Loop over a time window (10 sec.) in a time series to calculate indices of synchronization. Help needed. See comments for details as well.

Dear all,

in my time series of tow people walking side by side I calculate a synchronization index over the whole time series. Now I would like to calculate the index over time (time window 10 seconds). Here is my code so far:

%% compute GSI to quantify gait snychronization according to Tass et al. (1998) 

bin_size = 100; % NOTE: bin size effects GSI; 

%% condition together 

for i = 1:numel(data_trimmed_al)
    phi12 = data_trimmed_al(i).phase_angle_difference; % phase difference over time
    
 % bring phase difference into interval of [-pi, pi]
    phi12(phi12 < -pi) = phi12(phi12 < -pi) + 2*pi;
    phi12(phi12 > pi) = phi12(phi12 > pi) - 2*pi;
    
    % categorize phase angle difference into bin_size equally distanced bins
    bin_edges = linspace(-pi,pi,bin_size); % create equally distanced bins
    Y = histcounts(phi12,bin_edges); % count number of data in each bin
    p = Y/sum(Y); % normalize bin counts to get probability for each phi12 to be in bin x
    
    % Shannon entropy calculation (rho).
    
    S_max = log(bin_size);
    S = - sum(p.*log(p));
    rho = (S_max - S)/S_max;
    data_trimmed_al(i).GSI_together = rho; % indices of all participants as a mean score of complete time series. I put it in a structure. 
    
end

for synchronization over time:

% compute GSI over time for pair#1


synchTS_GSI = zeros (1, pnts); % time series of synchronization time points
pair_1_GSI = data_trimmed_al(1).phase_angle_difference; % use phase angle difference of pair#1
timevec_1 = (0:pnts-1/srate);
tidx = 1:2860; % time window
 
if pair_1_GSI

    for ti = 1:pnts

            phi12 = pair_1_GSI; 
            phi12(phi12 < -pi) = phi12(phi12 < -pi) + 2*pi;
            phi12(phi12 > pi) = phi12(phi12 > pi) - 2*pi;
    
            bin_edges = linspace(-pi,pi,bin_size); 
            Y = histcounts(phi12,bin_edges);
            p = Y/sum(Y); 

            S_max = log(bin_size);
            S = - sum(p.*log(p));
            synchTS_GSI(ti) = (S_max-S)/S_max(tidx); Time % this part is cricial and I don't get iz how to loop over time window tidx!
      
    end
end 

Help is welcome and appreciated.

Jonas

[Jon]

Since I am not familiar with gait analysis I can't easily understand from you question and the code you posted what exactly it is that you are trying to accomplish, and what it is that you don't know how to do. For me it would be helpful if you could just make a very simple example that captures the essence of what you are trying to accomplish, and state your question in the context of this simple example.

[Jonas Bender]

Dear Jon,

thanks for your response. The code calculate an syncrhonization index (do participants show a synch walk?) The index ranged from 0 to 1 (0 = no synchronization; 1 = perfect synchronization). The first part of code will calculate this index for the entire time window (7 minutes).

Now, I would like to calculate the synchronization index over time to show how the index varies over time to plot it in a graph. So for each time point (ti = 1:pnts) I would like to calcuate the index using a time window of 10 seconds (tidx).

Does this make sense?

Jonas

[Jon]

Sorry, I still don't really get what you are trying to do. Could you provide a simple standalone, runnable example, that sets the problem up, and explain the problem you are trying to solve in terms of this simple example.

[Jonas Bender]

Dear Jon,

here is an example. I attached the data for pair_1. This example is coded for an other indice. In this example I calculate 'synchronization over time' using ti and tidx. However, I don't get it how to calculate synchronization over time for the GSI as I posted above.

winsize = 2860; % 10 seconds
synchTS = zeros (1, pnts); % time series of synchronization time points

Unrecognized function or variable 'pnts'.

pair_1 = data_trimmed_al(1).euler_phase_angle_difference;
timevec_1 = (0:pnts-1/srate);

% loop over time points

for ti = 1:pnts

    tidx = max(1, ti - winsize) : min (pnts, ti + winsize); % time index 1:2860
    synchTS(ti) = abs (mean(pair_1(tidx)));
end

If you want to plot the data:

figure (30), clf
plot (timevec_1, synchTS, 'k', 'LineWidth',2)
set (gca, 'ylim', [0 1] )
set (gca, 'xlim', [0 120000])
xlabel ('Time')
ylabel ('Synchronization')
title ('Synchronization Over Time')

Does it help?

Regards and thank you for your time.

Jonas

[Jon]

I'm still not understanding at all (sorry, we just seem to have a communciation gap). As a start however, please modify your example so that it will run without errors.

To start with:

The variable pnts must be assigned.

While you provide a file with values for the variable pair_1, you immediately reassign pair_1 to the variable, data_trimmed_al(1).euler_phase_angle_difference. There is no point in providing the values if you just reassign them. Also the variable, data_trimmed_al(1).euler_phase_angle_difference, is not defined, so this assignment will throw an error.

[Jonas Bender]

Dear Jon,

sorry. Try this please:

%% compute ISPC over time for pair#1 (ISPC for each timepoint)


% load the data using your directionary of attachted file

load ("pair1_example.mat");  

% define some variables

pnts = 120120;
srate = 286;
winsize = 2860; % 10 seconds
synchTS = zeros (1, pnts); % time series of synchronization time points
timevec_1 = (0:pnts-1/srate);


% loop over time points

for ti = 1:pnts

    tidx = max(1,ti-winsize) : min(pnts, ti+winsize); 
    synchTS(ti) = abs (mean(pair_1(tidx)));
end

Now plot the data

figure (30), clf
plot (timevec_1, synchTS, 'k', 'LineWidth',2)
set (gca, 'ylim', [0 1] )
set (gca, 'xlim', [0 120000])
xlabel ('Time')
ylabel ('Synchronization')
title ('Synchronization Over Time')

Does it work now?

[Jon]

Thanks, yes, now the example code runs, and I get a plot of Synchronization Over Time.

So now, in terms of your example code, what is it that you want to do that you don't know how to do?

[Jonas Bender]

Hi Jon,

I don't know how to loop over time index tidx to get a plot 'synchronization over time' for the initial code I posted. This is an other index and I want to compare both indices.

The initial code will result in a ti = 1:pnts indices with the same score. This score is the mean score for the entire time window.

However, the code has to result in different scores. It ignores tidx. So I can't plot the synchronization over time.

There must be score like that (for the example that works).

Is it now clear.

Regards, Jonas

[Jon]

No sorry it is not clear.

The problem is that the original code you show is part of a very complex program with many variables and functions that I have no idea about what they are or what they do. So I can't really understand in terms of that code what you are trying to accomplish and why you can't. I was hoping you could provide a simple, runnable example which captures the essence of what it is you are trying to do, and where your problem with accomplishing this is.

It is good that you provided an example, but unfortunately it is an example of something that you know how to do without problems. What I need is a simple example showing what you are actually trying to do, and pointing out exactly where you are stuck and what it is that you don't know how to do.

Maybe someone else can understand from your description, what it is you are trying to do, and provide help for you. Otherwise, unless you can provide a better example of what you are trying to do, and where you are stuck I guess we should give up, so you don't just get frustrated with my lack of understanding.

[Jonas Bender]

Dear Jon,

thanks for your mission!

Jonas