Truncated SVD

Singular Value Decomposition (SVD) is a matrix factorization technique closely related to PCA that decomposes a data matrix into three matrices (U, Σ, and V), enabling data reduction by identifying the most important dimensions. Truncated SVD simplifies this by keeping only the top singular values in Σ and discarding the rest, allowing reconstruction of the original data with minimal information loss while significantly reducing computational complexity. This technique is demonstrated through image compression, where retaining only the largest singular values can effectively reconstruct an image while zeroing out less important coefficients.