Principal component analysis

Mathematical Foundation in Linear Algebra

Principal Component Analysis is fundamentally based on key linear algebra concepts:

1. Eigendecomposition of covariance/correlation matrices
2. Orthogonal transformations to a new coordinate system
3. Variance maximization along principal directions

The operation can be viewed as finding the eigenvectors of the covariance matrix, which represent the directions of maximum variance in the data.

See

• Statistical Learning

• Singular Value Decomposition

• Linear Discriminant Analysis

• Advanced Topics (in Linear Algebra)

• Non-negative Matrix Factorization