Joint Structured Graph Learning and Clustering Based on Concept Factorization

As one of the matrix factorization models, concept factorization (CF) achieved promising performance in learning data representation in both original feature space and reproducible kernel Hilbert space (RKHS). Based on the consensuses that 1) learning performance of models can be enhanced by exploiting the geometrical structure of data and 2) jointly performing structured graph learning and clustering can avoid the suboptimal solutions caused by the two-stage strategy in graph-based learning, we developed a new CF model with self-expression. Our model has a combined coefficient matrix which is able to learn more efficiently. In other words, we propose a CF-based joint structured graph learning and clustering model (JSGCF). A new efficient iterative method is developed to optimize the JSGCF objective function. Experimental results on representative data sets demonstrate the effectiveness of our new JSGCF algorithm.

[1]  Jiawei Han,et al.  Locally Consistent Concept Factorization for Document Clustering , 2011, IEEE Transactions on Knowledge and Data Engineering.

[2]  Andrzej Cichocki,et al.  Fast Nonnegative Matrix/Tensor Factorization Based on Low-Rank Approximation , 2012, IEEE Transactions on Signal Processing.

[3]  Xiaojun Wu,et al.  Graph Regularized Nonnegative Matrix Factorization for Data Representation , 2017, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Feiping Nie,et al.  The Constrained Laplacian Rank Algorithm for Graph-Based Clustering , 2016, AAAI.

[5]  Feiping Nie,et al.  Parallel Vector Field Regularized Non-Negative Matrix Factorization for Image Representation , 2018, 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[6]  K. Fan.  On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations: II. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

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

[8]  Allen Y. Yang,et al.  Robust Face Recognition via Sparse Representation , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[9]  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.

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

[11]  C. Ding,et al.  On the Equivalence of Nonnegative Matrix Factorization and K-means - Spectral Clustering , 2005 .

[12]  Jitendra Malik,et al.  Normalized cuts and image segmentation , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[13]  R. Vidal,et al.  Sparse Subspace Clustering: Algorithm, Theory, and Applications. , 2013, IEEE transactions on pattern analysis and machine intelligence.

[14]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorization T , 2007 .

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

[16]  Feiping Nie,et al.  Clustering and projected clustering with adaptive neighbors , 2014, KDD.

[17]  Nicu Sebe,et al.  Flexible Manifold Learning With Optimal Graph for Image and Video Representation , 2018, IEEE Transactions on Image Processing.

[18]  K. Fan.  On a Theorem of Weyl Concerning Eigenvalues of Linear Transformations I. , 1949, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Qinghua Zheng,et al.  Adaptive Unsupervised Feature Selection With Structure Regularization , 2018, IEEE Transactions on Neural Networks and Learning Systems.

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

[21]  Lei Zhang,et al.  Sparse representation or collaborative representation: Which helps face recognition? , 2011, 2011 International Conference on Computer Vision.