Image processing using Newton-based algorithm of nonnegative matrix factorization

In this paper, we propose a Newton-based algorithm for nonnegative matrix factorization in image processing. We employ the new algorithm to three real-world databases. Extensive numerical results show the feasibility and validity of the proposed algorithm.

[1]  Lin Dai,et al.  On Hermitian and skew-Hermitian splitting iteration methods for the linear matrix equation AXB=C , 2013, Comput. Math. Appl..

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

[3]  P. Smaragdis,et al.  Non-negative matrix factorization for polyphonic music transcription , 2003, 2003 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (IEEE Cat. No.03TH8684).

[4]  Zhong-Yun Liu,et al.  An alternating projected gradient algorithm for nonnegative matrix factorization , 2011, Appl. Math. Comput..

[5]  Chih-Jen Lin,et al.  Newton's Method for Large Bound-Constrained Optimization Problems , 1999, SIAM J. Optim..

[6]  Michael W. Berry,et al.  Document clustering using nonnegative matrix factorization , 2006, Inf. Process. Manag..

[7]  Michael W. Berry,et al.  Algorithms and applications for approximate nonnegative matrix factorization , 2007, Comput. Stat. Data Anal..

[8]  P. Paatero,et al.  Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values† , 1994 .

[9]  V. P. Pauca,et al.  Nonnegative matrix factorization for spectral data analysis , 2006 .

[10]  I. Dhillon,et al.  Fast Projection-Based Methods for the Least Squares Nonnegative Matrix Approximation Problem , 2008 .

[11]  Changshui Zhang,et al.  Efficient Nonnegative Matrix Factorization via projected Newton method , 2012, Pattern Recognit..

[12]  Xiang Wang,et al.  On positive-definite and skew-Hermitian splitting iteration methods for continuous Sylvester equation AX-XB=C , 2013, Comput. Math. Appl..

[13]  Daniel D. Lee,et al.  Statistical signal processing with nonnegativity constraints , 2003, INTERSPEECH.

[14]  Gene H. Golub,et al.  Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems , 2002, SIAM J. Matrix Anal. Appl..

[15]  Gene H. Golub,et al.  Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems , 2005, SIAM J. Sci. Comput..

[16]  Lu Lin.  Alternative gradient algorithms with applications to nonnegative matrix factorizations , 2010, Appl. Math. Comput..

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

[18]  Michael W. Berry,et al.  Text Mining Using Non-Negative Matrix Factorizations , 2004, SDM.

[19]  Lawrence K. Saul,et al.  Real-Time Pitch Determination of One or More Voices by Nonnegative Matrix Factorization , 2004, NIPS.