Linear Projection-based Non-negative Matrix Factorization
Yu Zhang · Acta Automatica Sinica · 2010
Non-negative matrix factorization(NMF) is a newly popular method for non-negative dimensionality reduction, feature extraction, data mining, etc.The mathematical model in NMF definition is based on nonlinear projection, therefore dimension reduction by NMF is implemented by iterative updates which lead to high computational load.Additionally, NMF features extracted by this model are usually not very sparse, and this fails to meet the expectation of designing NMF.To simultaneously resolve the above two problems, this paper proposes a new model, linear projectionbased NMF(LPBNMF), and designs an monotonic algorithm for it.From mathematical point of view, LPBNMF is a special mode for implementing NMF, which linearly implements dimension reduction.The high sparseness of LPBNMF features is assured by the inherent characteristics of its mathematic model.The comparison experiments validate that dimension reduction by LPBNMF is much more efficient than that by NMF, and that LPBNMF features are much more sparse and localized than NMF ones.Finally, experiments based on AR face database indicate that LPBNMF features are more suitable for nearest neighbor classification-based occluded face recognition than NMF, LDA, and PCA ones.