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Calculate the entropy of a list of 2D points in Matlab

I have a list of points in an array like this 

points = [[1,2];[2,5];[7,1]...[x,y]]

The x is between 0 and 1020 and y is between 0 and 1920.

How can I calculate the entropy of the points array in Matlab?

Many thanks!

Solution

  • I assume you want to consider each [x,y] point as one data point. Let us define some exemplary data:

    A = [[1,2];[2,5];[7,1];[1,2]];

    First we give equal points equal identifiers, we can do this using

    [~,~,ic] = unique(A, 'rows');

    Then we compute the frequency and with that the probability of each identifier:

    [frequency, ~] = histcounts(ic,max(ic));
probability = frequency/sum(frequency);

    With this we can immediately compute the entropy:

    entropy = -sum(probability .* log(probability))

    (Make sure you use the right logarithm, different fields conventionally use different bases.)