Two Efficient Algorithms for Approximately Orthogonal Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) with orthogonality constraints is quite important due to its close relation with the K-means clustering. While existing algorithms for orthogonal NMF impose strict orthogonality constraints, in this letter we propose a penalty method with the aim of performing approximately orthogonal NMF, together with two efficient algorithms respectively based on the Hierarchical Alternating Least Squares (HALS) and the Accelerated Proximate Gradient (APG) approaches. Experimental evidence was provided to show their high efficiency and flexibility by using synthetic and real-world data.

[1]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorization T , 2007 .

[2]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[3]  Andrzej Cichocki,et al.  Fast Nonnegative Matrix/Tensor Factorization Based on Low-Rank Approximation , 2012, IEEE Transactions on Signal Processing.

[4]  Chris H. Q. Ding,et al.  Orthogonal nonnegative matrix t-factorizations for clustering , 2006, KDD '06.

[5]  Zhaoshui He,et al.  Minimum-Volume-Constrained Nonnegative Matrix Factorization: Enhanced Ability of Learning Parts , 2011, IEEE Transactions on Neural Networks.

[6]  Sameer A. Nene,et al.  Columbia Object Image Library (COIL100) , 1996 .

[7]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorizations : An algorithmic perspective , 2014, IEEE Signal Processing Magazine.

[8]  Zhigang Luo,et al.  NeNMF: An Optimal Gradient Method for Nonnegative Matrix Factorization , 2012, IEEE Transactions on Signal Processing.

[9]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[10]  Seungjin Choi,et al.  Algorithms for orthogonal nonnegative matrix factorization , 2008, 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence).

[11]  Nicolas Gillis,et al.  Accelerated Multiplicative Updates and Hierarchical ALS Algorithms for Nonnegative Matrix Factorization , 2011, Neural Computation.

[12]  Nicolas Gillis,et al.  Two algorithms for orthogonal nonnegative matrix factorization with application to clustering , 2012, Neurocomputing.