基于超图正则化非负张量链分解的聚类分析

doi:10.19678/j.issn.1000-3428.0064740

摘要/Abstract

摘要： 非负张量链分解作为一种重要的张量分解模型，可保留数据内部结构信息，广泛应用于高维数据的特征提取和表示。从流形学习角度出发，高维数据信息通常潜在于低维空间的非线性流形结构中，然而现有图学习理论只能建模对象间的成对关系，很难准确刻画具有复杂流形结构的高维数据的相似关系。引入超图学习，提出一种超图正则化非负张量链(HGNTT)分解方法，在高维数据中提取低维表示的同时通过构建超图描述样本数据间的高阶关系，从而保留非线性流形结构，同时采用乘法更新方法对HGNTT模型进行优化求解并证明其收敛性。在ORL和Faces95这两个公开数据集上的聚类实验结果表明，相比于NMF、GNMF等方法，HGNTT方法的聚类准确率和归一化互信息分别提升了1.2%~7.6%和0.2%~3.0%，验证了HGNTT方法的有效性。

关键词: 非负张量链分解, 特征提取, 超图学习, 乘法更新方法, 聚类分析

Abstract: Non-negative Tensor Train（NTT） decomposition，as an important tensor decomposition model，can preserve the internal structure information of data and is widely used in feature extraction and representation tasks of high-dimensional data. From the perspective of manifold learning，high-dimensional data information is usually latent in the nonlinear manifold structure in low-dimensional space.However，existing graph learning theories can only model pairwise relationships between objects，and accurately portraying the similar relationships of high-dimensional data with a complex manifold structure is difficult.By introducing hyper-graph learning，this study proposes a Hyper-Graph regularized Non-negative Tensor Train（HGNTT） decomposition method for extracting low-dimensional representations from high-dimensional data while describing the higher-order relationships between sample data points by constructing hyper-graphs，thereby preserving the nonlinear manifold structure. Moreover，a Multiplicative Update（MU） method is used to optimally solve the HGNTT model and prove its convergence. Clustering experiments on two publicly available datasets，ORL and Faces95，show that the clustering accuracy and Normalized Mutual Information（NMI） of the HGNTT method improves by 1.2%-7.6% and 0.2%-3.0%，respectively，compared with those of NMF and GNMF，thereby validating the effectiveness of the HGNTT method.

Key words: Non-negative Tensor Train（NTT） decomposition, feature extraction, hyper-graph learning, Multiplicative Update（MU） method, clustering analysis

中图分类号:

TP391

戴浩磊, 黄永慧, 周郭许. 基于超图正则化非负张量链分解的聚类分析[J]. 计算机工程, 2023, 49(6): 81-89.

DAI Haolei, HUANG Yonghui, ZHOU Guoxu. Clustering Analysis Based on Hyper-graph Regularized Non-Negative Tensor Train Decomposition[J]. Computer Engineering, 2023, 49(6): 81-89.

https://www.ecice06.com/CN/Y2023/V49/I6/81

图/表 10

20230615164637

20230615164641

20230615164644

20230615164648

20230615164657

20230615164700

20230615164703

20230615164707

20230615164710

20230615164714

参考文献

[1] ZHOU G X,CICHOCKI A,XIE S L.Fast nonnegative matrix/tensor factorization based on low-rank approximation[J].IEEE Transactions on Signal Processing,2012,60(6):2928-2940.
[2] CICHOCKI A,MANDIC D,DE LATHAUWER L,et al.Tensor decompositions for signal processing applications:from two-way to multiway component analysis[J].IEEE Signal Processing Magazine,2015,32(2):145-163.
[3] QIU Y C,ZHOU G X,ZHANG Y,et al.Canonical Polyadic Decomposition(CPD) of big tensors with low multilinear rank[J].Multimedia Tools and Applications,2021,80(15):22987-23007.
[4] QIU Y C,SUN W J,ZHANG Y,et al.Approximately orthogonal nonnegative Tucker decomposition for flexible multiway clustering[J].Science China Technological Sciences,2021,64(9):1872-1880.
[5] KOLDA T G,BADER B W.Tensor decompositions and applications[J].SIAM Review,2009,51(3):455-500.
[6] LIU Y,LONG Z,HUANG H,et al.Low CP rank and Tucker rank tensor completion for estimating missing components in image data[J].IEEE Transactions on Circuits and Systems for Video Technology,2020,30:944-954.
[7] ZHAO Q B,ZHANG L Q,CICHOCKI A.Bayesian CP factorization of incomplete tensors with automatic rank determination[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2015,37(9):1751-1763.
[8] QIU Y N,ZHOU G X,CHEN X Q,et al.Semi-supervised non-negative Tucker decomposition for tensor data representation[J].Science China(Technological Sciences),2021,64(9):1881-1892.
[9] PAN J J,NG M K,LIU Y,et al.Orthogonal nonnegative Tucker decomposition[J].SIAM Journal on Scientific Computing,2021,43(1):55-81.
[10] OSELEDETS I V.Tensor-train decomposition[J].SIAM Journal on Scientific Computing,2011,33(5):2295-2317.
[11] BENGUA J A,PHIEN H N,TUAN H D,et al.Efficient tensor completion for color image and video recovery:low-rank tensor train[J].IEEE Transactions on Image Processing,2017,26(5):2466-2479.
[12] YANG Y,KROMPASS D,TRESP V.Tensor-train recurrent neural networks for video classification[EB/OL].[2022-04-11].https://arxiv.org/abs/1707.01786.
[13] LEE N,PHAN A H,CONG F,et al.Nonnegative tensor train decompositions for multi-domain feature extraction and clustering[C]//Proceedings of International Conference on Neural Information Processing.Berlin,Germany:Springer,2016:1-9.
[14] SHCHERBAKOVA E,TYRTYSHNIKOV E.Nonnegative tensor train factorizations and some applications[M].Berlin,Germany:Springer,2020.
[15] YUAN L H,ZHAO Q B,GUI L H,et al.High-order tensor completion via gradient-based optimization under Tensor Train format[J].Image Communication,2019,73(C):53-61.
[16] LI S Z,HOU X W,ZHANG H J,et al.Learning spatially localized,parts-based representation[C]//Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.Washington D.C.,USA:IEEE Press,2003:1-10.
[17] CAI D,HE X F,WU X Y,et al.Non-negative matrix factorization on manifold[C]//Proceedings of the 8th IEEE International Conference on Data Mining.Washington D.C.,USA:IEEE Press,2009:63-72.
[18] LENG C C,ZHANG H,CAI G R,et al.Graph regularized LP smooth non-negative matrix factorization for data representation[J].IEEE/CAA Journal of Automatica Sinica,2019,6(2):584-595.
[19] ROWEIS S T,SAUL L K.Nonlinear dimensionality reduction by locally linear embedding[J].Science,2000,290(5500):2323-2326.
[20] TENENBAUM J B,DE SILVA V,LANGFORD J C.A global geometric framework for nonlinear dimensionality reduction[J].Science,2000,290(5500):2319-2323.
[21] BELKIN M,NIYOGI P.Laplacian eigenmaps for dimensionality reduction and data representation[J].Neural Computation,2003,15(6):1373-1396.
[22] CAI D,HE X F,HAN J W,et al.Graph regularized nonnegative matrix factorization for data representation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2011,33(8):1548-1560.
[23] LI X L,CUI G S,DONG Y S.Graph regularized non-negative low-rank matrix factorization for image clustering[J].IEEE Transactions on Cybernetics,2017,47(11):3840-3853.
[24] QIU Y N,ZHOU G X,ZHANG Y,et al.Graph regularized nonnegative tucker decomposition for tensor data representation[C]//Proceedings of 2019 IEEE International Conference on Acoustics,Speech and Signal Processing.Washington D.C.,USA:IEEE Press,2019:8613-8617.
[25] SOFUOGLU S E,AVIYENTE S.Graph regularized tensor train decomposition[C]//Proceedings of 2020 IEEE International Conference on Acoustics,Speech and Signal Processing.Washington D.C.,USA:IEEE Press,2020:3912-3916.
[26] 吴泽鑫.图约束非负张量列分解算法及其在特征提取中的应用[D].广州:广东工业大学,2021.WU Z X.Graph constrained nonnegative tensor column decomposition algorithm and its application in feature extraction[D].Guangzhou:Guangdong University of Technology,2021.(in Chinese)
[27] GAO Y,ZHANG Z Z,LIN H J,et al.Hypergraph learning:methods and practices[J].IEEE Transactions on Pattern Analysis and Machine Intelligence,2022,44(5):2548-2566.
[28] SHENG H,AHMED E,DAN Y.On the effect of hyperedge weights on hypergraph learning[J].Image and Vision Computing,2017,57:89-101.
[29] SCHÖLKOPF B,PLATT J,HOFMANN T.Learning with hypergraphs:clustering,classification,and embedding[M].Cambridge,USA:MIT Press,2007.
[30] ZENG K,YU J,LI C H,et al.Image clustering by hyper-graph regularized non-negative matrix factorization[J].Neurocomputing,2014,138:209-217.
[31] 陈璐瑶,刘奇龙,许云霞,等.基于超图正则化非负Tucker分解的图像聚类算法[J].计算机工程,2022,48(4):197-205.CHEN L Y,LIU Q L,XU Y X,et al.Image clustering algorithm based on hypergraph regularized nonnegative Tucker decomposition[J].Computer Engineering,2022,48(4):197-205.(in Chinese)
[32] XU W,LIU X,GONG Y H.Document clustering based on non-negative matrix factorization[C]//Proceedings of the 26th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval.New York,USA:ACM Press,2003:267-273.
[33] MACQUEEN J B.Some methods for classification and analysis of multivariate observations[EB/OL].[2022-04-11].https://www.semanticscholar.org/paper/Some-methods-for-classification-and-analysis-of-MacQueen/ac8ab51a86f1a9ae74dd0e4576d1a019f5e654ed?p2df.

选择文件类型/文献管理软件名称

选择包含的内容