Tensor canonical correlation analysis for multi-view dimension reduction

Luo, Yong; Tao, Dacheng; Ramamohanarao, Kotagiri; Xu, Chao; Wen, Yonggang

doi:10.1109/icde.2016.7498374

Cited by 59 publications

(88 citation statements)

References 17 publications

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“…Several works extend it to more than two views, including MCCA [38] which maximizes the sum of pairwise correlations between projections and CCA-RLS [39]. [40] generalize CCA to tensors in order to support more than two views.…”

Section: Correlation and Covariance-basedmentioning

confidence: 99%

Multi-omic and multi-view clustering algorithms: review and cancer benchmark

Rappoport

Shamir

2018

Preprint

143

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High throughput experimental methods developed in recent years have been used to collect large biomedical omics datasets. Clustering of such datasets has proven invaluable for biological and medical research, and helped reveal structure in data from several domains. Such analysis is often based on investigation of a single omic. The decreasing cost and development of additional high throughput methods now enable measurement of multi-omic data. Clustering multi-omic data has the potential to reveal further systems-level insights, but raises computational and biological challenges. Here we review algorithms for multi-omics clustering, and discuss key issues in applying these algorithms. Our review covers methods developed specifically for multi-omic data as well as generic multi-view methods developed in the machine learning community for joint clustering of multiple data types.In addition, using cancer data from TCGA, we perform an extensive benchmark spanning ten different cancer types, providing the first systematic benchmark comparison of leading multi-omics and multiview clustering algorithms. The results highlight several key questions regarding the use of single-vs. multi-omics, the choice of clustering strategy, the power of generic multi-view methods and the use of approximated p-values for gauging solution quality. Due to the rapidly increasing use of multi-omics data, these issues may be important for future progress in the field.

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Section: Correlation and Covariance-basedmentioning

confidence: 99%

Multi-omic and multi-view clustering algorithms: review and cancer benchmark

Rappoport

Shamir

2018

Preprint

143

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“…Inspired by deep representation, [14] proposed a DNN-based model combining CCA and autoencoder-based terms to exploit the deep information from two views. Since those CCA based methods are limited by capability of only handling two-view features, tensor CCA [13] generalized CCA to handle the data of an arbitrary number of views by analyzing the covariance tensor of different views.…”

Section: Related Workmentioning

confidence: 99%

On Unifying Multi-view Self-Representations for Clustering by Tensor Multi-rank Minimization

et al. 2018

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In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to capture the low rank tensor subspace so that the refinement of the view-specific subspaces can be achieved, as well as the high order correlations underlying multi-view data can be explored. By introducing a recently proposed tensor factorization, namely tensor-Singular Value Decomposition (t-SVD) [16], we can impose a new type of low-rank tensor constraint on the rotated tensor to ensure the consensus among multiple views. Different from traditional unfolding based tensor norm, this low-rank tensor constraint has optimality properties similar to that of matrix rank derived from SVD, so the complementary information can be explored and propagated among all the views more thoroughly and effectively. The established model, called t-SVD based Multiview Subspace Clustering (t-SVD-MSC), falls into the applicable scope of augmented Lagrangian method, and its minimization problem can be efficiently solved with theoretical convergence guarantee and relatively low computational complexity. Extensive experimental testing on eight challenging image dataset shows that the proposed method has achieved highly competent objective performance compared to several state-of-the-art multi-view clustering methods.

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“…The multi-view method in [35] is based on the canonical correlation analysis in extraction of two-view filter-bank-based features for image classification task. Similarly, in [36] the authors rely on tensorbased canonical correlation analysis to perform multi-view dimensionality reduction. This approach can be used as a preprocessing step in multi-view learning in case of high-dimensional data.…”

Section: Introductionmentioning

confidence: 99%

Multi-view low-rank sparse subspace clustering

Brbić

Kopriva

2018

Pattern Recognition

349

119

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Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace representation by constructing affinity matrix shared among all views. Relying on the importance of both low-rank and sparsity constraints in the construction of the affinity matrix, we introduce the objective that balances between the agreement across different views, while at the same time encourages sparsity and low-rankness of the solution. Related low-rank and sparsity constrained optimization problem is for each view solved using the alternating direction method of multipliers. Furthermore, we extend our approach to cluster data drawn from nonlinear subspaces by solving the corresponding problem in a reproducing kernel Hilbert space. The proposed algorithm outperforms state-of-the-art multi-view subspace clustering algorithms on one synthetic and four real-world datasets.

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Tensor canonical correlation analysis for multi-view dimension reduction

Cited by 59 publications

References 17 publications

Multi-omic and multi-view clustering algorithms: review and cancer benchmark

Multi-omic and multi-view clustering algorithms: review and cancer benchmark

On Unifying Multi-view Self-Representations for Clustering by Tensor Multi-rank Minimization

Multi-view low-rank sparse subspace clustering

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