Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion
Abstract
Matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rows to be updated, that is, we assume that samples are dependent on each other. We derive the updating rules for ICGNMF by considering the correlation. We also present tests on widely used image datasets, and show ICGNMF reduces the error by comparing other methods.
 Authors:

 North China Electric Power Univ., Beijing (China). School of Control and Computer Engineering; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
 North China Electric Power Univ., Beijing (China). Dept. of Mathematics and Physics
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
 Publication Date:
 Research Org.:
 Lawrence Berkeley National LaboratoryNational Energy Research Scientific Computing Center (NERSC)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1526987
 Resource Type:
 Journal Article
 Journal Name:
 International Journal of Machine Learning and Cybernetics
 Additional Journal Information:
 Journal Volume: 10; Journal Issue: 6; Journal ID: ISSN 18688071
 Country of Publication:
 United States
 Language:
 English
Citation Formats
Zhang, Xiaoxia, Chen, Degang, and Wu, Kesheng. Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion. United States: N. p., 2018.
Web. doi:10.1007/s1304201808087.
Zhang, Xiaoxia, Chen, Degang, & Wu, Kesheng. Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion. United States. doi:10.1007/s1304201808087.
Zhang, Xiaoxia, Chen, Degang, and Wu, Kesheng. Thu .
"Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion". United States. doi:10.1007/s1304201808087.
@article{osti_1526987,
title = {Incremental nonnegative matrix factorization based on correlation and graph regularization for matrix completion},
author = {Zhang, Xiaoxia and Chen, Degang and Wu, Kesheng},
abstractNote = {Matrix factorization is widely used in recommendation systems, text mining, face recognition and computer vision. As one of the most popular methods, nonnegative matrix factorization and its incremental variants have attracted much attention. The existing incremental algorithms are established based on the assumption of samples are independent and only update the new latent variable of weighting coefficient matrix when the new sample comes, which may lead to inferior solutions. To address this issue, we investigate a novel incremental nonnegative matrix factorization algorithm based on correlation and graph regularizer (ICGNMF). The correlation is mainly used for finding out those correlated rows to be updated, that is, we assume that samples are dependent on each other. We derive the updating rules for ICGNMF by considering the correlation. We also present tests on widely used image datasets, and show ICGNMF reduces the error by comparing other methods.},
doi = {10.1007/s1304201808087},
journal = {International Journal of Machine Learning and Cybernetics},
issn = {18688071},
number = 6,
volume = 10,
place = {United States},
year = {2018},
month = {3}
}
Works referenced in this record:
A non negative matrix factorization for collaborative filtering recommender systems based on a Bayesian probabilistic model
journal, April 2016
 Hernando, Antonio; Bobadilla, Jesús; Ortega, Fernando
 KnowledgeBased Systems, Vol. 97
Learning the parts of objects by nonnegative matrix factorization
journal, October 1999
 Lee, Daniel D.; Seung, H. Sebastian
 Nature, Vol. 401, Issue 6755
Positive matrix factorization: A nonnegative factor model with optimal utilization of error estimates of data values
journal, June 1994
 Paatero, Pentti; Tapper, Unto
 Environmetrics, Vol. 5, Issue 2
Inferential, robust nonnegative matrix factorization analysis of microarray data
journal, November 2006
 Fogel, P.; Young, S. S.; Hawkins, D. M.
 Bioinformatics, Vol. 23, Issue 1
Graph Regularized Nonnegative Matrix Factorization for Data Representation
journal, August 2011
 Deng Cai,
 IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 33, Issue 8
Convex and SemiNonnegative Matrix Factorizations
journal, January 2010
 Ding, C. H. Q.; Jordan, M. I.
 IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 32, Issue 1
Online Nonnegative Matrix Factorization With Robust Stochastic Approximation
journal, July 2012
 Naiyang Guan,
 IEEE Transactions on Neural Networks and Learning Systems, Vol. 23, Issue 7
An Efficient NonNegative MatrixFactorizationBased Approach to Collaborative Filtering for Recommender Systems
journal, May 2014
 Xin Luo,
 IEEE Transactions on Industrial Informatics, Vol. 10, Issue 2
Predicting Quality of Service for Selection by NeighborhoodBased Collaborative Filtering
journal, March 2013
 Wu, Jian; Chen, Liang; Feng, Yipeng
 IEEE Transactions on Systems, Man, and Cybernetics: Systems, Vol. 43, Issue 2
Incremental subspace learning via nonnegative matrix factorization
journal, May 2009
 Bucak, Serhat S.; Gunsel, Bilge
 Pattern Recognition, Vol. 42, Issue 5
Online Blind Source Separation Using Incremental Nonnegative Matrix Factorization With Volume Constraint
journal, April 2011
 Guoxu Zhou,
 IEEE Transactions on Neural Networks, Vol. 22, Issue 4
A Global Geometric Framework for Nonlinear Dimensionality Reduction
journal, December 2000
 Tenenbaum, J. B.
 Science, Vol. 290, Issue 5500
Nonlinear Dimensionality Reduction by Locally Linear Embedding
journal, December 2000
 Roweis, S. T.
 Science, Vol. 290, Issue 5500