SVDBasis
SVDBasis refers to a basis for a data space formed from the singular vectors obtained via the singular value decomposition of a matrix. Given a real or complex matrix A of size m-by-n, the SVD expresses A = U Σ V^*, where U is m-by-r with left singular vectors, Σ is an m-by-n diagonal-like matrix of nonzero singular values, and V is n-by-r with right singular vectors, with r equal to the rank of A. The columns of U and V form orthonormal bases for the column space and row space of A, respectively. The singular values indicate the importance of each corresponding basis vector in representing A.
In practice, SVDBasis is often truncated: selecting the top k singular vectors yields a reduced basis that
Limitations include sensitivity to scaling, the computational cost of full or partial SVD, and linearity constraints.