Computing symmetric nonnegative rank factorizations
An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank. The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm2) operations in the dense case. The algorithm is based on geometric considerations and is easy to implement. The implications for matrix graphs are also discussed.
Keywords: nonnegativerankfactorization ; nonnegativematrixfactorization ; symmetric ; rotation ; isometry ; principal submatrix ; pivoted Cholesky factorization ; symmetric positive semidefinite ; arrowhead matrix ; extreme ray ; maximum independent set ; rank reduction
Record created on 2014-05-14, modified on 2016-08-09