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General Tensor Spectral Co-clustering for Higher-Order Data [article]

Tao Wu, Austin R. Benson, David F. Gleich
2016 arXiv   pre-print
We develop a new tensor spectral co-clustering method that applies to any non-negative tensor of data.  ...  Spectral clustering and co-clustering are well-known techniques in data analysis, and recent work has extended spectral clustering to square, symmetric tensors and hypermatrices derived from a network.  ...  We recently proposed a Tensor Spectral Clustering (TSC) framework as a generalization of spectral methods for higher-order graph data [6] .  ... 
arXiv:1603.00395v1 fatcat:44o3oryqa5getic3wy7h3us7aa

Tensor Spectral Clustering for Partitioning Higher-order Network Structures [chapter]

Austin R. Benson, David F. Gleich, Jure Leskovec
2015 Proceedings of the 2015 SIAM International Conference on Data Mining  
Here we propose a Tensor Spectral Clustering (TSC) algorithm that allows for modeling higher-order network structures in a graph partitioning framework.  ...  Higher-order network structures of interest are represented using a tensor, which we then partition by developing a multilinear spectral method.  ...  Generalizing spectral clustering to higher-order structures involves several challenges.  ... 
doi:10.1137/1.9781611974010.14 pmid:27812399 pmcid:PMC5089081 dblp:conf/sdm/BensonGL15 fatcat:hdbtnc4fhrbrfibdzzasfc43qa

Integration of Single-view Graphs with Diffusion of Tensor Product Graphs for Multi-view Spectral Clustering

Le Shu, Longin Jan Latecki
2015 Asian Conference on Machine Learning  
Since each cross-view TPG captures higher order relationships of data under two different views, it is no surprise that we obtain more reliable similarities.  ...  We linearly combine multiple cross-view TPGs to integrate higher order information.  ...  In this paper, we propose a novel multi-view spectral clustering approach based on Tensor Product Graphs (TPG). The key idea is to exploit higher order relations of single-view graphs.  ... 
dblp:conf/acml/ShuL15 fatcat:fmvihjfeezb2bmguxrz7u25p3m

Multiview Partitioning via Tensor Methods

Xinhai Liu, Shuiwang Ji, Wolfgang Glänzel, B. De Moor
2013 IEEE Transactions on Knowledge and Data Engineering  
Index Terms-Multi-view clustering, tensor decomposition, spectral clustering, multi-linear singular value decomposition, higher-order orthogonal iteration X. Liu is with the  ...  In this paper, we present a novel tensor-based framework for integrating heterogeneous multi-view data in the context of spectral clustering.  ...  De Lathauwer for deriving the version of HOOI with a single vector in one mode and for the theorem and proof in the Supplementary material 6. This work was supported by (1)  ... 
doi:10.1109/tkde.2012.95 fatcat:c3fzmbheh5fcphw33lciyyjavm

Low-rank Multi-view Clustering in Third-Order Tensor Space [article]

Ming Yin, Junbin Gao, Shengli Xie, Yi Guo
2016 arXiv   pre-print
As a consequence, the clustering performance for multi-view data is compromised.  ...  To address this issue, in this paper, a novel multi-view clustering method is proposed by using t-product in third-order tensor space.  ...  ACKNOWLEDGEMENT The authors would like to thank Eric Kernfel for his helpful discussion and Changqing Zhang for his opening code [47] .  ... 
arXiv:1608.08336v2 fatcat:o6nfpspgivfrljyif3aocau74a

Low-Rank Tensor Constrained Multiview Subspace Clustering

Changqing Zhang, Huazhu Fu, Si Liu, Guangcan Liu, Xiaochun Cao
2015 2015 IEEE International Conference on Computer Vision (ICCV)  
Our method regards the subspace representation matrices of different views as a tensor, which captures dexterously the high order correlations underlying multiview data.  ...  The inference process of the affinity matrix for clustering is formulated as a tensor nuclear norm minimization problem, constrained with an additional ℓ 2,1 -norm regularizer and some linear equalities  ...  We give the definition of tensor nuclear norm as used in [29, 36] , which generalizes the matrix (i.e., 2-mode or 2-order tensor) case (e.g., [28, 40, 41] ) to higher-order tensor as ||Z|| * = M m=1  ... 
doi:10.1109/iccv.2015.185 dblp:conf/iccv/ZhangFLLC15 fatcat:7zbd4cvo4bgx5bfwcl77dhhpse

Essential Tensor Learning for Multi-view Spectral Clustering [article]

Jianlong Wu, Zhouchen Lin, Hongbin Zha
2019 arXiv   pre-print
In this paper, we focus on the Markov chain based spectral clustering method and propose a novel essential tensor learning method to explore the high order correlations for multi-view representation.  ...  We also employ the tensor rotation operator for this task to better investigate the relationship among views as well as reduce the computation complexity.  ...  Yuan Xie for his selfless support in sharing codes and datasets as well as the valuable suggestions.  ... 
arXiv:1807.03602v2 fatcat:nute6fz6t5fuvojg5trnlwhpxe

Tensor-based Multi-view Spectral Clustering via Shared Latent Space [article]

Qinghua Tao, Francesco Tonin, Panagiotis Patrinos, Johan A.K. Suykens
2022 arXiv   pre-print
To boost higher-order correlations, tensor-based modelling is introduced without increasing computational complexity.  ...  Multi-view Spectral Clustering (MvSC) attracts increasing attention due to diverse data sources.  ...  To capture higher-order correlation, a Tensor-based RKM model (TMvKSCR) is constructed by simultaneously integrating all views into tensor representations, as exemplified in Figure 1 .  ... 
arXiv:2207.11559v1 fatcat:7rqz6fn35ngl3mgxlvjvzkrkp4

Spectral Clustering in Social-Tagging Systems [chapter]

Alexandros Nanopoulos, Hans-Henning Gabriel, Myra Spiliopoulou
2009 Lecture Notes in Computer Science  
To discover clusters of similar items, we extend spectral clustering, an approach successfully used for the clustering of complex data, into a method that captures multiple values of similarity between  ...  Our experiments with two real social-tagging data sets show that our new method is superior to conventional spectral clustering that ignores the existence of multiple values of similarity among the items  ...  [1] propose a method for multi-way clustering on tensors, thus extending co-clustering from matrices to tensors.  ... 
doi:10.1007/978-3-642-04409-0_15 fatcat:4zsf36lpo5artj7ao63bkxbmkm

Scalable Algorithm for Higher-Order Co-Clustering via Random Sampling

Daisuke Hatano, Takuro Fukunaga, Takanori Maehara, Ken-ichi Kawarabayashi
We propose a scalable and efficient algorithm for coclustering a higher-order tensor.  ...  Each iteration of our algorithm runs in polynomial on the size of hypergraphs, and thus it performs well even for higher-order tensors, which are difficult to deal with for state-of-the-art algorithm.  ...  Based on this algorithm, we propose a new algorithm for co-clustering higher-order tensors. In summary, our contributions can be summarized as follows: 1.  ... 
doi:10.1609/aaai.v31i1.10914 fatcat:33s6w3gimbdsfoml66it2kve4y

Introduction to the Issue on Robust Subspace Learning and Tracking: Theory, Algorithms, and Applications

T. Bouwmans, N. Vaswani, P. Rodriguez, R. Vidal, Z. Lin
2018 IEEE Journal on Selected Topics in Signal Processing  
For this, a higher numerical efficiency is provided by defining analytical SSA variants while a higher robustness is obtained by utilizing To be robust against spectral variability in inverse problems  ...  Hinojosa et al. design a set of coding patterns such that inter-class and intra-class data structure is preserved after the Compressive Spectral Imaging (CSI) acquisition in order to improve clustering  ... 
doi:10.1109/jstsp.2018.2879245 fatcat:z3ohqdl37nat3pjo65fzsf2ady

Tag-Aware Spectral Clustering Of Music Items

Ioannis Karydis, Alexandros Nanopoulos, Hans-Henning Gabriel, Myra Spiliopoulou
2009 Zenodo  
First, we define the n-mode product T × n M between a general N -order tensor T ∈ R I 1 ×...×I N and a matrix M ∈ R Jn×In .  ...  [9] proposed dimensionality reduction using higher order SVD for the purposes of personalised music recommendation.  ... 
doi:10.5281/zenodo.1417483 fatcat:6252juj53bddxoal7rda2agp6a

A Self-Organizing Tensor Architecture for Multi-View Clustering [article]

Lifang He, Chun-ta Lu, Yong Chen, Jiawei Zhang, Linlin Shen, Philip S. Yu, Fei Wang
2018 arXiv   pre-print
In this paper, we introduce a tensor-based approach to incorporate the higher-order interactions among multiple views as a tensor structure.  ...  Although several multi-view clustering methods have been proposed, most of them routinely assume one weight for one view of features, and thus inter-view correlations are only considered at the view-level  ...  interactions among multiple views, without the need to construct the higher-order tensor data physically.  ... 
arXiv:1810.07874v1 fatcat:7b2cxamlbbftxl7gkypnct4xr4

KDD2008 workshop report DMMT'08

Chris Ding, Tao Li, Shenghuo Zhu
2008 SIGKDD Explorations  
We provide a summary of the Workshop on Data Mining Using Matrices and Tensors (DMMT'08) held in conjunction with ACM SIGKDD 2008, on August 24th in Las Vegas, USA.  ...  probabilistic models for 2D (and higher-order) data.  ...  ., Multilinear Partial Least Squares (N-PLS), which is the generalization of Partial Least Squares (PLS) regression to higher-order datasets, was used to model the tensor.  ... 
doi:10.1145/1540276.1540293 fatcat:724tpyimyzfx7hzx2g6t3lkjrq

Robust Kernelized Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization [article]

Yanyun Qu, Jinyan Liu, Yuan Xie, Wensheng Zhang
2017 arXiv   pre-print
generic object clustering.  ...  In this paper, we make an optimization model for the kernelized multi-view self-representation clustering problem.  ...  And then, spectral clustering is utilized with the affinity matrix A to generate the clustering result. LRR can be extended to multi-view clustering.  ... 
arXiv:1709.05083v1 fatcat:emur4hsbebhqvcl3hrdktm6d6i
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