Singular Value Decomposition (SVD) is a factorization technique that decomposes a matrix into three matrices:
A = U Σ V^T
Where:
– A is the original matrix
– U is an orthogonal matrix (left-singular vectors)
– Σ is a diagonal matrix (singular values)
– V is an orthogonal matrix (right-singular vectors)
SVD is used in various applications, including:
– Dimensionality reduction
– Image compression
– Latent semantic analysis
– Data imputation
– Feature extraction
SVD helps to identify patterns, reduce noise, and improve data visualization