In this letter, we propose a new identification criterion that guarantees the recovery of the low-rank latent factors in the nonnegative matrix factorization (NMF) generative model, under mild conditions. Specifically, using the proposed criterion, it suffices to identify the latent factors if the rows of one factor are sufficiently scattered over the nonnegative orthant, while no structural assumption is imposed on the other factor except being full-rank. This is by far the mildest condition under which the latent factors are provably identifiable from the NMF model.
Bibliographical noteFunding Information:
Manuscript received December 4, 2017; accepted December 30, 2017. Date of publication January 11, 2018; date of current version February 1, 2018. This work is supported in part by National Science Foundation under Projects NSF ECCS-1608961 and NSF IIS-1447788. X. Fu and K. Huang contributed equally to this work. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yong Xiang. (Corresponding author: Xiao Fu.) X. Fu is with the School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR 97330 (e-mail: firstname.lastname@example.org).
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- Convex analysis
- Nonnegative matrix factorization (NMF)
- Sufficiently scattered