Joint non-negative and fuzzy coding with graph regularization for efficient data clustering

Abstract Non-negative matrix factorization (NMF) is an effective model in converting data into non-negative coefficient representation whose discriminative ability is usually enhanced to be used for diverse pattern recognition tasks. In NMF-based clustering, we often need to perform K-means on the learned coefficient as postprocessing step to get the final cluster assignments. This breaks the connection between the feature learning and recognition stages. In this paper, we propose to learn the non-negative coefficient matrix based on which we jointly perform fuzzy clustering, by viewing that each column of the dictionary matrix as a concept of each cluster. As a result, we formulate a new fuzzy clustering model, termed Joint Non-negative and Fuzzy Coding with Graph regularization (G-JNFC), and design an effective optimization method to solve it under the alternating direction optimization framework. Besides the convergence and computational complexity analysis on G-JNFC, we conduct extensive experiments on both synthetic and representative benchmark data sets. The results show that the proposed G-JNFC model is effective in data clustering.

[1]  Feiping Nie,et al.  Flexible Non-negative Matrix Factorization with Adaptively Learned Graph Regularization , 2019, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[2]  Meng Wang,et al.  Joint Label Prediction Based Semi-Supervised Adaptive Concept Factorization for Robust Data Representation , 2019, IEEE Transactions on Knowledge and Data Engineering.

[3]  René Vidal,et al.  Sparse Subspace Clustering: Algorithm, Theory, and Applications , 2012, IEEE transactions on pattern analysis and machine intelligence.

[4]  Wenbin Li,et al.  Graph regularized discriminative non-negative matrix factorization for face recognition , 2013, Multimedia Tools and Applications.

[5]  Jinhui Tang,et al.  Robust Structured Nonnegative Matrix Factorization for Image Representation , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Yu-Jin Zhang,et al.  Nonnegative Matrix Factorization: A Comprehensive Review , 2013, IEEE Transactions on Knowledge and Data Engineering.

[7]  Xuelong Li,et al.  Joint Learning of Fuzzy k-Means and Nonnegative Spectral Clustering With Side Information , 2019, IEEE Transactions on Image Processing.

[8]  Wei Liu,et al.  Nonnegative Local Coordinate Factorization for Image Representation , 2011, IEEE Transactions on Image Processing.

[9]  Shuyuan Yang,et al.  Group Low-Rank Nonnegative Matrix Factorization With Semantic Regularizer for Hyperspectral Unmixing , 2018, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[10]  Xuelong Li,et al.  A General Framework for Auto-Weighted Feature Selection via Global Redundancy Minimization , 2019, IEEE Transactions on Image Processing.

[11]  Samah Jamal Fodeh,et al.  Exploiting MEDLINE for gene molecular function prediction via NMF based multi-label classification , 2018, J. Biomed. Informatics.

[12]  Xin Liu,et al.  Document clustering based on non-negative matrix factorization , 2003, SIGIR.

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

[14]  B. Simhachalam,et al.  Performance comparison of fuzzy and non-fuzzy classification methods , 2016 .

[15]  Volkan Cevher,et al.  Sparse projections onto the simplex , 2012, ICML.

[16]  Feiping Nie,et al.  Semi-Supervised Feature Selection via Sparse Rescaled Linear Square Regression , 2020, IEEE Transactions on Knowledge and Data Engineering.

[17]  Yong Peng,et al.  Enhanced low-rank representation via sparse manifold adaption for semi-supervised learning , 2015, Neural Networks.

[18]  Yong Yu,et al.  Robust Recovery of Subspace Structures by Low-Rank Representation , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Yong Yu,et al.  Robust Subspace Segmentation by Low-Rank Representation , 2010, ICML.

[20]  Xuelong Li,et al.  Local Coordinate Concept Factorization for Image Representation , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Jean Charles Gilbert,et al.  Global linear convergence of an augmented Lagrangian algorithm for solving convex quadratic optimization problems , 2002 .

[22]  Yonghong Song,et al.  Multi-view gait recognition using NMF and 2DLDA , 2019, Multimedia Tools and Applications.

[23]  Yihong Gong,et al.  Nonlinear Learning using Local Coordinate Coding , 2009, NIPS.

[24]  Yong Peng,et al.  Discriminative extreme learning machine with supervised sparsity preserving for image classification , 2017, Neurocomputing.

[25]  Yihong Gong,et al.  Document clustering by concept factorization , 2004, SIGIR '04.

[26]  Feiping Nie,et al.  A New Simplex Sparse Learning Model to Measure Data Similarity for Clustering , 2015, IJCAI.

[27]  A. H. Sherman.  On Newton-Iterative Methods for the Solution of Systems of Nonlinear Equations , 1978 .

[28]  Muhammad Hameed Siddiqi,et al.  A robust clustering algorithm using spatial fuzzy C-means for brain MR images , 2020 .

[29]  Hongtao Lu,et al.  Non-negative Matrix Factorization with Pairwise Constraints and Graph Laplacian , 2015, Neural Processing Letters.

[30]  René Vidal,et al.  Sparse subspace clustering , 2009, CVPR.