Commit 446a993b authored by Julian Kosciessa's avatar Julian Kosciessa
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correct tutorial files

parent 65dfd1b6
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# Multi-Scale Entropy Computation Tutorial # Multi-Scale Entropy Computation Tutorial
written by Liliana Polyanska & Niels Kloosterman (Lifespan Neural Dynamics Group)
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### Introduction ### Introduction
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The msecomputation script was developed for calculating multi-scale entropy from EEG/MEG time series data. Data can be coarse-grained for higher scales using one of the two coarse-graining functions provided. In addition, memory usage is kept in check and the function is optimized for running on a gpu. Thanks to using a 3D matrix, data from all channels can be efficiently processed at the same time. The script computes mse for each of the specified time windows, thus allowing to look at entropy changes over time. The msecomputation script was developed for calculating multi-scale entropy from EEG/MEG time series data. Data can be coarse-grained for higher scales using one of the two coarse-graining functions provided. In addition, memory usage is kept in check and the function is optimized for running on a gpu. Thanks to using a 3D matrix, data from all channels can be efficiently processed at the same time. The script computes mse for each of the specified time windows, thus allowing to look at entropy changes over time.
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For the purpose of this tutorial, parameters were kept simple, so that to best exemplify the mechanics of the mse computations. Thus, data consists of 1 channel x 20 time points. The function is run only for scale 2. <br> For the purpose of this tutorial, parameters were kept simple, so that to best exemplify the mechanics of the mse computations. Thus, data consists of 1 channel x 20 time points. The function is run only for scale 2. <br>
Some variables are visualized to help understand how the function works. When you run it, no plots will automatically appear. <br><br> Some variables are visualized to help understand how the function works. When you run it, no plots will automatically appear. <br><br>
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This is what original time series data looks like. This is what original time series data looks like.
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``` python ``` python
display(original_data) display(original_data)
``` ```
%%%% Output: display_data %%%% Output: display_data
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) 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)
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
*** ***
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
You determine the number and length of the time windows for which mse will be computed. The script then iterates over these windows in the **itoi** loop. <br> You determine the number and length of the time windows for which mse will be computed. The script then iterates over these windows in the **itoi** loop. <br>
Quality check is done to verify that there is a sufficient number of trials in the current time window. Quality check is done to verify that there is a sufficient number of trials in the current time window.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
for itoi = 1:ntoi for itoi = 1:ntoi
% select time window of interest from each trial % select time window of interest from each trial
tmpcfg=[]; tmpcfg=[];
tmpcfg.toilim = [toi(itoi)-timwin*0.5 toi(itoi)+timwin*0.5]; tmpcfg.toilim = [toi(itoi)-timwin*0.5 toi(itoi)+timwin*0.5];
data_sel = ft_redefinetrial(tmpcfg, data); data_sel = ft_redefinetrial(tmpcfg, data);
% only take trials that have the whole interval % only take trials that have the whole interval
tmpcfg = []; tmpcfg = [];
tmpcfg.minlength = timwin; tmpcfg.minlength = timwin;
data_sel = ft_redefinetrial(tmpcfg, data_sel); data_sel = ft_redefinetrial(tmpcfg, data_sel);
% need 40 samples for mse calc, 3 smp per trial for scale 42: 40/3 = 13.3 trials, make 15 % need 40 samples for mse calc, 3 smp per trial for scale 42: 40/3 = 13.3 trials, make 15
ntrials = length(data_sel.trialinfo); ntrials = length(data_sel.trialinfo);
if ntrials < 1 if ntrials < 1
warning('Time point %g: Not enough trials remain', toi(itoi)) warning('Time point %g: Not enough trials remain', toi(itoi))
break % subsequent time points will also not work break % subsequent time points will also not work
end end
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
For each channel, **r_new** determines the portion of SD that corresponds to **r** (similarity criterion). For each channel, **r_new** determines the portion of SD that corresponds to **r** (similarity criterion).
The script will later look for points that comprise a pattern only within this range. <br> The script will later look for points that comprise a pattern only within this range. <br>
**r_new** is a *n channels* x *1* vector. **r_new** is a *n channels* x *1* vector.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
% calculate similarity criterion % calculate similarity criterion
r_new = r * std(cell2mat(data_sel.trial),1,2); r_new = r * std(cell2mat(data_sel.trial),1,2);
nchan = size(data_sel.trial{1},1); nchan = size(data_sel.trial{1},1);
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
#### Loop over scales #### Loop over scales
mse is calculated for each scale separately. mse is calculated for each scale separately.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
for s = 1:numel(timescales) % loop through timescales for s = 1:numel(timescales) % loop through timescales
sc = timescales(s); sc = timescales(s);
fprintf('Scale %d - %d\n', sc, length(timescales)) fprintf('Scale %d - %d\n', sc, length(timescales))
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
#### Coarse-grain time series at the current scale #### Coarse-grain time series at the current scale
You can choose from two coarse-graining methods: **filtskip** and **pointavg**. <br><br> You can choose from two coarse-graining methods: **filtskip** and **pointavg**. <br><br>
**filtskip** resamples the signal by grouping the original data points into multiple starting points, whose number depends on the current scale. E.g. scale 2 has 2 starting points, scale 3 has 3, etc. You can imagine coarse-graining with this method as dividing the number of time points in the original time series by the current scale and then allocating them to the corresponding starting points. For example, to coarse-grain at the scale 3, every first time point of the original time series would be allocated to starting point 1, every second to starting point 2, and every third to starting point 3. In addition, this coarse-graining method adds mean padding to avoid filter artifacts. <br><br> **filtskip** resamples the signal by grouping the original data points into multiple starting points, whose number depends on the current scale. E.g. scale 2 has 2 starting points, scale 3 has 3, etc. You can imagine coarse-graining with this method as dividing the number of time points in the original time series by the current scale and then allocating them to the corresponding starting points. For example, to coarse-grain at the scale 3, every first time point of the original time series would be allocated to starting point 1, every second to starting point 2, and every third to starting point 3. In addition, this coarse-graining method adds mean padding to avoid filter artifacts. <br><br>
With **pointavg** data is coarse-grained by taking the average of the adjacent time points according to the current scale. For instance, to coarse-grain at scale 3, this method will first average points 1 to 3, then points 2 to 4, then points 3 to 5, etc. <br><br> With **pointavg** data is coarse-grained by taking the average of the adjacent time points according to the current scale. For instance, to coarse-grain at scale 3, this method will first average points 1 to 3, then points 2 to 4, then points 3 to 5, etc. <br><br>
Regardless of the method you choose, at scale 1 (native sampling rate) no coarse-graining is done. <br><br> Regardless of the method you choose, at scale 1 (native sampling rate) no coarse-graining is done. <br><br>
Note that the number of loops over starting points depends on the coarse-graining function. If using **filtskip**, the function will loop over starting points, which correspond to the current scale. If using **pointavg**, there is only one starting point for each scale. <br><br> Note that the number of loops over starting points depends on the coarse-graining function. If using **filtskip**, the function will loop over starting points, which correspond to the current scale. If using **pointavg**, there is only one starting point for each scale. <br><br>
Coarse-grained data is stored in a variable **cg_data**, which is a cell array of size *n starting points* x *1*, containing in each cell: *1* x *n trials* cell array, which again in each cell contains a matrix of size *n channels* x *n sample points* (for current coarse-graining level). Coarse-grained data is stored in a variable **cg_data**, which is a cell array of size *n starting points* x *1*, containing in each cell: *1* x *n trials* cell array, which again in each cell contains a matrix of size *n channels* x *n sample points* (for current coarse-graining level).
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
cg_data = {}; cg_data = {};
if sc == 1 % no caorse graining for native sampling rate if sc == 1 % no caorse graining for native sampling rate
cg_data{1} = data_sel.trial; %only keep trial data cg_data{1} = data_sel.trial; %only keep trial data
nloops = 1; % no loop across starting points nloops = 1; % no loop across starting points
else % coarse-grain time series at this time scale else % coarse-grain time series at this time scale
switch coarsegrainmethod switch coarsegrainmethod
case 'filtskip' case 'filtskip'
L = sc-1; % from Semmlow book L = sc-1; % from Semmlow book
cutoff = 1/(1+L); % Butter defines the cutoff % frequency in terms of fs/2 cutoff = 1/(1+L); % Butter defines the cutoff % frequency in terms of fs/2
filtord = 6; filtord = 6;
[B,A] = butter(filtord,cutoff); % Define filter [B,A] = butter(filtord,cutoff); % Define filter
padlength = 512; padlength = 512;
x_pad = cellfun(@(a) ft_preproc_padding(a, 'mean', padlength), data_sel.trial, 'UniformOutput', false ); % add padding x_pad = cellfun(@(a) ft_preproc_padding(a, 'mean', padlength), data_sel.trial, 'UniformOutput', false ); % add padding
x_pad = cellfun(@transpose, x_pad, 'UniformOutput', false); % transpose for filtfilt: time x chan x_pad = cellfun(@transpose, x_pad, 'UniformOutput', false); % transpose for filtfilt: time x chan
resamp_x_pad = cellfun(@(x_pad) filtfilt(B,A,x_pad), x_pad, 'UniformOutput', false ); % add padding% Filter resamp_x_pad = cellfun(@(x_pad) filtfilt(B,A,x_pad), x_pad, 'UniformOutput', false ); % add padding% Filter
resamp_x_pad = cellfun(@transpose, resamp_x_pad, 'UniformOutput', false); % transpose back : chan x time again resamp_x_pad = cellfun(@transpose, resamp_x_pad, 'UniformOutput', false); % transpose back : chan x time again
resamp_x = cellfun(@(resamp_x_pad) ft_preproc_padding(resamp_x_pad, 'remove', padlength), resamp_x_pad, 'UniformOutput', false ); % add padding% Filter resamp_x = cellfun(@(resamp_x_pad) ft_preproc_padding(resamp_x_pad, 'remove', padlength), resamp_x_pad, 'UniformOutput', false ); % add padding% Filter
% close all; figure; plot(x_pad); hold on; plot(resamp_x) % close all; figure; plot(x_pad); hold on; plot(resamp_x)
nloops = sc; nloops = sc;
cg_data = cell(nloops,1); % make cell: cg_data{istart}{trials}(chan-by-time) cg_data = cell(nloops,1); % make cell: cg_data{istart}{trials}(chan-by-time)
for is = 1:nloops % loop over starting points here! for is = 1:nloops % loop over starting points here!
cg_data{is} = cellfun(@(resamp_x) resamp_x(:, is:(L+1):end), resamp_x, 'UniformOutput', false ); % add padding% Filter cg_data{is} = cellfun(@(resamp_x) resamp_x(:, is:(L+1):end), resamp_x, 'UniformOutput', false ); % add padding% Filter
end end
case 'pointavg' % original point averaging coarse graining, no loop over starting points case 'pointavg' % original point averaging coarse graining, no loop over starting points
nloops = 1; % no loop across starting points nloops = 1; % no loop across starting points
nchan = size(data_sel.trial{1},1); nchan = size(data_sel.trial{1},1);
for itrial = 1:length(data_sel.trial) for itrial = 1:length(data_sel.trial)
num_cg_tpts = floor(length(data_sel.trial{itrial})/sc); % number of coarse-grained time points num_cg_tpts = floor(length(data_sel.trial{itrial})/sc); % number of coarse-grained time points
cg_data{1}{itrial} = zeros(nchan, num_cg_tpts); % preallocate cg_data matrix cg_data{1}{itrial} = zeros(nchan, num_cg_tpts); % preallocate cg_data matrix
for t = 1:num_cg_tpts % calculate coarse_grained time series for t = 1:num_cg_tpts % calculate coarse_grained time series
cg_data{1}{itrial}(:,t) = mean( data_sel.trial{itrial}(:, (t-1)*sc + [1:sc]) ,2); cg_data{1}{itrial}(:,t) = mean( data_sel.trial{itrial}(:, (t-1)*sc + [1:sc]) ,2);
end end
end end
end end
end end
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
This is what data now looks like, after it's been coarse-grained with the **filtskip** method. This is what data now looks like, after it's been coarse-grained with the **filtskip** method.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
display(cg_data) display(cg_data)
``` ```
%%%% Output: display_data %%%% Output: display_data
![](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQAAAQABAAD//gAYTUFUTEFCIEhhbmRsZSBHcmFwaGljc//+AB1NQVRMQUIsIFRoZSBNYXRoV29ya3MsIEluYy7/2wBDAAgGBgcGBQgHBwcJCQgKDBQNDAsLDBkSEw8UHRofHh0aHBwgJC4nICIsIxwcKDcpLDAxNDQ0Hyc5PTgyPC4zNDL/2wBDAQkJCQwLDBgNDRgyIRwhMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjIyMjL/wAARCAIIAxcDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD3CiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArndb8d+GPDl6tlqurwW9yQD5WGdlB6FgoOPxroq8tsJrzwP4i8RDUPC+o6oNU1B7u31DT4BOWjfG2F84KhOevHJx7lm9v8wulv+dvxO21fxj4e0LTrW/1HVYIba7UNbuCX85SAcqFBJGCDkeop+heK9D8SyXMejahHeG1EZm8sHC7wSvJGD0PTpjBxXDaw1xonjbQvE0vh2e5s20UWf9nWiLLNYybg2VTuADsyvoe2Mu+Gd4t/4+8d3a6a+nLK1k32ZwoZf3b8sF4BP3iOxJzzS6/8Aelv+D+h6ZPPDa28txcSpFDEheSRzhVUDJJPYAVwGp/FbRpbvR7Xw7qFpfT3er29lcRurgrE5IZ1zjOCBzyOfetv4i6LfeIfAGr6XpuPtc0amNS2N+11crn3CkenPNcJreoXXiS98IQ2fgfVdPGn61avPNNaBFgQHlFxyU7luANo9RT5W/8AgC5kv+H/AKud/q3j7wvoWrf2XqesQ295gMyMrEKD03MBheOeT0I9aoeJ/iVo3hTxFpOl3zjyr2J55bgFiIEAOw4CnduYEcHjGa888XWvifUL3xNa38HiyaZpJhp8OnBRZNbbfk3nHzHHVep6dTW3e2+o6PD8MdYbRNRvIdK094ryG1g3yxs9tGgBTg9c59MGnyS6p/18vyuPmh0/Nf0vmd5qfjbw7o2lWOp6hqaQ2l+oe2YoxMilQ2QoGcYI7cZHrUi+LtBfT9Pv49SiktdQuls7aRAWDzNkBOBweD1xiuF8b3Wu3ur6ROkHie38P3GniTy9HiUXKXLHO2UdVAXH4596p+Bra90TQGj1HwvfXklx4tyi3se+W2VlXFyzbSDtwcuMAknBFHJLez+7/gW/EOaG3X1R7DXO63478MeHL1bLVdXgt7kgHysM7KD0LBQcfjXRV5bYTXngfxF4iGoeF9R1QapqD3dvqGnwCctG+NsL5wVCc9eOTj3Vm9v8xXS3/O34nbat4w8P6HptrqGo6rbw2t2oa3cEv5wIByoXJIwQcj1FWNM8SaNrGjvq1hqME1hGGMkwbAj2jJ3Z+7gcnNcLq0V7o/jDRPFj+Gbq608aMtk1jZxrLLYSlt+Qg4PB2ZX0Ptmhb2Pig6N468Q6HpU+l3WrNbnT7GRAswEY2ySbOgZgWIHXI+hJyy3/AK+/uHNHr+f6fqd5oPjnw14mumtdI1WK4uFUuYirIxA6kBgM9e1V7f4j+EbqTT44Nahkk1BxHbIqPuYlygyMZXLAjnFeceHNO1Gb4meF9RFr4tktIhdCa41xRhGMJHygD5ASR168AdDXa/CHR20n4b6bHdacbO+ZpXnWSHy5CfNcKWyM52hcZ7Yp8klv+X+dvy/zHzR6fmv0uX3+JngxNQaxbxBaiZW2EndsBzjG/G3r71f1/wAZeHvC8kcesapDayyLuSMgs5XOM7VBOM9/Y+lePnTNX0+3OmeG9G8U285lBXTNRgin04At86mRv4fvc5yf1rY8XeHdQs/iHqmtzp4mbT76KHyJvD7gvGUTaySIRnGRuBHHPfJwvZz2/R/5X/B/MFKF/wDgr/hvxPW9O1Gz1awivtPuY7m1mGY5Y2yrc4P6gioNa13S/Dunm/1a9itLYNt3yH7zcnAA5J4PA9K4bwn4PFz4PuLKO48T6GsupvdiSa5RLqXKBSW2rwpOTg85XNR+K9EudAuPB+ohb3xBa6PcXAnhnkEtzN5q/K4BADlCOAOeBjuQOLXX8/yf+YXj0/T8zp7H4h+FNSFwbLWIpvs1m99NtR8xwocMx44I9OvI4qWx8d+GdS1W00yy1aKe9u4xLDEisSV2b+TjCnbzg4NeX3V83iLx14pltNDu7CWfwdcxpbzRBZ523gBii5IJ4UA8/KPUV6L4f0670v4WWVvpdlHbasmkKY4mjCEXJhz8wPcv1z3zmhJ7g2u34/8AALGm/EDwrq+r/wBlWOswS3m4oseGAcjOdrEYboehNVbXxzYWlrqNzrup2EMEOtS6ZDJCsgVSBlUkLDhwM5I+X3ryqDTtev8AU/Cs9zaeMLi6t9XtJL9tRQC2iYN8xjUDOBz83QDr1rXn8O6hdW8tvcaRcywy/EQ3Mkb27FXtiMGQgjmMjv0p+zn1/X/gBzw6fmj03Q/HHhrxJeyWek6tDc3MYLGMBlJA6kZAyPcVBefEPwlp+rNpd1rtrHdq/lupJKo3cMwG1T9TWd4i0uVvif4GvLWxc29ut8s80cXyxgwgIGIGAM5Az715ha+Er3R9NuND1m08bzTs8isNJdHs7lSxw2SOMg8huf5Bcknt+T/S4c0Ov5r9bHt+v+KdE8L28U2s6hFaLKSIw2WZ8YzhQCTjIzxxmsjwl40TxV4l8RWlnJbT6Zp4tTa3EOcyeZGWbdk9mXHQY5zXM3On3vhjxD4b19/D9/qOn2+gx6a1vCq3FxZygg7iBgMSPlLL79sZvfDuK7k8a+M9Tm0K60i3vms3gini2bsI4J44ySckDOC2DzRyvd/lp94uZbL8/wBDtta13S/Dunm/1a9itLYNt3yH7zcnAA5J4PA9K5rRPiBa+I/Hv9kaRcW11pf9km8M6BhIsomCFCD0G0g4IzyKh+IFherrfhnxDBpcuq2ekzTm6soVDyMJEAWRVPDFCM+uSMdyMCyl1nVfiNq+u6V4bvtKeTw1LDaPeW4j864EgKFuwOcDDHOFz0o5ZPX+vvDmS/4f9DttN+IHhXV9X/sqx1mCW83FFjwwDkZztYjDdD0JrLtPinoM3jTUfDc8vkTW9zHaW8mHb7TK3ysuAvy7X+XJOD16V5pBp2vX+p+FZ7m08YXF1b6vaSX7aigFtEwb5jGoGcDn5ugHXrXd2dxd+H/i14ie50LU57XWpLFba7trfzIk2R7GZ2z8oBbn6E0+SXVP8f8AL9B80On5o6XVvH3hfQtW/svU9Yht7zAZkZWIUHpuYDC8c8noR610asrorowZWGQQcgivCvF1r4n1C98TWt/B4smmaSYafDpwUWTW235N5x8xx1XqenU1654OgltvBGgQTxPFNFptukkbqVZGEaggg9CDS5ZLV/1+H+fqF4vb+v68zjl+I97qfxPk8LaQdLW3trhYZWuhL5s+0EzeXtG0FQrD5uCQME5ro7z4i+EdP1htKutdto7xH2OpyVRvRnA2g+uTxVHw1YXMHxP8c3c1rLHb3H2DyJnjIWTbCQ209Dg8HFcPbQanongHUPAlx4N1C+1aUTxJewwK9vO0jMUmMp6EAjryNo6dnyPpf8/6Qc66/ml+h6nqvi/QNDvnstT1OG1uEthdFZAR+7L7AQcYJ3cYHPtV3R9Ysde0uHU9Mn8+zm3eXJtK7sMVPBAPUGuC0bwzc2nxN0b+0LP7THp/hSK2+2NEWjFwsuDtYj72Cx9cE16UAAMAAD2pWa3FdPY5jUviL4R0jU306+1u3iuo22yJhmCH0YgEA/U1f1bxXoOh6bBqOo6pbw2lwA0Em7d5oIyCgGS3BB49a8q16wvdO1nW/wCxNM8XWd7d3MsqxQQx3FjcyknEhLZwrcE56dO1buoWOr6L4j8O+J77w+2pQQaKljcWdhGrtZXGQzSRx9COqfKenfpk5J/0v6/C/wCgc0P6a/pfM7W28Y+Hrvw7Pr8GqQvpkGRLPyNhGPlIxndyOMZOR61nN4+0bUfC+t6p4fv4L2fTrOW48tlZcFUZl3KcHBK1heJNT13VPBj32g6JquleZqcf2tEgRbyW2CjfIqf3shVA64X0rjtO0bVJdZ8TXMen+JpLe48KXUEEusLvmkkLDCDaOM84Xr1PcU+ST2T+5/5aff8AIfNFevqv6Z6lH430qw8I6LrPiC+t7F9QtIp9nJ3MyKzBVGWIGfftWxouu6X4i08X2k3sV3bFtpeM/dbrgg8g8jg+teQat4X1aNfCOsS2+vfY7fw/BZTpo7Bbq3mUAnKMMkHOCBzleegB634Y6Utlc63fJZ+IYReGAmbXGTzJiofkKBkYBGSevHoaO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%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
#### Loop mse computation over starting points #### Loop mse computation over starting points
Here, the data is converted to a format that speeds up the computations: coarse-grained time series of the current starting point from all trials are concatenated into one matrix (**y**). In addition, converting this matrix to type single ensures that it takes up as little memory as possible, to avoid problems with further computations. <br><br> Here, the data is converted to a format that speeds up the computations: coarse-grained time series of the current starting point from all trials are concatenated into one matrix (**y**). In addition, converting this matrix to type single ensures that it takes up as little memory as possible, to avoid problems with further computations. <br><br>
Now that the data matrix is aggregated over trials, time points that were separated in time become adjacent. To avoid counting patterns over the trial borders, a logical mask is created and the two last time points of each trial are masked with 0s. <br><br> Now that the data matrix is aggregated over trials, time points that were separated in time become adjacent. To avoid counting patterns over the trial borders, a logical mask is created and the two last time points of each trial are masked with 0s. <br><br>
Also, checks are implemented to make sure that the coarse-grained time series is long enough to make mse computation meaningful. <br><br> Also, checks are implemented to make sure that the coarse-grained time series is long enough to make mse computation meaningful. <br><br>
The rationale for this portion of the code can be found in *Grandy, T. H., Garrett, D. D., Schmiedek, F., & Werkle-Bergner, M. (2016). On the estimation of brain signal entropy from sparse neuroimaging data. Scientific Reports, http://doi.org/10.1038/srep23073* The rationale for this portion of the code can be found in *Grandy, T. H., Garrett, D. D., Schmiedek, F., & Werkle-Bergner, M. (2016). On the estimation of brain signal entropy from sparse neuroimaging data. Scientific Reports, http://doi.org/10.1038/srep23073*
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
% after coarsegraining, loop mse computation across starting points % after coarsegraining, loop mse computation across starting points
allcont = zeros(sc, nchan, m+1); % start_chan_m allcont = zeros(sc, nchan, m+1); % start_chan_m
for istart = 1:nloops for istart = 1:nloops
if max(cellfun(@(x) size(x,2), cg_data{istart})) == m % TODO check this at start if max(cellfun(@(x) size(x,2), cg_data{istart})) == m % TODO check this at start
fprintf('Coarse grained trials below %d + 1 samples, skipping remaining starting points\n', m) fprintf('Coarse grained trials below %d + 1 samples, skipping remaining starting points\n', m)
break break
end end
% concatenate trials and convert to single % concatenate trials and convert to single
y = single(cell2mat(cg_data{istart})); y = single(cell2mat(cg_data{istart}));
% collect trial bounds and create mask with valid time points for pats % collect trial bounds and create mask with valid time points for pats
trl_bounds = cumsum(cellfun(@(x) size(x,2), cg_data{istart}))'; trl_bounds = cumsum(cellfun(@(x) size(x,2), cg_data{istart}))';
trl_mask = true(size(y,2),1); trl_mask = true(size(y,2),1);
if allowgpu && gpuavailable if allowgpu && gpuavailable
trl_mask = gpuArray(trl_mask); trl_mask = gpuArray(trl_mask);
end end
trl_mask([trl_bounds-1; trl_bounds]) = false; trl_mask([trl_bounds-1; trl_bounds]) = false;
% return if n possible matches < 40 (Grandy) % return if n possible matches < 40 (Grandy)
npossiblepats = length(find(trl_mask)); % TODO check this at start npossiblepats = length(find(trl_mask)); % TODO check this at start
if npossiblepats < 40 if npossiblepats < 40
fprintf('N data points < 40, returning\n') fprintf('N data points < 40, returning\n')
return return
end end
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
If **normalized_r** was set to 1 (default), the similarity criterion (**r_new**) will be recomputed for each starting point. <br><br> If **normalized_r** was set to 1 (default), the similarity criterion (**r_new**) will be recomputed for each starting point. <br><br>
*Chunking* is applied to avoid memory problems when **ymat** is squared later on. Data for each starting point (**y**) is divided into chunks based on the maximum amount of memory assigned in the settings (in the variable called **mem_available**) and the number of time points in **y**. Note that more efficient memory usage is ensured by storing the elements of the time series as single. <br> *Chunking* is applied to avoid memory problems when **ymat** is squared later on. Data for each starting point (**y**) is divided into chunks based on the maximum amount of memory assigned in the settings (in the variable called **mem_available**) and the number of time points in **y**. Note that more efficient memory usage is ensured by storing the elements of the time series as single. <br>
Chunks are programmed to overlap, as they would otherwise create artificial borders in the data. Chunks are programmed to overlap, as they would otherwise create artificial borders in the data.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
% Calculate sample entropy of coarse grained time series % Calculate sample entropy of coarse grained time series
if normalized_r % calculate similarity criterion FOR EACH SCALE and sp SEPARATELY. if normalized_r % calculate similarity criterion FOR EACH SCALE and sp SEPARATELY.
r_new = r * std(y,1,2); r_new = r * std(y,1,2);
end end
% chunk y to keep memory usage in check % chunk y to keep memory usage in check
max_numel = mem_available/4; % single = 4 bytes max_numel = mem_available/4; % single = 4 bytes
chunk_size = round(max_numel/numel(y)); chunk_size = round(max_numel/numel(y));
n_chunks = ceil(size(y,2)/chunk_size); n_chunks = ceil(size(y,2)/chunk_size);
temp = 1; temp = 1;
chunk_borders = zeros(n_chunks,2); chunk_borders = zeros(n_chunks,2);
for ic = 1:n_chunks for ic = 1:n_chunks
chunk_borders(ic,:) = [temp temp+chunk_size]; chunk_borders(ic,:) = [temp temp+chunk_size];
temp = temp+chunk_size-1; % chunks need to overlap to avoid missing pats at chunk borders temp = temp+chunk_size-1; % chunks need to overlap to avoid missing pats at chunk borders
end end
chunk_borders(end) = size(y,2); chunk_borders(end) = size(y,2);
clear temp clear temp
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
Using 3D matrices allows to simultaneously determine patterns over all time points of a current chunk, all pattern points, and all channels, which speeds up computations. <br> Using 3D matrices allows to simultaneously determine patterns over all time points of a current chunk, all pattern points, and all channels, which speeds up computations. <br>
**ymat** determines the patterns by squaring the time point vector for each channel and taking the difference of all points, while also accounting for the similarity criterion. As the patterns are squared, the matrix is divided diagonally and only one half of it is taken as an end result. <br> **ymat** is a logical gpu array with dimensions *n elements in the current chunk* x *all sample points of the current starting point* x *n channels*. **ymat** determines the patterns by squaring the time point vector for each channel and taking the difference of all points, while also accounting for the similarity criterion. As the patterns are squared, the matrix is divided diagonally and only one half of it is taken as an end result. <br> **ymat** is a logical gpu array with dimensions *n elements in the current chunk* x *all sample points of the current starting point* x *n channels*.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
fprintf('starting point %d\n', istart) fprintf('starting point %d\n', istart)
cont = zeros(m+1, n_chunks, nchan); cont = zeros(m+1, n_chunks, nchan);
y_chunk1 = shiftdim(y', -1 ); % insert singleton dim y_chunk1 = shiftdim(y', -1 ); % insert singleton dim
r_new2 = shiftdim(r_new, -2); r_new2 = shiftdim(r_new, -2);
if allowgpu && gpuavailable if allowgpu && gpuavailable
cont = gpuArray(cont); cont = gpuArray(cont);
y_chunk1 = gpuArray(y_chunk1); y_chunk1 = gpuArray(y_chunk1);
r_new2 = gpuArray(r_new2); r_new2 = gpuArray(r_new2);
end end
fprintf('%d chunks: ', n_chunks) fprintf('%d chunks: ', n_chunks)
for ic = 1:n_chunks for ic = 1:n_chunks
fprintf('%d ', ic) fprintf('%d ', ic)
y_inds = transpose(chunk_borders(ic,1):chunk_borders(ic,2)); y_inds = transpose(chunk_borders(ic,1):chunk_borders(ic,2));
y_chunk2 = permute(y_chunk1(1,y_inds,:), [2 1 3]); % insert singleton dim y_chunk2 = permute(y_chunk1(1,y_inds,:), [2 1 3]); % insert singleton dim
if allowgpu && gpuavailable if allowgpu && gpuavailable
y_chunk2 = gpuArray(y_chunk2); y_chunk2 = gpuArray(y_chunk2);
end end
ymat = bsxfun(@le, abs(bsxfun(@minus, y_chunk1, y_chunk2 )), r_new2 ); ymat = bsxfun(@le, abs(bsxfun(@minus, y_chunk1, y_chunk2 )), r_new2 );
for ichan=1:nchan % loop since triu only supports 2D for ichan=1:nchan % loop since triu only supports 2D
ymat(:,:,ichan) = triu(ymat(:,:,ichan), chunk_borders(ic,1)); ymat(:,:,ichan) = triu(ymat(:,:,ichan), chunk_borders(ic,1));
end end
``` ```
%% Cell type:markdown id: tags: %% Cell type:markdown id: tags:
For starting point 1 of scale 2, **ymat** computations can be visualized as follows. Here, violet color stands for 0, yellow stands for 1. For starting point 1 of scale 2, **ymat** computations can be visualized as follows. Here, violet color stands for 0, yellow stands for 1.
%% Cell type:code id: tags: %% Cell type:code id: tags:
``` python ``` python
display(ymat_1_2) display(ymat_1_2)
``` ```
%%%% Output: display_data %%%% Output: display_data
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