What is the mathematics behind PCA?

Question

Accepted Answer

PCA is a mathematical technique used for dimensionality reduction by finding the principal components of a dataset.

PCA involves calculating the eigenvectors and eigenvalues of the covariance matrix of the data.
The eigenvectors represent the directions of maximum variance in the data, while the eigenvalues indicate the amount of variance along each eigenvector.
The principal components are the eigenvectors corresponding to the largest eigenvalues, which capture the most variance in the data.
PCA can be used for data visualization, noise reduction, and feature extraction.
Example: In a dataset with multiple features, PCA can help identify the most important features that explain the variance in the data.

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