral density for epoch 235
computing cross-spectral density for epoch 236
computing cross-spectral density for epoch 237
computing cross-spectral density for epoch 238
computing cross-spectral density for epoch 239
computing cross-spectral density for epoch 240
computing cross-spectral density for epoch 241
computing cross-spectral density for epoch 242
computing cross-spectral density for epoch 243
computing cross-spectral density for epoch 244
computing cross-spectral density for epoch 245
computing cross-spectral density for epoch 246
computing cross-spectral density for epoch 247
computing cross-spectral density for epoch 248
computing cross-spectral density for epoch 249
computing cross-spectral density for epoch 250
computing cross-spectral density for epoch 251
computing cross-spectral density for epoch 252
computing cross-spectral density for epoch 253
computing cross-spectral density for epoch 254
computing cross-spectral density for epoch 255
computing cross-spectral density for epoch 256
computing cross-spectral density for epoch 257
computing cross-spectral density for epoch 258
computing cross-spectral density for epoch 259
computing cross-spectral density for epoch 260
computing cross-spectral density for epoch 261
computing cross-spectral density for epoch 262
computing cross-spectral density for epoch 263
computing cross-spectral density for epoch 264
computing cross-spectral density for epoch 265
computing cross-spectral density for epoch 266
computing cross-spectral density for epoch 267
computing cross-spectral density for epoch 268
computing cross-spectral density for epoch 269
computing cross-spectral density for epoch 270
computing cross-spectral density for epoch 271
computing cross-spectral density for epoch 272
computing cross-spectral density for epoch 273
computing cross-spectral density for epoch 274
computing cross-spectral density for epoch 275
computing cross-spectral density for epoch 276
computing cross-spectral density for epoch 277
computing cross-spectral density for epoch 278
computing cross-spectral density for epoch 279
computing cross-spectral density for epoch 280
computing cross-spectral density for epoch 281
computing cross-spectral density for epoch 282
computing cross-spectral density for epoch 283
computing cross-spectral density for epoch 284
computing cross-spectral density for epoch 285
computing cross-spectral density for epoch 286
computing cross-spectral density for epoch 287
computing cross-spectral density for epoch 288
computing cross-spectral density for epoch 289
computing cross-spectral density for epoch 290
computing cross-spectral density for epoch 291
computing cross-spectral density for epoch 292
computing cross-spectral density for epoch 293
computing cross-spectral density for epoch 294
computing cross-spectral density for epoch 295
computing cross-spectral density for epoch 296
computing cross-spectral density for epoch 297
computing cross-spectral density for epoch 298
computing cross-spectral density for epoch 299
computing cross-spectral density for epoch 300
[Connectivity computation done]


The results from the simulation are shown in the figure below. In the case without noise, the difference between wPLI and PLI is made obvious. In PLI, no connectivity is detected, as the $$-\frac{\pi}{100}$$ phase differences are weighted in the exact same way as the $$\frac{\pi}{2}$$ relationships. wPLI is able to avoid the cancellation of the $$\frac{\pi}{2}$$ relationships.

As noise gets added, PLI increases since the $$-\frac{\pi}{100}$$ relationships are made positive more often than the $$\frac{\pi}{2}$$ relationships are made negative. However, wPLI maintains an advantage in its ability to distinguish the underlying structure. Beyond a certain point, the noise dominates any pre-defined structure, and both methods behave similarly, tending toward $$0$$. For a more detailed analysis of this result and the properties of wPLI, please refer to (Vinck et al, 2011) [2].

plt.figure()
plt.plot(A_list, conn[0], "o-", label="PLI")
plt.plot(A_list, conn[1], "o-", label="wPLI")
plt.legend()
plt.xlabel("Noise Amplitude")
plt.ylabel("Connectivity Measure")
plt.title("wPLI and PLI Under Increasing Noise")
plt.show()


## Demo On MEG Data#

To finish this example, we also quickly demonstrate these methods on some sample MEG data recorded during visual stimulation.

data_path = sample.data_path()
raw_fname = data_path / "MEG/sample/sample_audvis_filt-0-40_raw.fif"
event_fname = data_path / "MEG/sample/sample_audvis_filt-0-40_raw-eve.fif"

picks = mne.pick_types(
)

# Create epochs
event_id, tmin, tmax = 3, -0.2, 1.5  # need a long enough epoch for 5 cycles
epochs = mne.Epochs(
raw,
events,
event_id,
tmin,
tmax,
picks=picks,
baseline=(None, 0),
)

fmin, fmax = 4.0, 9.0  # compute connectivity within 4-9 Hz
sfreq = raw.info["sfreq"]  # the sampling frequency
tmin = 0.0  # exclude the baseline period

# Compute PLI, wPLI, and dPLI
con_pli = spectral_connectivity_epochs(
epochs,
method="pli",
mode="multitaper",
sfreq=sfreq,
fmin=fmin,
fmax=fmax,
faverage=True,
tmin=tmin,
n_jobs=1,
)

con_wpli = spectral_connectivity_epochs(
epochs,
method="wpli",
mode="multitaper",
sfreq=sfreq,
fmin=fmin,
fmax=fmax,
faverage=True,
tmin=tmin,
n_jobs=1,
)

con_dpli = spectral_connectivity_epochs(
epochs,
method="dpli",
mode="multitaper",
sfreq=sfreq,
fmin=fmin,
fmax=fmax,
faverage=True,
tmin=tmin,
n_jobs=1,
)

Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_filt-0-40_raw.fif...
Read a total of 4 projection items:
PCA-v1 (1 x 102)  idle
PCA-v2 (1 x 102)  idle
PCA-v3 (1 x 102)  idle
Average EEG reference (1 x 60)  idle
Range : 6450 ... 48149 =     42.956 ...   320.665 secs
73 matching events found
Setting baseline interval to [-0.19979521315838786, 0.0] s
Applying baseline correction (mode: mean)
0 projection items activated
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
Rejecting  epoch based on EOG : ['EOG 061']
NOTE: pick_types() is a legacy function. New code should use inst.pick(...).
Connectivity computation...
only using indices for lower-triangular matrix
computing connectivity for 20503 connections
using t=0.000s..1.498s for estimation (226 points)
frequencies: 4.7Hz..8.6Hz (7 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: PLI
computing cross-spectral density for epoch 1
computing cross-spectral density for epoch 2
computing cross-spectral density for epoch 3
computing cross-spectral density for epoch 4
computing cross-spectral density for epoch 5
computing cross-spectral density for epoch 6
computing cross-spectral density for epoch 7
computing cross-spectral density for epoch 8
computing cross-spectral density for epoch 9
computing cross-spectral density for epoch 10
computing cross-spectral density for epoch 11
computing cross-spectral density for epoch 12
computing cross-spectral density for epoch 13
computing cross-spectral density for epoch 14
computing cross-spectral density for epoch 15
computing cross-spectral density for epoch 16
computing cross-spectral density for epoch 17
computing cross-spectral density for epoch 18
computing cross-spectral density for epoch 19
computing cross-spectral density for epoch 20
computing cross-spectral density for epoch 21
computing cross-spectral density for epoch 22
computing cross-spectral density for epoch 23
computing cross-spectral density for epoch 24
computing cross-spectral density for epoch 25
computing cross-spectral density for epoch 26
computing cross-spectral density for epoch 27
computing cross-spectral density for epoch 28
computing cross-spectral density for epoch 29
computing cross-spectral density for epoch 30
computing cross-spectral density for epoch 31
computing cross-spectral density for epoch 32
computing cross-spectral density for epoch 33
computing cross-spectral density for epoch 34
computing cross-spectral density for epoch 35
computing cross-spectral density for epoch 36
computing cross-spectral density for epoch 37
computing cross-spectral density for epoch 38
computing cross-spectral density for epoch 39
computing cross-spectral density for epoch 40
computing cross-spectral density for epoch 41
computing cross-spectral density for epoch 42
computing cross-spectral density for epoch 43
computing cross-spectral density for epoch 44
computing cross-spectral density for epoch 45
computing cross-spectral density for epoch 46
computing cross-spectral density for epoch 47
computing cross-spectral density for epoch 48
computing cross-spectral density for epoch 49
assembling connectivity matrix
[Connectivity computation done]
Replacing existing metadata with 3 columns
Connectivity computation...
only using indices for lower-triangular matrix
computing connectivity for 20503 connections
using t=0.000s..1.498s for estimation (226 points)
frequencies: 4.7Hz..8.6Hz (7 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: WPLI
computing cross-spectral density for epoch 1
computing cross-spectral density for epoch 2
computing cross-spectral density for epoch 3
computing cross-spectral density for epoch 4
computing cross-spectral density for epoch 5
computing cross-spectral density for epoch 6
computing cross-spectral density for epoch 7
computing cross-spectral density for epoch 8
computing cross-spectral density for epoch 9
computing cross-spectral density for epoch 10
computing cross-spectral density for epoch 11
computing cross-spectral density for epoch 12
computing cross-spectral density for epoch 13
computing cross-spectral density for epoch 14
computing cross-spectral density for epoch 15
computing cross-spectral density for epoch 16
computing cross-spectral density for epoch 17
computing cross-spectral density for epoch 18
computing cross-spectral density for epoch 19
computing cross-spectral density for epoch 20
computing cross-spectral density for epoch 21
computing cross-spectral density for epoch 22
computing cross-spectral density for epoch 23
computing cross-spectral density for epoch 24
computing cross-spectral density for epoch 25
computing cross-spectral density for epoch 26
computing cross-spectral density for epoch 27
computing cross-spectral density for epoch 28
computing cross-spectral density for epoch 29
computing cross-spectral density for epoch 30
computing cross-spectral density for epoch 31
computing cross-spectral density for epoch 32
computing cross-spectral density for epoch 33
computing cross-spectral density for epoch 34
computing cross-spectral density for epoch 35
computing cross-spectral density for epoch 36
computing cross-spectral density for epoch 37
computing cross-spectral density for epoch 38
computing cross-spectral density for epoch 39
computing cross-spectral density for epoch 40
computing cross-spectral density for epoch 41
computing cross-spectral density for epoch 42
computing cross-spectral density for epoch 43
computing cross-spectral density for epoch 44
computing cross-spectral density for epoch 45
computing cross-spectral density for epoch 46
computing cross-spectral density for epoch 47
computing cross-spectral density for epoch 48
computing cross-spectral density for epoch 49
assembling connectivity matrix
[Connectivity computation done]
Replacing existing metadata with 3 columns
Connectivity computation...
only using indices for lower-triangular matrix
computing connectivity for 20503 connections
using t=0.000s..1.498s for estimation (226 points)
frequencies: 4.7Hz..8.6Hz (7 points)
connectivity scores will be averaged for each band
Using multitaper spectrum estimation with 7 DPSS windows
the following metrics will be computed: DPLI
computing cross-spectral density for epoch 1
computing cross-spectral density for epoch 2
computing cross-spectral density for epoch 3
computing cross-spectral density for epoch 4
computing cross-spectral density for epoch 5
computing cross-spectral density for epoch 6
computing cross-spectral density for epoch 7
computing cross-spectral density for epoch 8
computing cross-spectral density for epoch 9
computing cross-spectral density for epoch 10
computing cross-spectral density for epoch 11
computing cross-spectral density for epoch 12
computing cross-spectral density for epoch 13
computing cross-spectral density for epoch 14
computing cross-spectral density for epoch 15
computing cross-spectral density for epoch 16
computing cross-spectral density for epoch 17
computing cross-spectral density for epoch 18
computing cross-spectral density for epoch 19
computing cross-spectral density for epoch 20
computing cross-spectral density for epoch 21
computing cross-spectral density for epoch 22
computing cross-spectral density for epoch 23
computing cross-spectral density for epoch 24
computing cross-spectral density for epoch 25
computing cross-spectral density for epoch 26
computing cross-spectral density for epoch 27
computing cross-spectral density for epoch 28
computing cross-spectral density for epoch 29
computing cross-spectral density for epoch 30
computing cross-spectral density for epoch 31
computing cross-spectral density for epoch 32
computing cross-spectral density for epoch 33
computing cross-spectral density for epoch 34
computing cross-spectral density for epoch 35
computing cross-spectral density for epoch 36
computing cross-spectral density for epoch 37
computing cross-spectral density for epoch 38
computing cross-spectral density for epoch 39
computing cross-spectral density for epoch 40
computing cross-spectral density for epoch 41
computing cross-spectral density for epoch 42
computing cross-spectral density for epoch 43
computing cross-spectral density for epoch 44
computing cross-spectral density for epoch 45
computing cross-spectral density for epoch 46
computing cross-spectral density for epoch 47
computing cross-spectral density for epoch 48
computing cross-spectral density for epoch 49
assembling connectivity matrix
[Connectivity computation done]


In this example, there is strong connectivity between sensors 190-200 and sensors 110-160.

Moreover, after observing the presence of connectivity, dPLI can be used to ascertain the direction of the phase relationship. Here, it appears that the dPLI connectivity in this area is less than $$0.5$$, and thus sensors 190-200 are lagging sensors 110-160.

In keeping with the previous simulation, we can see that wPLI identifies stronger connectivity relationships than PLI. This is due to its robustness against volume conduction effects decreasing the detected connectivity strength, as was mentioned earlier.

fig, axs = plt.subplots(1, 3, figsize=(14, 5), sharey=True)
axs[0].imshow(con_pli.get_data("dense"), vmin=0, vmax=1)
axs[0].set_title("PLI")
axs[0].set_ylabel("Sensor 1")
axs[0].set_xlabel("Sensor 2")

axs[1].imshow(con_wpli.get_data("dense"), vmin=0, vmax=1)
axs[1].set_title("wPLI")
axs[1].set_xlabel("Sensor 2")

im = axs[2].imshow(con_dpli.get_data("dense"), vmin=0, vmax=1)
axs[2].set_title("dPLI")
axs[2].set_xlabel("Sensor 2")

fig.colorbar(im, ax=axs.ravel())
plt.show()


## Conclusions#

Both wPLI and dPLI are extensions upon the original PLI method, and provide complementary information about underlying connectivity.

• To identify the presence of an underlying phase relationship, wPLI is the method of choice for most researchers as it provides an improvement in robustness over the original PLI method

• To know the directionality of the connectivity identified by wPLI, dPLI should be used

Ultimately, these methods work great together, providing a comprehensive estimate of phase-based connectivity.

## References#

Total running time of the script: (0 minutes 16.426 seconds)

Gallery generated by Sphinx-Gallery