Semi-paired multiview clustering based on nonnegative matrix factorization.

*(English. Russian original)*Zbl 1435.62253
J. Comput. Syst. Sci. Int. 58, No. 4, 579-594 (2019); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upravl. 2019, No. 4, 83-98 (2019).

Summary: As data that have multiple views become widely available, the clusterization of such data based on nonnegative matrix factorization has been attracting greater attention. In the majority of studies, the statement in which all objects have images in all representations is considered. However, this is often not the case in practical problems. To resolve this issue, a novel semi-paired multiview clustering algorithm is proposed. For incomplete data, it is assumed that their views have the same indicator vector, and the paired matrix is introduced. The objects that are close to each other in each view must have identical indicators, which makes regularization and reconstruction of the manifold geometric structure possible. The proposed algorithm can work both with incomplete and complete data having multiple views. The experimental results obtained on four datasets prove its effectiveness compared to other modern algorithms.

##### MSC:

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

15A23 | Factorization of matrices |

62H35 | Image analysis in multivariate analysis |

68T10 | Pattern recognition, speech recognition |

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\textit{X. Yao} et al., J. Comput. Syst. Sci. Int. 58, No. 4, 579--594 (2019; Zbl 1435.62253); translation from Izv. Ross. Akad. Nauk, Teor. Sist. Upravl. 2019, No. 4, 83--98 (2019)

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##### References:

[1] | L. Wang and S. Chen,“Joint representation classification for collective face recognition” Pattern Recognit. 63, 182-192 (2017). |

[2] | T. Scheffer and S. Bickel,“Multi-view clustering” in Proceedings of the IEEE International Conference on Data Mining (IEEE Computer Soc., Washington, DC, 2004), pp. 19-26. |

[3] | D. D. Lee and H. S. Seung,“Learning the parts of objects by non-negative matrix factorization” Nature (London, U.K.) 401, 788-791 (1999). · Zbl 1369.68285 |

[4] | D. D. Lee and H. S. Seung,“Algorithms for non-negative matrix factorization” in Proceedings of the 13th International Conference on Neural Information Processing Systems (MIT Press, Cambridge, MA, 2000), pp. 535-541. |

[5] | W. Xu, X. Liu, and Y. Gong,“Document clustering based on non-negative matrix factorization” in Proceedings of the 26th Annual International ACM SIGIR Conference Research and Development in Information Retrieval, Canada, Toronto,2003, pp. 267-273. |

[6] | J. Qiang, Y. Li, Y. Yuan, and W. Liu,“Snapshot ensembles of non-negative matrix factorization for stability of topic modelling” Appl. Intell. 48, 3963-3975 (2018). |

[7] | K. Vorontsov and A. Potapenko,“Additive regularization of topic models” Mach. Learning 101, 303-323 (2015). · Zbl 1383.62069 |

[8] | C. Y. Sang and D. H. Sun,“Co-clustering over multiple dynamic data streams based on non-negative matrix factorization” Appl. Intell. 41, 487-502 (2014). |

[9] | J. Liu, C. Wang, J. Gao, and J. Han,“Multi-view clustering via joint nonnegative matrix factorization” in Proceedings of the SIAM International Conference on Data Mining, Austin, TX,2013, pp. 252-260. |

[10] | L. Wang, S. Chen, and Y. Wang,“A unified algorithm for mixed <Emphasis Type”Itali“>l2, <Emphasis Type”Itali“>p-minimizations and its application in feature selection” Comput. Optimiz. Appl. 58, 409-421 (2014). · Zbl 1305.90339 |

[11] | K. Liu, H. Wang, S. Risacher, A. Saykin, and L. Shen,“Multiple incomplete views clustering via non-negative matrix factorization with its application in Alzheimer’s disease analysis” in Proceedings of the IEEE 15th International Symposium on Biomedical Imaging, Washington, DC,2018, pp. 1402-1405. |

[12] | Y. Ling, X. Pan, G. Li, and X. Hu,“Clinical documents clustering based on medication/symptom names using multi-view nonnegative matrix factorization” IEEE Trans. Nanobiosci. 14, 500-504 (2015). |

[13] | M. M. Kalayeh, H. Idrees, and M. Shah,“NMF-KNN: image annotation using weighted multi-view non-negative matrix factorization” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Columbus, OH,2014, pp. 184-191. |

[14] | R. Rad and M. Jamzad,“Image annotation using multi-view non-negative matrix factorization with different number of basis vectors” J. Visual Commun. Image Repres. 46, 1-12 (2017). |

[15] | F. Zhong and L. Ma,“Image annotation using multi-view non-negative matrix factorization and semantic co-occurrence” in Proceedings of the IEEE Region 10 Conference TENCON, Singapore,2016, pp. 2453-2456. |

[16] | X. Zhang, H. Gao, G. Li, J. Zhao, J. Huo, J. Yin, Y. Liu, and L. Zheng,“Multi-view clustering based on graph-regularized nonnegative matrix factorization for object recognition” Inform. Sci. 432, 463-478 (2018). |

[17] | W. Shao, L. He, C. Lu, and P. S. Yu,“Online multi-view clustering with incomplete views” in Proceedings of the IEEE International Conference on Big Data, Washington, DC,2016, pp. 1012-1017. |

[18] | W. Shao, L. He, C. Lu, X. Wei, and P. S. Yu,“Online unsupervised multi-view feature selection” in Proceedings of the 16th IEEE International Conference on Data Mining, Barcelona, Spain,2016, pp. 1203-1208. |

[19] | S. T. Roweis and L. K. Saul,“Nonlinear dimensionality reduction by locally linear embedding” Science (Washington, DC, U. S.) 290 (5500), 2323-2326 (2000). |

[20] | J. B. Tenenbaum, V. de Silva, and J. C. Langford,“A global geometric framework for nonlinear dimensionality reduction” Science (Washington, DC, U. S.) 290 (5500), 2319-2323 (2000). |

[21] | M. Belkin and P. Niyogi,“Laplacian eigenmaps and spectral techniques for embedding and clustering” in Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic, Vancouver, Canada,2001, pp. 585-591. |

[22] | L. Tao, H. H. Ip, Y. Wang, and X. Shu,“Low rank approximation with sparse integration of multiple manifolds for data representation” Appl. Intell. 42, 430-446 (2015). |

[23] | R. Hadsell, S. Chopra, and Y. LeCun,“Dimensionality reduction by learning an invariant mapping” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, New York,2006, pp. 1735-1742. |

[24] | D. Cai, X. He, J. Han, and T. S. Huang,“Graph regularized nonnegative matrix factorization for data representation” IEEE TPAMI 33, 1548-1560 (2011). |

[25] | L. Zong, X. Zhang, L. Zhao, H. Yu, and Q. Zhao,“Multi-view clustering via multi-manifold regularized non-negative matrix factorization” Neuron Networks 88, 74-89 (2017). |

[26] | W. Yang, Y. Gao, L. Cao, M. Yang, and Y. Shi,“mPadal: a joint local-and-global multi-view feature selection method for activity recognition” Appl. Intell. 41, 776-790 (2014). |

[27] | H. Zhao, Z. Ding, and Y. Fu,“Multi-view clustering via deep matrix factorization” in Proceedings of the 31st AAAI Conference on Artificial Intelligence, San Francisco, CA,2017, pp. 2921-2927. |

[28] | X. Xie and S. Sun,“Multi-view laplacian twin support vector machines” Appl. Intell. 41, 1059-1068 (2014). |

[29] | W. Shao, L. He, and S. Y. Philip, Multiple Incomplete Views Clustering via Weighted Nonnegative Matrix Factorization with L2, 1Regularization, Vol. 9284 of Lecture Notes in Computer Science, Ed. by A. Appice, P. Rodrigues, V. Santos Costa, C. Soares, J. Gama, and A. Jorge (Springer, Cham, 2015). |

[30] | S. Y. Zhi and H. Zhou,“Partial multi-view clustering” in Proceedings of the 28th AAAI Conference on Artificial Intelligence, Quebec, Canada,2014, pp. 1968-1974. |

[31] | N. Rai, S. Negi, S. Chaudhury, and O. Deshmukh,“Partial multi-view clustering using graph regularized NMF” in Proceedings of the 23rd International Conference on Pattern Recognition, Cancun, Mexico,2016, pp. 2192-2197. |

[32] | H. Zhao, H. Liu, and Y. Fu,“Incomplete multi-modal visual data grouping” in Proceedings of the 25th International Joint Conference on Artificial Intelligence, New York,2016, pp. 2392-2398. |

[33] | M. Hu and S. Chen,“Doubly aligned incomplete multi-view clustering” in Proceedings of the 27th International Joint Conference on Artificial Intelligence, Macao, China,2018, pp. 2262-2268. |

[34] | J. Wang, F. Tian, H. Yu, C. H. Liu, K. Zhan, and X. Wang,“Diverse non-negative matrix factorization for multiview data representation” IEEE Trans. Cybern. 48, 2620-2632 (2018). |

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