Matrix Co-Factorization on Compressed Sensing
Jiho Yoo and Seungjin Choi
In this paper we address the problem of performing matrix factorizations (MFs) on compressively sampled measurements which are obtained by random projections. While this approach improves the scalability of matrix factorizations, its performance is not satisfactory. We present a method for matrix co-factorization (MCF) where compressed measurements and a small number of uncompressed measurements are jointly decomposed, sharing a factor matrix. We evaluate the performance of three matrix factorizations in terms of Cram{\'e}r-Rao bounds, including: (1) MF on uncompressed data; (2) MF on compressed data (CS-MF); (3) MCF on compressed and uncompressed data (CS-MCF). Numerical experiments demonstrate that CS-MCF improves the performance of CS-MF since side information (a small number of uncompressed measurements) is exploited.