SVD Overview
SVD factors a matrix into three components.
Matrix Factorization
A = UΣV^T. U: left singular vectors. Σ: singular values (diagonal). V: right singular vectors.
Truncated SVD keeps top k components. This is PCA when A is centered.
Applications
Recommender systems: matrix factorization for user-item. Image compression: keep top k components.
Text: latent semantic analysis uses SVD on term-document matrix.
Relationship to PCA
SVD on centered data gives same result as PCA. Different computation, same result.
Key Takeaways
- SVD factors matrix into three components
- Truncated SVD approximates original
- Foundation for many ML methods