How to interpret an answer given by PCA

Hello,

I have matrix consisted of 30 variables(columns) and 14 observation(rows). Many of these variables are basically measuring similar activities. Thus I decided to use PCA to decrease the dimensionality.

There are two major problem:

1- These variables have different unites some are time values and some are number of repetitions. can I use the row data for PCA, or do I need to normalize them beforehand? In the latter case, what would be the best way of normalization?

2- If I decided to take the first two pca components how could I find out which variables are explained by which component? You can find it out by SPSS, but I would not know how to do it by MATLAB.

your helps would be highly appreciated,

cheers

Yoolla

Answer 1

[Aditya]

Hi Yoolla,

When performing PCA, especially with variables measured in different units, it's crucial to ensure that the data is properly prepared. Here's how you can address the issues you've mentioned:

1. Normalization
2. Interpreting PCA Components

% Assume your data matrix is named 'dataMatrix' with size 14x30
normalizedData = zscore(dataMatrix);
% Min-Max Scaling
minVals = min(dataMatrix);
maxVals = max(dataMatrix);
scaledData = (dataMatrix - minVals) ./ (maxVals - minVals);
% Perform PCA on the normalized data
[coeff, score, latent, tsquared, explained] = pca(normalizedData);
% Display the coefficients for the first two principal components
disp('Coefficients for the first two principal components:');
disp(coeff(:, 1:2));

% You can also visualize the loadings
figure;
biplot(coeff(:, 1:2), 'Scores', score(:, 1:2), 'VarLabels', arrayfun(@(x) sprintf('Var%d', x), 1:size(dataMatrix, 2), 'UniformOutput', false));
title('Biplot of First Two Principal Components');
xlabel('Principal Component 1');
ylabel('Principal Component 2');