Low-Rank Tensor Constrained Multiview Subspace Clustering

Zhang, Changqing; Fu, Huazhu; Liu, Si; Liu, Guangcan; Cao, Xiaochun

doi:10.1109/iccv.2015.185

Cited by 440 publications

(237 citation statements)

References 27 publications

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“…A natural extension of factorization methods for multi-omic data is to use tensors, which are higher order matrices. One such method is developed in [64]. This method writes each omic matrix as X m = Z m X m + E m , diag(Z m ) = 0, where Z m is an n x n matrix and E m are error matrices.…”

Section: Tensor-based Methodsmentioning

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: Tensor-based Methodsmentioning

confidence: 99%

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

Rappoport

Shamir

2018

Preprint

143

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“…Without prior, we set ξ 1 = … = ξ M = 1 /M . 𝓚 ∈ ℝ I 1 × I 2 ×…× I M is a M -order tensor, and K ( m ) is the matrix by unfolding the tensor 𝓚 along the m th mode defined as unfold m (𝓚) = K ( m ) ∈ ℝ I m ×( I 1 ×…× I m −1 × I m +1 …× I M ) (De Lathauwer et al 2000; Zhang et al 2015). The nuclear norm ||·|| * controls the tensor under a low-rank constraint.…”

Section: Problem Formulationmentioning

confidence: 99%

Multi-view feature selection and classification for Alzheimer’s Disease diagnosis

Zhang

Yang

Shen

et al. 2016

Multimed Tools Appl

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In this paper, we propose a novel multi-view learning method for Alzheimer’s Disease (AD) diagnosis, using neuroimaging and genetics data. Generally, there are several major challenges associated with traditional classification methods on multi-source imaging and genetics data. First, the correlation between the extracted imaging features and class labels is generally complex, which often makes the traditional linear models ineffective. Second, medical data may be collected from different sources (i.e., multiple modalities of neuroimaging data, clinical scores or genetics measurements), therefore, how to effectively exploit the complementarity among multiple views is of great importance. In this paper, we propose a Multi-Layer Multi-View Classification (ML-MVC) approach, which regards the multi-view input as the first layer, and constructs a latent representation to explore the complex correlation between the features and class labels. This captures the high-order complementarity among different views, as we exploit the underlying information with a low-rank tensor regularization. Intrinsically, our formulation elegantly explores the nonlinear correlation together with complementarity among different views, and thus improves the accuracy of classification. Finally, the minimization problem is solved by the Alternating Direction Method of Multipliers (ADMM). Experimental results on Alzheimers Disease Neuroimaging Initiative (ADNI) data sets validate the effectiveness of our proposed method.

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“…The existing multi-view learning methods can be divided into two categories, i.e., supervised/semi-supervised [7], [28], [29], [30] and unsupervised methods [31], [10], [22], [32], [33]. For unsupervised multi-view dimensionality reduction, Canonical Correlation Analysis (CCA) and its variants [10], [23] are widely utilized as a joint dimensionality reduction technique.…”

Section: B Multi-view Learningmentioning

confidence: 99%

Flexible Multi-View Dimensionality Co-Reduction

Zhang

et al. 2017

IEEE Trans. on Image Process.

Self Cite

125

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Dimensionality reduction aims to map the high-dimensional inputs onto a low-dimensional subspace, in which the similar points are close to each other and vice versa. In this paper, we focus on unsupervised dimensionality reduction for the data with multiple views, and propose a novel method, called Multi-view Dimensionality co-Reduction. Our method flexibly exploits the complementarity of multiple views during the dimensionality reduction and respects the similarity relationships between data points across these different views. The kernel matching constraint based on Hilbert-Schmidt Independence Criterion enhances the correlations and penalizes the disagreement of different views. Specifically, our method explores the correlations within each view independently, and maximizes the dependence among different views with kernel matching jointly. Thus, the locality within each view and the consistence between different views are guaranteed in the subspaces corresponding to different views. More importantly, benefiting from the kernel matching, our method need not depend on a common low-dimensional subspace, which is critical to reduce the influence of the unbalanced dimensionalities of multiple views. Specifically, our method explicitly produces individual low-dimensional projections for individual views, which could be applied for new coming data in the out-of-sample manner. Experiments on both clustering and recognition tasks demonstrate the advantages of the proposed method over the state-of-the-art approaches.

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Low-Rank Tensor Constrained Multiview Subspace Clustering

Cited by 440 publications

References 27 publications

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

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

Multi-view feature selection and classification for Alzheimer’s Disease diagnosis

Flexible Multi-View Dimensionality Co-Reduction

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