Plot CDF or PDF to compare matrices

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Ricardo Duarte
Ricardo Duarte 2023-6-18
评论： Ricardo Duarte 2023-6-20
Hello everyone,
I'm looking for some recomendation regarding the best way to plot my data.
I have several a matricis (size 307 x 176) that I want to compare. They represent a heatmap of a specific species distribution.
The thing is: comparing all maps through a figure is difficult, not precise and consequently not recomended.
For this reason, I was thinking to use a cdf or a pdf functions to compare all of those matrices. The problem is I don't know how to use these functions in matrices.
Thank you in advance

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回答（2 个）

Gourab
Gourab 2023-6-19
Hi Ricardo,
I understand that you want to compare the heatmaps using cdf or pdf function.
The "histogram()" function in MATLAB is used to plot the PDF and "ecdf()" function in MATLAB is used to plot CDFs for each heatmap. The function computes the empirical cumulative distribution function (ECDF) for each heatmap.
You can refer to the below code snippet.
load heatmaps.mat;
% Plot PDFs for each heatmap
figure;
hold on;
colors = {'r', 'g', 'b', 'm', 'c'};
for i = 1:numel(heatmaps)
h = histogram(heatmaps{i}(:), 'Normalization', 'pdf', 'FaceColor', colors{i}, 'EdgeColor', 'none');
end
legend({'Heatmap 1', 'Heatmap 2', 'Heatmap 3', 'Heatmap 4', 'Heatmap 5'}, 'Location', 'northeast');
xlabel('Value');
ylabel('Probability Density');
title('Heatmap PDF Comparison');
figure;
hold on;
for i = 1:numel(heatmaps)
[f, x] = ecdf(heatmaps{i}(:));
plot(x, f, colors{i}, 'LineWidth', 2);
end
legend({'Heatmap 1', 'Heatmap 2', 'Heatmap 3', 'Heatmap 4', 'Heatmap 5'}, 'Location', 'southeast');
xlabel('Value');
ylabel('Cumulative Probability');
title('Heatmap CDF Comparison');
You can refer to the below documentation link for more information on "histogram()" and "ecdf()" function.
https://in.mathworks.com/help/matlab/ref/matlab.graphics.chart.primitive.histogram.html
https://in.mathworks.com/help/stats/ecdf.html
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Gourab
Gourab 2023-6-20
Hello Ricardo
Here heatmaps is used as a cell array.Can you add the following lines to make sure heatmaps is a cell array.
heatmaps_data = load('heatmaps.mat');
heatmaps = struct2cell(heatmaps_data);
Ricardo Duarte
Ricardo Duarte 2023-6-20
Hello @Gourab
Probably I was not precise in my explaination.
In reality I don't have a heatmap. What I have is a matrix that I used to create a kind of heatmap using the surf function. Let's say I have longitude, latitude and distribution and I used that to create a plot similar to a heatmap.
Maybe because of that the error remains.
Thank you.

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Sharad
Sharad 2023-6-19
Hi,
In order to compare the matrices with the help of CDF and PDF functions in MATLAB, you can follow these steps.
  • Install the Statistics and Machine Learning Toolbox from the MATLAB add on explorer. This toolbox is necessary for using these functions.
  • Calculate the CDF and PDF for each of the matrices, using cdf and pdf functions. Here is an example:
% Taking two example matrices
h1 = rand(307, 176);
h2 = rand(307,176);
% Reshape the matrix into a vector
vector1 = reshape(h1, [], 1);
vector2 = reshape(h2, [], 1);
% Calculate the cdf and pdf
cdf1 = cdf('norm', vector1, mean(vector1), std(vector1)); % Assuming a normal distribution
pdf1 = pdf('norm', vector1, mean(vector1), std(vector1));
cdf2 = cdf('norm', vector2, mean(vector2), std(vector2));
pdf2 = pdf('norm', vector2, mean(vector2), std(vector2));
  • Analyze the two distributions using tests like the Kolmogorov-Smirnov test and metrics like Kullback-Leibler (KL) divergence.
% Perform Kolmogorov-Smirnov test
[h, p] = kstest2(cdf1, cdf2);
if h
disp('The CDFs are significantly different.');
else
disp('The CDFs are not significantly different.');
end
% Calculate KL divergence
kl_divergence = sum(pdf1 .* log(pdf1 ./ pdf2));
disp(['KL Divergence: ', num2str(kl_divergence)]);

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