PCA

08/06/2025

How to calculate PCA

Given a data matrix $𝒳\in {ℝ}^{n\times d}$ with $n$ samples and d features:

• Center the data (subtract the mean of the each column).
• Compute the covariance matrix:

• Compute the eigenvectors and eigenvalues of the covariance matrix
• Sort the eigenvectors by decreasing eigenvalues
• Select the top $k$ eigenvectors -- these are your principal components.
• Project the original data onto these vectors:

, where $W$ is a matrix whose columns are the selected eigenvectors.

Pros & Cons

Cons: Assumes linear relationship

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