Sparse General Non-Negative Matrix Factorization Based on Left Semi-Tensor Product

The dimension reduction of large scale high-dimensional data is a challenging task, especially the dimension reduction of face data and the accuracy increment of face recognition in the large scale face recognition system, which may cause large storage space and long recognition time. In order to further reduce the recognition time and the storage space in the large scale face recognition systems, on the basis of the general non-negative matrix factorization based on left semi-tensor (GNMFL) without dimension matching constraints proposed in our previous work, we propose a sparse GNMFL/L (SGNMFL/L) to decompose a large number of face data sets in the large scale face recognition systems, which makes the decomposed base matrix sparser and suppresses the decomposed coefficient matrix. Therefore, the dimension of the basis matrix and the coefficient matrix can be further reduced. Two sets of experiments are conducted to show the effectiveness of the proposed SGNMFL/L on two databases. The experiments are mainly designed to verify the effects of two hyper-parameters on the sparseness of basis matrix factorized by SGNMFL/L, compare the performance of the conventional NMF, sparse NMF (SNMF), GNMFL, and the proposed SGNMFL/L in terms of storage space and time efficiency, and compare their face recognition accuracies with different noises. Both the theoretical derivation and the experimental results show that the proposed SGNMF/L can effectively save the storage space and reduce the computation time while achieving high recognition accuracy and has strong robustness.

[1]  Bhavin J. Shastri,et al.  Face recognition using localized features based on non-negative sparse coding , 2007, Machine Vision and Applications.

[2]  MengChu Zhou,et al.  Generating Highly Accurate Predictions for Missing QoS Data via Aggregating Nonnegative Latent Factor Models , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[3]  Qiang Zhang,et al.  Fisher’s linear discriminant (FLD) and support vector machine (SVM) in non-negative matrix factorization (NMF) residual space for face recognition , 2010 .

[4]  Jiang-She Zhang,et al.  Learning latent features by nonnegative matrix factorization combining similarity judgments , 2015, Neurocomputing.

[5]  Sheng Tang,et al.  Sparse Ensemble Learning for Concept Detection , 2012, IEEE Transactions on Multimedia.

[6]  Bin Fang,et al.  Incremental Nonnegative Matrix Factorization for Face Recognition , 2008 .

[7]  MengChu Zhou,et al.  Temporal Pattern-Aware QoS Prediction via Biased Non-Negative Latent Factorization of Tensors , 2020, IEEE Transactions on Cybernetics.

[8]  MengChu Zhou,et al.  A Nonnegative Latent Factor Model for Large-Scale Sparse Matrices in Recommender Systems via Alternating Direction Method , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Ji-Xiang Du,et al.  Face Aging Simulation Based on NMF Algorithm with Sparseness Constraints , 2011, ICIC.

[10]  Jia Chen,et al.  Randomized latent factor model for high-dimensional and sparse matrices from industrial applications , 2018, 2018 IEEE 15th International Conference on Networking, Sensing and Control (ICNSC).

[11]  Binbin Pan,et al.  Supervised kernel nonnegative matrix factorization for face recognition , 2016, Neurocomputing.

[12]  Yu Zhang,et al.  A Fast Non-Smooth Nonnegative Matrix Factorization for Learning Sparse Representation , 2016, IEEE Access.

[13]  Hongwei Liu,et al.  Nonnegative matrix factorization with bounded total variational regularization for face recognition , 2010, Pattern Recognit. Lett..

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

[15]  Ying Chen,et al.  Clustering-based initialization for non-negative matrix factorization , 2008, Appl. Math. Comput..

[16]  Yongxin Ge,et al.  Face recognition using two-dimensional nonnegative principal component analysis , 2012, J. Electronic Imaging.

[17]  Changfeng Ma,et al.  Image processing using Newton-based algorithm of nonnegative matrix factorization , 2015, Appl. Math. Comput..

[18]  Yan Chen,et al.  Noise modeling and representation based classification methods for face recognition , 2015, Neurocomputing.

[19]  D. Cheng,et al.  An Introduction to Semi-Tensor Product of Matrices and Its Applications , 2012 .

[20]  Hongtao Lu,et al.  Group Sparse Non-negative Matrix Factorization for Multi-Manifold Learning , 2011, BMVC.

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

[22]  MengChu Zhou,et al.  Incorporation of Efficient Second-Order Solvers Into Latent Factor Models for Accurate Prediction of Missing QoS Data , 2018, IEEE Transactions on Cybernetics.

[23]  Hyunsoo Kim,et al.  Sparse Non-negative Matrix Factorizations via Alternating Non-negativity-constrained Least Squares , 2006 .

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

[25]  Guillermo Sapiro,et al.  Online Learning for Matrix Factorization and Sparse Coding , 2009, J. Mach. Learn. Res..

[26]  MengChu Zhou,et al.  Non-Negativity Constrained Missing Data Estimation for High-Dimensional and Sparse Matrices from Industrial Applications , 2020, IEEE Transactions on Cybernetics.

[27]  Richard Bellman,et al.  Introduction to Matrix Analysis , 1972 .

[28]  David White,et al.  Error Rates in Users of Automatic Face Recognition Software , 2015, PloS one.

[29]  Lucas C. Parra,et al.  Recovery of constituent spectra using non-negative matrix factorization , 2003, SPIE Optics + Photonics.

[30]  Haipeng Peng,et al.  A Novel Digital Watermarking Based on General Non-Negative Matrix Factorization , 2018, IEEE Transactions on Multimedia.

[31]  Lixiang Li,et al.  Attributed community mining using joint general non-negative matrix factorization with graph Laplacian , 2018 .

[32]  Daoqiang Zhang,et al.  Non-negative Matrix Factorization on Kernels , 2006, PRICAI.

[33]  Li Bin,et al.  Discriminant non-negative graph embedding for face recognition , 2015, Neurocomputing.

[34]  Nanning Zheng,et al.  Non-negative matrix factorization for visual coding , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[35]  Liang Dai,et al.  Convergent Projective Non-negative Matrix Factorization with Kullback-Leibler Divergence , 2014, Pattern Recognit. Lett..

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

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

[38]  Daizhan Cheng,et al.  Semi-tensor product of matrices and its application to Morgen’s problem , 2007, Science in China Series : Information Sciences.

[39]  Jiang-She Zhang,et al.  Large margin based nonnegative matrix factorization and partial least squares regression for face recognition , 2011, Pattern Recognit. Lett..