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Orthogonal Non-negative Matrix Factorization From ONMF to NN-PCA

Losseau, Bruno
(2019)

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Details

Supervisors
Absil, Pierre-Antoine ; Gillis, Nicolas
Faculty
Ecole polytechnique de Louvain
Degree label
Master [120] : ingénieur civil en mathématiques appliquées
Abstract
Low Rank Matrix Approximation (LRMA) is a well studied problem in the context of Matrix Factorisation (MF). Adding Constraints (CLRMA) makes it possible to extract information from large datasets. We investigate how the combination of the non-negative and orthogonality constraints, the Orthogonal Non-negative Matrix Factorisation ONMF, affects the modelling of the problem, and the link it has with other constraint MF. We show in what way it relates to the NN-PCA model. Based on Pompili's work we focus on the hard-enforcement of the orthogonality to develop algorithms, taking advantage of the problem's geometry to solve it on the Stiefel manifold using a quadratic penalty method. We present the RQNN-PCA algorithm.