calculate array element persistence algorithm

Question

I have a large array 15x15x2200. THis is merely a collection of 15x15 sparse matrices depicting the links between 15 nodes and how they vary over 2200 time units. I need to calculate for how much time does each link persist. By this I mean, suppose A[4,11] is 0 till time unit 5 and stays 1 till time unit 20 and then becomes 0 and again becomes 1 from 42 to 46, I would like to have an array of this information into an array which stores these lengths separately like LEN = {...15, 4, ....}

I am trying to do this in matlab and then generate a histogram. What is the best way to do this?

Answer 1

Let's try to do this without loops.

%# random adjacency matrix
array = randi([0 1], [15 15 2200]);

%# get the size of the array
[n1,n2,n3] = size(array);

%# reshape it so that it becomes n3 by n1*n2
array2d = reshape(array,[],n3)';

%# make sure that every run has a beginning and an end by padding 0's
array2d = [zeros(1,n1*n2);array2d;zeros(1,n1*n2)];

%# take the difference. +1 indicates a start, -1 indicates an end
arrayDiff = diff(array2d,1,1);
[startIdx,startCol] = find(arrayDiff==1);
[endIdx,endCol] = find(arrayDiff==-1);

%# since every sequence has a start and an end, and since find searches down the columns
%# every start is matched with the corresponding end. Simply take the difference
persistence = endIdx-startIdx; %# you may have to add 1, if 42 to 46 is 5, not 4

%# plot a histogram - make sure you play with the number of bins a bit
nBins = 20;
figure,hist(persistence,nBins)

Edit:

To see another visual representation of the persistence of your tracks, call

figure,imshow(array2d)

This shows white stripes wherever you have a sequence of links, and it will show you overall patterns.