Hyper-Laplacian regularized multi-view subspace clustering with jointing representation learning and weighted tensor nuclear norm constraint

In recent years, tensor-Singular Value Decomposition (t-SVD) based tensor nuclear norm has achieved remarkable progress in multi-view subspace clustering. However, most existing clustering methods still have the following shortcomings: (a) It has no meaning in practical applications for singular values to be treated equally. (b) They often ignore that data samples in the real world usually exist in multiple nonlinear subspaces. In order to solve the above shortcomings, we propose a hyper-Laplacian regularized multi-view subspace clustering model that joints representation learning and weighted tensor nuclear norm constraint, namely JWHMSC. Specifically, in the JWHMSC model, firstly, in order to capture the global structure between different views, the subspace representation matrices of all views are stacked into a low-rank constrained tensor. Secondly, hyper-Laplace graph regularization is adopted to preserve the local geometric structure embedded in the high-dimensional ambient space. Thirdly, considering the prior information of singular values, the weighted tensor nuclear norm (WTNN) based on t-SVD is introduced to treat singular values differently, which makes the JWHMSC more accurately obtain the sample distribution of classification information. Finally, representation learning, WTNN constraint and hyper-Laplacian graph regularization constraint are integrated into a framework to obtain the overall optimal solution of the algorithm. Compared with the state-of-the-art method, the experimental results on eight benchmark datasets show the good performance of the proposed method JWHMSC in multi-view clustering.

Hypergraph-Supervised Deep Subspace Clustering

Auto-encoder (AE)-based deep subspace clustering (DSC) methods aim to partition high-dimensional data into underlying clusters, where each cluster corresponds to a subspace. As a standard module in current AE-based DSC, the self-reconstruction cost plays an essential role in regularizing the feature learning. However, the self-reconstruction adversely affects the discriminative feature learning of AE, thereby hampering the downstream subspace clustering. To address this issue, we propose a hypergraph-supervised reconstruction to replace the self-reconstruction. Specifically, instead of enforcing the decoder in the AE to merely reconstruct samples themselves, the hypergraph-supervised reconstruction encourages reconstructing samples according to their high-order neighborhood relations. By the back-propagation training, the hypergraph-supervised reconstruction cost enables the deep AE to capture the high-order structure information among samples, facilitating the discriminative feature learning and, thus, alleviating the adverse effect of the self-reconstruction cost. Compared to current DSC methods, relying on the self-reconstruction, our method has achieved consistent performance improvement on benchmark high-dimensional datasets.

DISA tool: discriminative and informative subspace assessment with categorical and numerical outcomes

Motivation: Pattern discovery and subspace clustering play a central role in the biological domain, supporting for instance putative regulatory module discovery from omic data for both descriptive and predictive ends. In the presence of target variables (e.g. phenotypes), regulatory patterns should further satisfy delineate discriminative power properties, well-established in the presence of categorical outcomes, yet largely disregarded for numerical outcomes, such as risk profiles and quantitative phenotypes. Results: DISA (Discriminative and Informative Subspace Assessment), a Python software package, is proposed to assess patterns in the presence of numerical outcomes using well-established measures together with a novel principle able to statistically assess the correlation gain of the subspace against the overall space. Results confirm the possibility to soundly extend discriminative criteria towards numerical outcomes without the drawbacks well-associated with discretization procedures. A case study is provided to show the properties of the proposed method. Availability: DISA is freely available at https://github.com/JupitersMight/DISA under the MIT license.

Optimization algorithm for omic data subspace clustering

Subspace clustering identifies multiple feature subspaces embedded in a dataset together with the underlying sample clusters. When applied to omic data, subspace clustering is a challenging task, as additional problems have to be addressed: the curse of dimensionality, the imperfect data quality and cluster separation, the presence of multiple subspaces representative of divergent views of the dataset, and the lack of consensus on the best clustering method. First, we propose a computational method discover to perform subspace clustering on tabular high dimensional data by maximizing the internal clustering score (i.e. cluster compactness) of feature subspaces. Our algorithm can be used in both unsupervised and semi-supervised settings. Secondly, by applying our method to a large set of omic datasets (i.e. microarray, bulk RNA-seq, scRNA-seq), we show that the subspace corresponding to the provided ground truth annotations is rarely the most compact one, as assumed by the methods maximizing the internal quality of clusters. Our results highlight the difficulty of fully validating subspace clusters (justified by the lack of feature annotations). Tested on identifying the ground-truth subspace, our method compared favorably with competing techniques on all datasets. Finally, we propose a suite of techniques to interpret the clustering results biologically in the absence of annotations. We demonstrate that subspace clustering can provide biologically meaningful sample-wise and feature-wise information, typically missed by traditional methods.