Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit
作者： Anru R. Zhang , Miaoyan Wang , Rungang Han , Yuetian Luo
DOI:
关键词: Cluster analysis 、 Computer science 、 Algorithm 、 Limit (mathematics) 、 Spectral clustering 、 Tensor (intrinsic definition) 、 Block model
摘要: … two SNR regions apply to matrix biclustering (d = 2) while the … derived by the algebraic property of SVD. However, for high-order … Also we define Gd(N,1/2,κ) as the hypergraphic planted …
arxiv.org参考文章(66)
Quentin Berthet, Philippe Rigollet, Complexity Theoretic Lower Bounds for Sparse Principal Component Detection conference on learning theory. pp. 1046- 1066 ,(2013)
Volker Tresp, Hans-peter Kriegel, Maximilian Nickel, A Three-Way Model for Collective Learning on Multi-Relational Data international conference on machine learning. pp. 809- 816 ,(2011)
Will Wei Sun, Junwei Lu, Han Liu, Guang Cheng, Provable sparse tensor decomposition Journal of The Royal Statistical Society Series B-statistical Methodology. ,vol. 79, pp. 899- 916 ,(2017) , 10.1111/RSSB.12190
Jiaming Xu, Yudong Chen, Statistical-computational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices Journal of Machine Learning Research. ,vol. 17, pp. 882- 938 ,(2016)
Marta Melé, Pedro G Ferreira, Ferran Reverter, David S DeLuca, Jean Monlong, Michael Sammeth, Taylor R Young, Jakob M Goldmann, Dmitri D Pervouchine, Timothy J Sullivan, Rory Johnson, Ayellet V Segrè, Sarah Djebali, Anastasia Niarchou, The GTEx Consortium, Fred A Wright, Tuuli Lappalainen, Miquel Calvo, Gad Getz, Emmanouil T Dermitzakis, Kristin G Ardlie, Roderic Guigó, None, The human transcriptome across tissues and individuals Science. ,vol. 348, pp. 660- 665 ,(2015) , 10.1126/SCIENCE.AAA0355
Chandler Davis, W. M. Kahan, The Rotation of Eigenvectors by a Perturbation. III SIAM Journal on Numerical Analysis. ,vol. 7, pp. 1- 46 ,(1970) , 10.1137/0707001
Anil K. Jain, Data clustering: 50 years beyond K-means international conference on pattern recognition. ,vol. 31, pp. 651- 666 ,(2010) , 10.1016/J.PATREC.2009.09.011
Lieven De Lathauwer, Bart De Moor, Joos Vandewalle, A Multilinear Singular Value Decomposition SIAM Journal on Matrix Analysis and Applications. ,vol. 21, pp. 1253- 1278 ,(2000) , 10.1137/S0895479896305696
Lieven De Lathauwer, Bart De Moor, Joos Vandewalle, On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors SIAM Journal on Matrix Analysis and Applications. ,vol. 21, pp. 1324- 1342 ,(2000) , 10.1137/S0895479898346995
Tamara G. Kolda, Brett W. Bader, Tensor Decompositions and Applications Siam Review. ,vol. 51, pp. 455- 500 ,(2009) , 10.1137/07070111X