principal component analysis in matlab

Principal Component Analysis (PCA) is a tool that is used to reduce the dimensionality of data while retaining as much of the information as possible. PCA is usually applied on a dataset containing features in a large number to extract a smaller number of useful features that capture most of the variance in the original dataset.

Here's how to perform PCA in MATLAB:

Assume you have a dataset 'X' of n observations on p variables, where each row contains an observation and each column contains a variable.

1. First, you need to standardize your data. This is done to ensure that each variable has the same weight. You can use MATLAB's zscore function to standardize your dataset.

main.m
X = zscore(dataset);
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2. Compute the covariance matrix of the standardized dataset.

main.m
covariance = cov(X);
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3. Use MATLAB's eig function to obtain the eigenvectors and eigenvalues of the covariance matrix.

main.m
[eigen_vectors,eigen_values] = eig(covariance);
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The eigenvectors are the principal components of the dataset, and the eigenvalues measure the amount of variance in the data explained by each principal component.

4. Order the eigenvectors in descending order of their corresponding eigenvalues.

main.m
[~, order] = sort(diag(eigen_values), 'descend');
eigen_vectors = eigen_vectors(:, order);
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5. Compute the principal components by projecting the standardized dataset onto the eigenvectors.

main.m
pc = X * eigen_vectors;
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Now 'pc' matrix contains the principal components.

That's it! You have successfully performed PCA on your dataset using MATLAB.