Orthogonal incremental non-negative matrix factorization algorithm and its application in image classification

To improve the sparseness of the base matrix in incremental non-negative matrix factorization, we in this paper present a new method, orthogonal incremental non-negative matrix factorization algorithm (OINMF), which combines the orthogonality constraint with incremental learning. OINMF adopts batch update in the process of incremental learning, and its iterative formulae are obtained using the gradient on the Stiefel manifold. The experiments on image classification show that the proposed method achieves much better sparseness and orthogonality, while retaining time efficiency of incremental learning.

[1]  Seungjin Choi,et al.  Orthogonal Nonnegative Matrix Factorization: Multiplicative Updates on Stiefel Manifolds , 2008, IDEAL.

[2]  Jorma Laaksonen,et al.  Projective Non-Negative Matrix Factorization with Applications to Facial Image Processing , 2007, Int. J. Pattern Recognit. Artif. Intell..

[3]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[4]  Yu-Jin Zhang,et al.  Linear Projection-based Non-negative Matrix Factorization: Linear Projection-based Non-negative Matrix Factorization , 2010 .

[5]  Thomas S. Huang,et al.  Graph Regularized Nonnegative Matrix Factorization for Data Representation. , 2011, IEEE transactions on pattern analysis and machine intelligence.

[6]  Huchuan Lu,et al.  On-line learning parts-based representation via incremental orthogonal projective non-negative matrix factorization , 2013, Signal Process..

[7]  Andrzej Cichocki,et al.  New Algorithms for Non-Negative Matrix Factorization in Applications to Blind Source Separation , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[8]  E. Stiefel.  Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten , 1935 .

[9]  Jordi Vitrià,et al.  Non-negative Matrix Factorization for Face Recognition , 2002, CCIA.

[10]  H. Sebastian Seung,et al.  Learning the parts of objects by non-negative matrix factorization , 1999, Nature.

[11]  Erkki Oja,et al.  Projective Nonnegative Matrix Factorization for Image Compression and Feature Extraction , 2005, SCIA.

[12]  Patrik O. Hoyer,et al.  Non-negative Matrix Factorization with Sparseness Constraints , 2004, J. Mach. Learn. Res..

[13]  Pushpinder Singh,et al.  A Recent Development of Numerical Methods for Solving Convection-Diffusion Problems , 2012 .

[14]  Zhezhou Yu,et al.  Incremental Graph Regulated Nonnegative Matrix Factorization for Face Recognition , 2014, J. Appl. Math..

[15]  Jianyu Yang,et al.  Target recognition in synthetic aperture radar images via non-negative matrix factorisation , 2015 .

[16]  Paris Smaragdis,et al.  Optimal cost function and magnitude power for NMF-based speech separation and music interpolation , 2012, 2012 IEEE International Workshop on Machine Learning for Signal Processing.

[17]  Serhat Selcuk Bucak,et al.  Incremental subspace learning via non-negative matrix factorization , 2009, Pattern Recognit..

[18]  Horst Bischof,et al.  Person Re-identification by Descriptive and Discriminative Classification , 2011, SCIA.

[19]  Xuelong Li,et al.  Constrained Nonnegative Matrix Factorization for Image Representation , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[20]  Huchuan Lu,et al.  Incremental orthogonal projective non-negative matrix factorization and its applications , 2011, 2011 18th IEEE International Conference on Image Processing.

[21]  Jie Yang,et al.  Incremental Robust Nonnegative Matrix Factorization for Object Tracking , 2016, ICONIP.