[1]YU Qinru,LU Guifu,LI Hua.Nonnegative low-rank matrix factorization with adaptive graph neighbors[J].CAAI Transactions on Intelligent Systems,2022,17(2):325-332.[doi:10.11992/tis.202102007]
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Nonnegative low-rank matrix factorization with adaptive graph neighbors
CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume:
17
Number of periods:
2022 2
Page number:
325-332
Column:
学术论文—机器感知与模式识别
Public date:
2022-03-05
- Title:
- Nonnegative low-rank matrix factorization with adaptive graph neighbors
- Keywords:
- cluster; feature extraction; dimensionality reduction; manifold learning; nonnegative matrix factorization; low-rank constrain; graph regularization; adaptive clustering
- CLC:
- TP391.4
- DOI:
- 10.11992/tis.202102007
- Abstract:
- The exsting graph regularization nonnegative matrix factorization (GNMF) method still has some shortcomings: The GNMF algorithm does not consider the low-rank structure of data. In the GNMF algorithm, the Laplacian graph uses the K-nearest neighbor (KNN) method, and the KNN method cannot always obtain the optimal diagram, which makes the performance of the GNMF algorithm not optimal. For this reason, we propose an algorithm called nonnegative low-rank matrix factorization with adaptive graph neighbors (NLMFAN). On the one hand, by introducing low-rank constraints, NLMFAN can obtain the effective low-rank structure of the original dataset. On the other hand, a method for adaptively solving the similarity matrix is designed to construct the graph. This implies that the structure of the graph and the results of the matrix decomposition are integrated into an integrated framework so that the similarity of the nodes in the graph is automatically learned from the data. In addition, an effective algorithm for solving NLMFAN is given, and experiments on a variety of datasets verify the effectiveness of the algorithm.
- References:
-
[1] ZHAO K, HAIQI P, STEVEN C H H, et al. Robust graph learning from noisy data[J]. IEEE transactions on cybernetics, 2019, 50(5): 1833–1843.
[2] CHEN C F, WEI C P, WANG Y C F. Low-rank matrix recovery with structural incoherence for robust face recognition[C]//Proceedings of 2012 IEEE Conference on Computer Vision and Pattern Recognition. Providence, USA, 2012: 2618?2625.
[3] DUDA R O, HART P E, STORK D G. Pattern classification[M]. 2nd ed. New York: Wiley-Interscience, 2000.
[4] MAKHOUL J, ROUCOS S, GISH H. Vector quantization in speech coding[J]. Proceedings of the IEEE, 1985, 73(11): 1551–1588.
[5] TURK M, PENTLAND A. Eigenfaces for recognition[J]. Journal of cognitive neuroence, 1991, 13(6): 556–562.
[6] LEE D D, SEUNG H S. Algorithms for non-negative matrix factorization[J]. Nips, 2000, 13(6): 556–562.
[7] YANG C F, YE Mao, ZHAO Jing. Document clustering based on nonnegative sparse matrix factorization[C]//Proceedings of the First International Conference on Natural Computation. Changsha, China, 2005: 557?563.
[8] LIU Guangcan, LIN Zhouchen, YAN Shuicheng, et al. Robust recovery of subspace structures by low-rank representation[J]. IEEE transactions on pattern analysis and machine intelligence, 2013, 35(1): 171–184.
[9] LU Yuwu, YUAN Chun, ZHU Wenwu, et al. Structurally incoherent low-rank nonnegative matrix factorization for image classification[J]. IEEE transactions on image processing, 2018, 27(11): 5248–5260.
[10] ROWEIS S T, SAUL L K. Nonlinear dimensionality reduction by locally linear embedding[J]. Science, 2000, 290(5500): 2323–2326.
[11] BELKIN M, NIYOGI P. Laplacian eigenmaps and spectral techniques for embedding and clustering[C]//Proceedings of the 14th International Conference on Neural Information Processing Systems: Natural and Synthetic. Vancouver, British Columbia, Canada, 2001: 585?2591.
[12] BELKIN M, NIYOGI P, SINDHWANI V. Manifold regularization: a geometric framework for learning from labeled and unlabeled examples[J]. Journal of machine learning research, 2006, 7(11): 2399–2434.
[13] CAI Deng, HE Xiaofei, HAN Jiawei, et al. Graph regularized nonnegative matrix factorization for data representation[J]. IEEE transactions on pattern analysis and machine intelligence, 2011, 33(8): 1548–1560.
[14] CAI Deng, HE Xiaofei, WU Xiaoyun, et al. Non-negative matrix factorization on manifold[C]//Proceedings of 2008 Eighth IEEE International Conference on Data Mining. Pisa, Italy, 2008.
[15] BOTTOU L, VAPNIK V. Local learning algorithm[J]. Neural computation, 1992, 4(6): 888–900.
[16] GU Quanquan, ZHOU Jie. Local learning regularized nonnegative matrix factorization[C]//Proceedings of the 21st International Joint Conference on Artificial Intelligence. Pasadena, USA, 2009: 1046?1051.
[17] LI Xuelong, CUI Guosheng, DONG Yongsheng. Graph regularized non-negative low-rank matrix factorization for image clustering[J]. IEEE transactions on cybernetics, 2017, 47(11): 3840–3853.
[18] DU H, HU Q, ZHANG X, et al. Image feature extraction via graph embedding regularized projective non-negative matrix factorization[J]. Communications in computer & information ence, 2014, 483(1): 196–209.
[19] YIN Ming, GAO Junbin, LIN Zhouchen. Laplacian regularized low-rank representation and its applications[J]. IEEE transactions on pattern analysis and machine intelligence, 2016, 38(3): 504–517.
[20] WANG Jianzhong, ZHAO Rui, WANG Yang, et al. Locality constrained graph optimization for dimensionality reduction[J]. Neurocomputing, 2017, 245: 55–67.
[21] MENG Yang, SHANG Ronghua, JIAO Licheng, et al. Dual-graph regularized non-negative matrix factorization with sparse and orthogonal constraints[J]. Engineering applications of artificial intelligence, 2018, 69: 24–35.
[22] NIE Feiping, WANG Xiaoqian, HUANG Heng. Clustering and projected clustering with adaptive neighbors[C]//Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, USA, 2014.
[23] LEMARéCHAL C, BOYD S, VANDENBERGHE L. convex optimization, Cambridge university press, 2004 hardback, 65 US$, ISBN 0 521 83378 7[J]. European journal of operational research, 2006, 170(1): 326–327.
[24] ZHOU Tianyi, TAO Dacheng. GoDec: randomized low-rank & sparse matrix decomposition in noisy case[C]//Proceedings of the 28th International Conference on Machine Learning. Bellevue, USA, 2011: 33?240.
[25] HUANG Shudong, XU Zenglin, KANG Zhao, et al. Regularized nonnegative matrix factorization with adaptive local structure learning[J]. Neurocomputing, 2020, 382(11): 196–209.
[26] WHITLARK D, DUNTEMAN G H. Principal components analysis[J]. Journal of marketing research, 1990, 27(2): 243.
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