How to Apply Random Projections to Nonnegative Matrix Factorization with Missing Entries?

Farouk Yahaya (1) , Matthieu Puigt (1) , Gilles Delmaire (1) , Gilles Roussel (1)

1 LISIC - Laboratoire d'Informatique Signal et Image de la Côte d'Opale

Random projections belong to the major techniques to process big data and have been successfully applied to Nonnegative Matrix Factorization (NMF). However, they cannot be applied in the case of missing entries in the matrix to factorize, which occurs in many actual problems with large data matrices. In this paper, we thus aim to solve this issue and we propose a novel framework to apply random projections in weighted NMF, where the weight models the confidence in the data (or the absence of confidence in the case of missing data). We experimentally show the proposed framework to significantly speed-up state-of-the-art NMF methods under some mild conditions. In particular, the proposed strategy is particularly efficient when combined with Nesterov gradient or alternating least squares.

Mots clés: big data; low-rank matrix completion; random projections; missing data; Nonnegative matrix factorization; Index Terms-Nonnegative matrix factorization; blind source separation

Domaines: Traitement du signal et de l'image [eess.SP]

Farouk Yahaya, Matthieu Puigt, Gilles Delmaire, Gilles Roussel. How to Apply Random Projections to Nonnegative Matrix Factorization with Missing Entries?. 27th European Signal Processing Conference, Sep 2019, A Coruña, Spain. pp.1-5, ⟨10.23919/EUSIPCO.2019.8903036⟩. ⟨hal-02151521⟩