-
Notifications
You must be signed in to change notification settings - Fork 77
/
chapter27.m
538 lines (412 loc) · 19.8 KB
/
chapter27.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
%% Analyzing Neural Time Series Data
% Matlab code for Chapter 27
% Mike X Cohen
%
% This code accompanies the book, titled "Analyzing Neural Time Series Data"
% (MIT Press). Using the code without following the book may lead to confusion,
% incorrect data analyses, and misinterpretations of results.
% Mike X Cohen assumes no responsibility for inappropriate or incorrect use of this code.
%% an aside on covariance and correlation
a = randn(1,100);
b = randn(1,100);
corr1 = corrcoef(a,b);
a1=a-mean(a);
b1=b-mean(b);
corr2 = (a1*b1')/sqrt( (a1*a1')*(b1*b1') );
c = [a1; b1];
covmat = c*c';
% notice the following:
covmat(1,1) == a1*a1'
covmat(2,2) == b1*b1'
covmat(2,1) == a1*b1'
% actually, some of these might not be exactly equal due to very small computer rounding errors.
% try this instead:
(covmat(2,1)-a1*b1')<0.0000000000001
corr3 = covmat(1,2)/sqrt(covmat(1)*covmat(end));
fprintf([ '\nMatlab corrcoef function: ' num2str(corr1(1,2)) '\n' ...
'covariance scaled by variances: ' num2str(corr2) '\n' ...
'covariance computed as matrix: ' num2str(corr3) '\n\n' ])
%% Figure 27.1
anscombe = [
% series 1 series 2 series 3 series 4
10 8.04 10 9.14 10 7.46 8 6.58;
8 6.95 8 8.14 8 6.77 8 5.76;
13 7.58 13 8.76 13 12.74 8 7.71;
9 8.81 9 8.77 9 7.11 8 8.84;
11 8.33 11 9.26 11 7.81 8 8.47;
14 9.96 14 8.10 14 8.84 8 7.04;
6 7.24 6 6.13 6 6.08 8 5.25;
4 4.26 4 3.10 4 5.39 8 5.56;
12 10.84 12 9.13 12 8.15 8 7.91;
7 4.82 7 7.26 7 6.42 8 6.89;
5 5.68 5 4.74 5 5.73 19 12.50;
];
% plot and compute correlations
figure
for i=1:4
subplot(2,2,i)
plot(anscombe(:,(i-1)*2+1),anscombe(:,(i-1)*2+2),'.')
lsline
corr_p = corr(anscombe(:,(i-1)*2+1),anscombe(:,(i-1)*2+2),'type','p');
corr_s = corr(anscombe(:,(i-1)*2+1),anscombe(:,(i-1)*2+2),'type','s');
title([ 'r_p=' num2str(round(corr_p*1000)/1000) '; r_s=' num2str(round(corr_s*1000)/1000) ])
end
%% Figure 27.2
load sampleEEGdata
sensor2use = 'fz';
centerfreq = 10; % in Hz
% setup wavelet convolution and outputs
time = -1:1/EEG.srate:1;
half_of_wavelet_size = (length(time)-1)/2;
% FFT parameters
n_wavelet = length(time);
n_data = EEG.pnts*EEG.trials;
n_convolution = n_wavelet+n_data-1;
wavelet_cycles= 4.5;
% FFT of data (note: this doesn't change on frequency iteration)
fft_data = fft(reshape(EEG.data(strcmpi(sensor2use,{EEG.chanlocs.labels}),:,:),1,EEG.pnts*EEG.trials),n_convolution);
% create wavelet and run convolution
fft_wavelet = fft(exp(2*1i*pi*centerfreq.*time) .* exp(-time.^2./(2*( wavelet_cycles /(2*pi*centerfreq))^2)),n_convolution);
convolution_result_fft = ifft(fft_wavelet.*fft_data,n_convolution) * sqrt(wavelet_cycles /(2*pi*centerfreq));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
convolution_result_fft = abs(reshape(convolution_result_fft,EEG.pnts,EEG.trials)).^2;
% trim edges so the distribution is not driven by edge artifact outliers
% (note: here we just use visual inspection to remove edges)
convolution_result_fft = convolution_result_fft(100:end-100,:);
% plot distirbution of power data
figure
subplot(121)
hist(convolution_result_fft(:),500)
title('Distribution of power values')
axis square
subplot(122)
hist(log10(convolution_result_fft(:)),500)
title('Distribution of log_1_0power values')
axis square
% test for normal distribution, if you have the stats toolbox
if exist('kstest','file')
[h,p1] = kstest(convolution_result_fft(:));
[h,p2] = kstest(log10(convolution_result_fft(:)));
[h,p3] = kstest(randn(numel(convolution_result_fft),1));
disp([ 'KS test for normality of power: ' num2str(p1) ' (>.05 means normal distribution) ' ])
disp([ 'KS test for normality of log10(power): ' num2str(p2) ' (>.05 means normal distribution) ' ])
disp([ 'KS test for normality of random data: ' num2str(p3) ' (>.05 means normal distribution) ' ])
end
%% Figure 27.3
lots_of_corr_coefs = rand(1000,1)*2-1;
fisher_z_coefs = .5 * log( (1+lots_of_corr_coefs)./(1-lots_of_corr_coefs) );
figure
subplot(221)
hist(lots_of_corr_coefs,50)
xlabel('Correlation coefficient')
ylabel('Count')
axis square
set(gca,'xlim',[-1 1],'xtick',-1:.5:1)
subplot(222)
hist(fisher_z_coefs,50)
xlabel('Fisher-Z transformed coefficients')
ylabel('Count')
axis square
set(gca,'xlim',[-5 5],'xtick',-4:2:4)
subplot(223)
plot(lots_of_corr_coefs,fisher_z_coefs,'.')
xlabel('Correlation coefficient')
ylabel('Fisher-Z transformed coefficients')
set(gca,'xlim',[-1 1],'xtick',-1:.5:1)
axis square
subplot(224)
plot(atanh(lots_of_corr_coefs),fisher_z_coefs,'.')
xlabel('atanh')
ylabel('Fisher-Z')
r=corr(atanh(lots_of_corr_coefs),fisher_z_coefs);
legend([ 'Correlation = ' num2str(r) ])
axis square
set(gca,'xtick',-4:2:4,'ytick',-4:2:4)
axis([-4 4 -4 4])
%% Figure 27.4
sensor1 = 'fz';
sensor2 = 'p5';
centerfreq = 6; % in Hz
trial2plot = 10;
times2plot = dsearchn(EEG.times',[-300 1200]');
fft_data1 = fft(reshape(EEG.data(strcmpi(sensor1,{EEG.chanlocs.labels}),:,:),1,EEG.pnts*EEG.trials),n_convolution);
fft_data2 = fft(reshape(EEG.data(strcmpi(sensor2,{EEG.chanlocs.labels}),:,:),1,EEG.pnts*EEG.trials),n_convolution);
% create wavelet and run convolution
fft_wavelet = fft(exp(2*1i*pi*centerfreq.*time) .* exp(-time.^2./(2*( wavelet_cycles /(2*pi*centerfreq))^2)),n_convolution);
convolution_result_fft = ifft(fft_wavelet.*fft_data1,n_convolution) * sqrt(wavelet_cycles /(2*pi*centerfreq));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
convolution_result_fft1 = reshape(convolution_result_fft,EEG.pnts,EEG.trials);
fft_wavelet = fft(exp(2*1i*pi*centerfreq.*time) .* exp(-time.^2./(2*( wavelet_cycles /(2*pi*centerfreq))^2)),n_convolution);
convolution_result_fft = ifft(fft_wavelet.*fft_data2,n_convolution) * sqrt(wavelet_cycles /(2*pi*centerfreq));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
convolution_result_fft2 = reshape(convolution_result_fft,EEG.pnts,EEG.trials);
% keep only requested time regions
convolution_result_fft1 = convolution_result_fft1(times2plot(1):times2plot(2),:);
convolution_result_fft2 = convolution_result_fft2(times2plot(1):times2plot(2),:);
figure
subplot(211)
plot(EEG.times(times2plot(1):times2plot(2)),abs(convolution_result_fft1(:,trial2plot)).^2)
hold on
plot(EEG.times(times2plot(1):times2plot(2)),abs(convolution_result_fft2(:,trial2plot)).^2,'r')
xlabel('Time (ms)')
set(gca,'xlim',EEG.times(times2plot))
legend({sensor1;sensor2})
subplot(223)
plot(abs(convolution_result_fft1(:,trial2plot)).^2,abs(convolution_result_fft2(:,trial2plot)).^2,'.')
title('Power relationship')
xlabel([ sensor1 ' ' num2str(centerfreq) 'Hz power' ])
ylabel([ sensor2 ' ' num2str(centerfreq) 'Hz power' ])
r=corr(abs(convolution_result_fft1(:,trial2plot)).^2,abs(convolution_result_fft2(:,trial2plot)).^2,'type','p');
legend([ 'Pearson R = ' num2str(r) ]);
subplot(224)
plot(tiedrank(abs(convolution_result_fft1(:,trial2plot)).^2),tiedrank(abs(convolution_result_fft2(:,trial2plot)).^2),'.')
title('Rank-power relationship')
xlabel([ sensor1 ' ' num2str(centerfreq) 'Hz rank-power' ])
ylabel([ sensor2 ' ' num2str(centerfreq) 'Hz rank-power' ])
r=corr(abs(convolution_result_fft1(:,trial2plot)).^2,abs(convolution_result_fft2(:,trial2plot)).^2,'type','s');
legend([ 'Spearman Rho = ' num2str(r) ]);
set(gca,'ylim',get(gca,'xlim'))
%% Figure 27.5
% Compute how many time points are in one cycle, and limit xcov to this lag
nlags = round(EEG.srate/centerfreq);
% note that data are first tiedrank'ed, which results in a Spearman rho
% instead of a Pearson r.
[corrvals,corrlags] = xcov(tiedrank(abs(convolution_result_fft1(:,trial2plot)).^2),tiedrank(abs(convolution_result_fft2(:,trial2plot)).^2),nlags,'coeff');
% convert correlation lags from indices to time in ms
corrlags = corrlags * 1000/EEG.srate;
figure
plot(corrlags,corrvals,'-o','markerface','w')
hold on
plot([0 0],get(gca,'ylim'))
xlabel([ sensor1 ' leads --- Time lag in ms --- ' sensor2 ' leads' ])
ylabel('Correlation coefficient')
%% Figure 27.6
sensor1 = 'poz';
sensor2 = 'fz';
timewin1 = [ -300 -100 ]; % in ms relative to stim onset
timewin2 = [ 200 400 ];
centerfreq1 = 6; % in Hz
centerfreq2 = 6;
% convert time from ms to index
timeidx1 = zeros(size(timewin1));
timeidx2 = zeros(size(timewin2));
for i=1:2
[junk,timeidx1(i)] = min(abs(EEG.times-timewin1(i)));
[junk,timeidx2(i)] = min(abs(EEG.times-timewin2(i)));
end
% setup wavelet convolution and outputs
time = -1:1/EEG.srate:1;
half_of_wavelet_size = (length(time)-1)/2;
% FFT parameters
n_wavelet = length(time);
n_data = EEG.pnts*EEG.trials;
n_convolution = n_wavelet+n_data-1;
wavelet_cycles= 4.5;
% FFT of data (note: this doesn't change on frequency iteration)
fft_data1 = fft(reshape(EEG.data(strcmpi(sensor1,{EEG.chanlocs.labels}),:,:),1,EEG.pnts*EEG.trials),n_convolution);
fft_data2 = fft(reshape(EEG.data(strcmpi(sensor2,{EEG.chanlocs.labels}),:,:),1,EEG.pnts*EEG.trials),n_convolution);
% initialize output time-frequency data
corrdata = zeros(EEG.trials,2);
% create wavelet and run convolution
fft_wavelet = fft(exp(2*1i*pi*centerfreq1.*time) .* exp(-time.^2./(2*( wavelet_cycles /(2*pi*centerfreq1))^2)),n_convolution);
convolution_result_fft = ifft(fft_wavelet.*fft_data1,n_convolution) * sqrt(wavelet_cycles /(2*pi*centerfreq1));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
convolution_result_fft = reshape(convolution_result_fft,EEG.pnts,EEG.trials);
analyticsignal1 = abs(convolution_result_fft).^2;
fft_wavelet = fft(exp(2*1i*pi*centerfreq2.*time) .* exp(-time.^2./(2*( wavelet_cycles /(2*pi*centerfreq2))^2)),n_convolution);
convolution_result_fft = ifft(fft_wavelet.*fft_data2,n_convolution) * sqrt(wavelet_cycles /(2*pi*centerfreq2));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
convolution_result_fft = reshape(convolution_result_fft,EEG.pnts,EEG.trials);
analyticsignal2 = abs(convolution_result_fft).^2;
% Panel A: correlation in a specified window
tfwindowdata1 = mean(analyticsignal1(timeidx1(1):timeidx1(2),:),1);
tfwindowdata2 = mean(analyticsignal2(timeidx2(1):timeidx2(2),:),1);
figure
subplot(121)
plot(tfwindowdata1,tfwindowdata2,'.')
axis square
title([ 'TF window correlation, r_p=' num2str(corr(tfwindowdata1',tfwindowdata2','type','p')) ])
xlabel([ sensor1 ': ' num2str(timewin1(1)) '-' num2str(timewin1(2)) '; ' num2str(centerfreq1) ' Hz' ])
ylabel([ sensor2 ': ' num2str(timewin2(1)) '-' num2str(timewin2(2)) '; ' num2str(centerfreq2) ' Hz' ])
% also plot rank-transformed data
subplot(122)
plot(tiedrank(tfwindowdata1),tiedrank(tfwindowdata2),'.')
axis square
xlabel([ sensor1 ': ' num2str(timewin1(1)) '-' num2str(timewin1(2)) '; ' num2str(centerfreq1) ' Hz' ])
ylabel([ sensor2 ': ' num2str(timewin2(1)) '-' num2str(timewin2(2)) '; ' num2str(centerfreq2) ' Hz' ])
title([ 'TF window correlation, r_p=' num2str(corr(tfwindowdata1',tfwindowdata2','type','s')) ])
% panel B: correlation over time
corr_ts = zeros(size(EEG.times));
for ti=1:EEG.pnts
corr_ts(ti) = corr(analyticsignal1(ti,:)',analyticsignal2(ti,:)','type','s');
end
figure
plot(EEG.times,corr_ts)
set(gca,'xlim',[-200 1200])
xlabel('Time (ms)'), ylabel('Spearman''s rho')
% Panel C: exploratory time-frequency power correlations
times2save = -200:25:1200;
frex = logspace(log10(2),log10(40),20);
times2save_idx = zeros(size(times2save));
for i=1:length(times2save)
[junk,times2save_idx(i)] = min(abs(EEG.times-times2save(i)));
end
% rank-transforming the data can happen outside the frequency loop
seeddata_rank = tiedrank(tfwindowdata2);
% initialize output correlation matrix
expl_corrs = zeros(length(frex),length(times2save));
for fi=1:length(frex)
% get power (via wavelet convolution) from signal1
fft_wavelet = fft(exp(2*1i*pi*frex(fi).*time) .* exp(-time.^2./(2*( wavelet_cycles /(2*pi*frex(fi)))^2)),n_convolution);
convolution_result_fft = ifft(fft_wavelet.*fft_data1,n_convolution) * sqrt(wavelet_cycles /(2*pi*frex(fi)));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
convolution_result_fft = reshape(convolution_result_fft,EEG.pnts,EEG.trials);
analyticsignal1 = abs(convolution_result_fft).^2;
for ti=1:length(times2save)
expl_corrs(fi,ti) = 1-6*sum((seeddata_rank-tiedrank(analyticsignal1(times2save_idx(ti),:))).^2)/(EEG.trials*(EEG.trials^2-1));
end
end
figure
contourf(times2save,frex,expl_corrs,40,'linecolor','none')
set(gca,'clim',[-.4 .4],'yscale','log','ytick',round(logspace(log10(frex(1)),log10(frex(end)),8)))
xlabel('Time (ms)'), ylabel('Frequency (Hz)')
title([ 'Correlation over trials from seed ' sensor2 ', ' num2str(centerfreq2) ' Hz and ' num2str(timewin2(1)) '-' num2str(timewin2(2)) ' ms' ])
colorbar
%% Figure 27.7
seed_chan = 'fz';
target_chan = 'f6';
control_chan = 'f1';
clim = [0 .6];
% wavelet parameters
min_freq = 2;
max_freq = 40;
num_frex = 15;
% downsampled times
times2save = -200:50:800;
% times2save = EEG.times; % uncomment this line for figure 27.8
% other wavelet parameters
frequencies = logspace(log10(min_freq),log10(max_freq),num_frex);
time = -1:1/EEG.srate:1;
half_of_wavelet_size = (length(time)-1)/2;
% FFT parameters
n_wavelet = length(time);
n_data = EEG.pnts*EEG.trials;
n_convolution = n_wavelet+n_data-1;
wavelet_cycles= 4.5;
times2saveidx = dsearchn(EEG.times',times2save');
% FFT of data (note: this doesn't change on frequency iteration)
fft_data_seed = fft(reshape(EEG.data(strcmpi(seed_chan,{EEG.chanlocs.labels}),:,:),1,EEG.pnts*EEG.trials),n_convolution);
fft_data_trgt = fft(reshape(EEG.data(strcmpi(target_chan,{EEG.chanlocs.labels}),:,:),1,EEG.pnts*EEG.trials),n_convolution);
fft_data_ctrl = fft(reshape(EEG.data(strcmpi(control_chan,{EEG.chanlocs.labels}),:,:),1,EEG.pnts*EEG.trials),n_convolution);
% initialize output time-frequency data
tf_corrdata = zeros(length(frequencies),length(times2save),2);
for fi=1:length(frequencies)
% create wavelet and get its FFT
fft_wavelet = fft(exp(2*1i*pi*frequencies(fi).*time) .* exp(-time.^2./(2*( wavelet_cycles /(2*pi*frequencies(fi)))^2))/frequencies(fi),n_convolution);
% convolution for all three sites (save only power)
convolution_result_fft = ifft(fft_wavelet.*fft_data_seed,n_convolution) * sqrt(wavelet_cycles /(2*pi*frequencies(fi)));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
conv_result_seed = abs(reshape(convolution_result_fft,EEG.pnts,EEG.trials)).^2;
convolution_result_fft = ifft(fft_wavelet.*fft_data_trgt,n_convolution) * sqrt(wavelet_cycles /(2*pi*frequencies(fi)));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
conv_result_trgt = abs(reshape(convolution_result_fft,EEG.pnts,EEG.trials)).^2;
convolution_result_fft = ifft(fft_wavelet.*fft_data_ctrl,n_convolution) * sqrt(wavelet_cycles /(2*pi*frequencies(fi)));
convolution_result_fft = convolution_result_fft(half_of_wavelet_size+1:end-half_of_wavelet_size);
conv_result_ctrl = abs(reshape(convolution_result_fft,EEG.pnts,EEG.trials)).^2;
% downsample and rank transform all data
conv_result_seed = tiedrank(conv_result_seed(times2saveidx,:)')';
conv_result_trgt = tiedrank(conv_result_trgt(times2saveidx,:)')';
conv_result_ctrl = tiedrank(conv_result_ctrl(times2saveidx,:)')';
for ti=1:length(times2save)
% compute bivariate correlations
r_st = 1-6*sum((conv_result_seed(ti,:)-conv_result_trgt(ti,:)).^2)/(EEG.trials*(EEG.trials^2-1));
r_sc = 1-6*sum((conv_result_seed(ti,:)-conv_result_ctrl(ti,:)).^2)/(EEG.trials*(EEG.trials^2-1));
r_tc = 1-6*sum((conv_result_ctrl(ti,:)-conv_result_trgt(ti,:)).^2)/(EEG.trials*(EEG.trials^2-1));
% bivariate correlation for comparison
tf_corrdata(fi,ti,1) = r_st;
% compute partial correlation and store in results matrix
tf_corrdata(fi,ti,2) = (r_st-r_sc*r_tc) / ( sqrt(1-r_sc^2)*sqrt(1-r_tc^2) );
end
end
% plot
figure
for i=1:2
subplot(1,2,i)
contourf(times2save,frequencies,squeeze(tf_corrdata(:,:,i)),40,'linecolor','none')
set(gca,'clim',clim,'xlim',[-200 800],'yscale','log','ytick',logspace(log10(frequencies(1)),log10(frequencies(end)),6),'yticklabel',round(logspace(log10(frequencies(1)),log10(frequencies(end)),6)*10)/10)
axis square
if i==1
title([ 'Correlation between ' seed_chan ' and ' target_chan ])
else
title([ 'Partial correlation between ' seed_chan ' and ' target_chan ])
end
xlabel('Time (ms)'), ylabel('Frequency (Hz)')
end
%% Figure 27.8
% Re-run the code for the previous figure but comment out the
% following line towards the top:
% times2save = EEG.times; % uncomment this line for figure 27.8
% Then run this section of code.
ds_timesidx = dsearchn(EEG.times',(-200:50:800)'); % ds = downsampled
[~,lofreq] = min(abs(frequencies-4.7));
[~,hifreq] = min(abs(frequencies-32));
figure
subplot(221)
contourf(times2save,frequencies,squeeze(tf_corrdata(:,:,2)),40,'linecolor','none')
hold on
plot(get(gca,'xlim'),frequencies([lofreq lofreq]),'k--')
plot(get(gca,'xlim'),frequencies([hifreq hifreq]),'k--')
set(gca,'clim',clim,'xlim',[-200 800],'yscale','log','ytick',logspace(log10(frequencies(1)),log10(frequencies(end)),6),'yticklabel',round(logspace(log10(frequencies(1)),log10(frequencies(end)),6)*10)/10)
title('Original (256 Hz)')
subplot(222)
contourf(times2save(ds_timesidx),frequencies,squeeze(tf_corrdata(:,ds_timesidx,2)),40,'linecolor','none')
hold on
plot(get(gca,'xlim'),frequencies([lofreq lofreq]),'k--')
plot(get(gca,'xlim'),frequencies([hifreq hifreq]),'k--')
set(gca,'clim',clim,'xlim',[-200 800],'yscale','log','ytick',logspace(log10(frequencies(1)),log10(frequencies(end)),6),'yticklabel',round(logspace(log10(frequencies(1)),log10(frequencies(end)),6)*10)/10)
title('Down-sampled (20 Hz)')
subplot(223)
plot(EEG.times,squeeze(tf_corrdata(lofreq,:,2)))
hold on
plot(EEG.times(ds_timesidx),squeeze(tf_corrdata(lofreq,ds_timesidx,2)),'ro-','markerface','w')
title('Effect of downsampling on low-frequency activity')
set(gca,'xlim',[-200 800],'ylim',[.25 .65])
subplot(224)
plot(EEG.times,squeeze(tf_corrdata(hifreq,:,2)))
hold on
plot(EEG.times(ds_timesidx),squeeze(tf_corrdata(hifreq,ds_timesidx,2)),'ro-','markerface','w')
title('Effect of downsampling on high-frequency activity')
set(gca,'xlim',[-200 800],'ylim',[-.1 .6])
legend({'Original (256 Hz)';'Down-sampled (20 Hz)'})
%% Figure 27.9
% note: this cell takes a while to run, particularly on slow computers!
n = 1000;
ncorrs = 100000;
t=[0 0 0];
for i=1:ncorrs
% create random variables
a = rand(2,n);
tic
% Matlab corr function
c2 = corr(a','type','s');
t(1) = t(1) + toc;
tic
% self-written Spearman correlation (must first rank-transform)
a1 = tiedrank(a')'; % tiedrank accepts matrix input, but make sure the matrix is in the correct orientation!!
c1 = 1-6*sum((a1(1,:)-a1(2,:)).^2)/(n*(n^2-1));
t(2) = t(2) + toc;
tic
% ordinary least squares
% Note: Uncommenting the following line will normalize the data to give
% you a correlation coefficient. If you don't need the correlation coefficient
% (and instead can use unstandardized regression coefficients), leave this
% line commented out for a ten-fold increase in speed.
%a = bsxfun(@rdivide,bsxfun(@minus,a,mean(a,2)),std(a,[],2));
c3 = (a(1,:)*a(1,:)')\a(1,:)*a(2,:)';
t(3) = t(3) + toc;
end
figure
bar(t)
set(gca,'xticklabel',{'corr function';'manual';'ols'},'xlim',[.5 3.5])
ylabel([ 'Time for ' num2str(ncorrs) ' iterations (s)' ])
%% end.