First Order Methods for Robust Non-negative Matrix Factorization for Large Scale Noisy Data
This work addresses scalability and noise issues in NMF for applications like data analysis, but it is incremental as it builds on existing LP-based approaches.
The paper tackles robust non-negative matrix factorization for large-scale noisy data by using first-order methods to reduce computational complexity, showing performance on real and synthetic datasets.
Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or rows) [1]. In real applications, however, such separability assumption is hard to satisfy. Following [4] and [5], in this paper, we look at the Linear Programming (LP) based reformulation to locate the extreme rays of the convex cone but in a noisy setting. Furthermore, in order to deal with the large scale data, we employ First-Order Methods (FOM) to mitigate the computational complexity of LP, which primarily results from a large number of constraints. We show the performance of the algorithm on real and synthetic data sets.