Identifying subspace gene clusters from microarray data using low-rank representation

Robust Principal Component Analysis Based On Hypergraph Regularization for Sample Clustering and Co-Characteristic Gene Selection

Extracting genes involved in cancer lesions from gene expression data is critical for cancer research and drug development. The method of feature selection has attracted much attention in the field of bioinformatics. Principal Component Analysis (PCA) is a widely used method for learning low-dimensional representation. Some variants of PCA have been proposed to improve the robustness and sparsity of the algorithm. However, the existing methods ignore the high-order relationships between data. In this paper, a new model named Robust Principal Component Analysis via Hypergraph Regularization (HRPCA) is proposed. In detail, HRPCA utilizes L2,1-norm to reduce the effect of outliers and make data sufficiently row-sparse. And the hypergraph regularization is introduced to consider the complex relationship among data. Important information hidden in the data are mined, and this method ensures the accuracy of the resulting data relationship information. Extensive experiments on multi-view biological data demonstrate that the feasible and effective of the proposed approach.

A truncated nuclear norm and graph-Laplacian regularized low-rank representation method for tumor clustering and gene selection

Background

Clustering and feature selection act major roles in many communities. As a matrix factorization, Low-Rank Representation (LRR) has attracted lots of attentions in clustering and feature selection, but sometimes its performance is frustrated when the data samples are insufficient or contain a lot of noise.

Results

To address this drawback, a novel LRR model named TGLRR is proposed by integrating the truncated nuclear norm with graph-Laplacian. Different from the nuclear norm minimizing all singular values, the truncated nuclear norm only minimizes some smallest singular values, which can dispel the harm of shrinkage of the leading singular values. Finally, an efficient algorithm based on Linearized Alternating Direction with Adaptive Penalty is applied to resolving the optimization problem.

Conclusions

The results show that the TGLRR method exceeds the existing state-of-the-art methods in aspect of tumor clustering and gene selection on integrated gene expression data.

One-Step Robust Low-Rank Subspace Segmentation for Tumor Sample Clustering

Clustering of tumor samples can help identify cancer types and discover new cancer subtypes, which is essential for effective cancer treatment. Although many traditional clustering methods have been proposed for tumor sample clustering, advanced algorithms with better performance are still needed. Low-rank subspace clustering is a popular algorithm in recent years. In this paper, we propose a novel one-step robust low-rank subspace segmentation method (ORLRS) for clustering the tumor sample. For a gene expression data set, we seek its lowest rank representation matrix and the noise matrix. By imposing the discrete constraint on the low-rank matrix, without performing spectral clustering, ORLRS learns the cluster indicators of subspaces directly, i.e., performing the clustering task in one step. To improve the robustness of the method, capped norm is adopted to remove the extreme data outliers in the noise matrix. Furthermore, we conduct an efficient solution to solve the problem of ORLRS. Experiments on several tumor gene expression data demonstrate the effectiveness of ORLRS.

Tensor Low-Rank Representation for Data Recovery and Clustering

Multi-way or tensor data analysis has attracted increasing attention recently, with many important applications in practice. This article develops a tensor low-rank representation (TLRR) method, which is the first approach that can exactly recover the clean data of intrinsic low-rank structure and accurately cluster them as well, with provable performance guarantees. In particular, for tensor data with arbitrary sparse corruptions, TLRR can exactly recover the clean data under mild conditions; meanwhile TLRR can exactly verify their true origin tensor subspaces and hence cluster them accurately. TLRR objective function can be optimized via efficient convex programing with convergence guarantees. Besides, we provide two simple yet effective dictionary construction methods, the simple TLRR (S-TLRR) and robust TLRR (R-TLRR), to handle slightly and severely corrupted data respectively. Experimental results on two computer vision data analysis tasks, image/video recovery and face clustering, clearly demonstrate the superior performance, efficiency and robustness of our developed method over state-of-the-arts including the popular LRR and SSC methods.

Non-Negative Symmetric Low-Rank Representation Graph Regularized Method for Cancer Clustering Based on Score Function

As an important approach to cancer classification, cancer sample clustering is of particular importance for cancer research. For high dimensional gene expression data, examining approaches to selecting characteristic genes with high identification for cancer sample clustering is an important research area in the bioinformatics field. In this paper, we propose a novel integrated framework for cancer clustering known as the non-negative symmetric low-rank representation with graph regularization based on score function (NSLRG-S). First, a lowest rank matrix is obtained after NSLRG decomposition. The lowest rank matrix preserves the local data manifold information and the global data structure information of the gene expression data. Second, we construct the Score function based on the lowest rank matrix to weight all of the features of the gene expression data and calculate the score of each feature. Third, we rank the features according to their scores and select the feature genes for cancer sample clustering. Finally, based on selected feature genes, we use the K-means method to cluster the cancer samples. The experiments are conducted on The Cancer Genome Atlas (TCGA) data. Comparative experiments demonstrate that the NSLRG-S framework can significantly improve the clustering performance.

Multi-cancer samples clustering via graph regularized low-rank representation method under sparse and symmetric constraints

Background

Identifying different types of cancer based on gene expression data has become hotspot in bioinformatics research. Clustering cancer gene expression data from multiple cancers to their own class is a significance solution. However, the characteristics of high-dimensional and small samples of gene expression data and the noise of the data make data mining and research difficult. Although there are many effective and feasible methods to deal with this problem, the possibility remains that these methods are flawed.

Results

In this paper, we propose the graph regularized low-rank representation under symmetric and sparse constraints (sgLRR) method in which we introduce graph regularization based on manifold learning and symmetric sparse constraints into the traditional low-rank representation (LRR). For the sgLRR method, by means of symmetric constraint and sparse constraint, the effect of raw data noise on low-rank representation is alleviated. Further, sgLRR method preserves the important intrinsic local geometrical structures of the raw data by introducing graph regularization. We apply this method to cluster multi-cancer samples based on gene expression data, which improves the clustering quality. First, the gene expression data are decomposed by sgLRR method. And, a lowest rank representation matrix is obtained, which is symmetric and sparse. Then, an affinity matrix is constructed to perform the multi-cancer sample clustering by using a spectral clustering algorithm, i.e., normalized cuts (Ncuts). Finally, the multi-cancer samples clustering is completed.

Conclusions

A series of comparative experiments demonstrate that the sgLRR method based on low rank representation has a great advantage and remarkable performance in the clustering of multi-cancer samples.

Low Rank Subspace Clustering via Discrete Constraint and Hypergraph Regularization for Tumor Molecular Pattern Discovery

Tumor clustering is a powerful approach for cancer class discovery which is crucial to the effective treatment of cancer. Many traditional clustering methods such as NMF-based models, have been widely used to identify tumors. However, they cannot achieve satisfactory results. Recently, subspace clustering approaches have been proposed to improve the performance by dividing the original space into multiple low-dimensional subspaces. Among them, low rank representation is becoming a popular approach to attain subspace clustering. In this paper, we propose a novel Low Rank Subspace Clustering model via Discrete Constraint and Hypergraph Regularization (DHLRS). The proposed method learns the cluster indicators directly by using discrete constraint, which makes the clustering task simple. For each subspace, we adopt Schatten -norm to better approximate the low rank constraint. Moreover, Hypergraph Regularization is adopted to infer the complex relationship between genes and intrinsic geometrical structure of gene expression data in each subspace. Finally, the molecular pattern of tumor gene expression data sets is discovered according to the optimized cluster indicators. Experiments on both synthetic data and real tumor gene expression data sets prove the effectiveness of proposed DHLRS.

Incorporating gene ontology into fuzzy relational clustering of microarray gene expression data

The product of gene expression works together in the cell for each living organism in order to achieve different biological processes. Many proteins are involved in different roles depending on the environment of the organism for the functioning of the cell. In this paper, we propose gene ontology (GO) annotations based semi-supervised clustering algorithm called GO fuzzy relational clustering (GO-FRC) where one gene is allowed to be assigned to multiple clusters which are the most biologically relevant behavior of genes. In the clustering process, GO-FRC utilizes useful biological knowledge which is available in the form of a gene ontology, as a prior knowledge along with the gene expression data. The prior knowledge helps to improve the coherence of the groups concerning the knowledge field. The proposed GO-FRC has been tested on the two yeast (Saccharomyces cerevisiae) expression profiles datasets (Eisen and Dream5 yeast datasets) and compared with other state-of-the-art clustering algorithms. Experimental results imply that GO-FRC is able to produce more biologically relevant clusters with the use of the small amount of GO annotations.

Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework

Subspace clustering refers to the problem of segmenting data drawn from a union of subspaces. State-of-the-art approaches for solving this problem follow a two-stage approach. In the first step, an affinity matrix is learned from the data using sparse or low-rank minimization techniques. In the second step, the segmentation is found by applying spectral clustering to this affinity. While this approach has led to the state-of-the-art results in many applications, it is suboptimal, because it does not exploit the fact that the affinity and the segmentation depend on each other. In this paper, we propose a joint optimization framework - Structured Sparse Subspace Clustering (S³C) - for learning both the affinity and the segmentation. The proposed S³C framework is based on expressing each data point as a structured sparse linear combination of all other data points, where the structure is induced by a norm that depends on the unknown segmentation. Moreover, we extend the proposed S³C framework into Constrained S³C (CS³C) in which available partial side-information is incorporated into the stage of learning the affinity. We show that both the structured sparse representation and the segmentation can be found via a combination of an alternating direction method of multipliers with spectral clustering. Experiments on a synthetic data set, the Extended Yale B face data set, the Hopkins 155 motion segmentation database, and three cancer data sets demonstrate the effectiveness of our approach.

Improved genome-scale multi-target virtual screening via a novel collaborative filtering approach to cold-start problem

Conventional one-drug-one-gene approach has been of limited success in modern drug discovery. Polypharmacology, which focuses on searching for multi-targeted drugs to perturb disease-causing networks instead of designing selective ligands to target individual proteins, has emerged as a new drug discovery paradigm. Although many methods for single-target virtual screening have been developed to improve the efficiency of drug discovery, few of these algorithms are designed for polypharmacology. Here, we present a novel theoretical framework and a corresponding algorithm for genome-scale multi-target virtual screening based on the one-class collaborative filtering technique. Our method overcomes the sparseness of the protein-chemical interaction data by means of interaction matrix weighting and dual regularization from both chemicals and proteins. While the statistical foundation behind our method is general enough to encompass genome-wide drug off-target prediction, the program is specifically tailored to find protein targets for new chemicals with little to no available interaction data. We extensively evaluate our method using a number of the most widely accepted gene-specific and cross-gene family benchmarks and demonstrate that our method outperforms other state-of-the-art algorithms for predicting the interaction of new chemicals with multiple proteins. Thus, the proposed algorithm may provide a powerful tool for multi-target drug design.