We describe Nonnegative Double Singular Value Decomposition (NNDSVD), a new method designed to enhance the initialization stage of nonnegative matrix factorization (NMF). NNDSVD can readily be combined with existing NMF algorithms. The basic algorithm contains no randomization and is based on two SVD processes, one approximating the data matrix, the other approximating positive sections of the resulting partial SVD factors utilizing an algebraic property of unit rank matrices. Simple practical variants for NMF with dense factors are described. NNDSVD is also well suited to initialize NMF algorithms with sparse factors. Many numerical examples suggest that NNDSVD leads to rapid reduction of the approximation error of many NMF algorithms.
Moreover, for a general positive integer K, it is shown in REF that nonnegative double singular value decomposition (nndsvd), a deterministic SVDbased approach, can be used to enhance the initialization of NMF, leading to a faster reduction of the approximation error of many NMF algorithms.
SVD based initialization: A head start for nonnegative matrix factorization
PATTERN RECOGNITION
Computer Science Mathematics