In the context of machine learning, how do eigenvalues and eigenvectors contribute to dimensionality reduction techniques such as Principal Component Analysis (PCA)?

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Seekh · Accepted Answer

In PCA, the data’s covariance matrix is computed and then broken into eigenvalues and eigenvectors. The eigenvectors give directions (principal components) that capture the most variation, while the eigenvalues tell how much variance each direction holds. By keeping only the eigenvectors with the largest eigenvalues, we keep the most important patterns and drop the rest, shrinking the data’s dimension. For example, if a 3‑dimensional dataset has eigenvalues 5, 1, and 0. 1, we might keep only the first two eigenvectors, reducing the data from three to two dimensions while preserving most of the information.

In the context of machine learning, how do eigenvalues and eigenvectors contribute to dimensionality reduction techniques such as Principal Component Analysis (PCA)?

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