Xiang-Zhen Kong

Molecular cancer class discovery using non-negative matrix factorization with sparseness constraint

In cancer diagnosis and treatment, clustering based on gene expression data has been shown to be a powerful method in cancer class discovery. In this paper, we discuss the use of nonnegative matrix factorization with sparseness constraints (NMFSC), a method which can be used to learn a parts representation of the data, to analysis gene expression data. We illustrate how to choose appropriate sparseness factors in the algorithm and demonstrate the improvement of NMFSC by direct comparison with the nonnegative matrix factorization (NMF). In addition, when using it on the two well-studied datasets, we obtain pretty much the same results with the sparse non-negative matrix factorization (SNMF).

Identifying drug-pathway association pairs based on L 1 L 2,1 -integrative penalized matrix decomposition

The traditional methods of drug discovery follow the “one drug-one target” approach, which ignores the cellular and physiological environment of the action mechanism of drugs. However, pathway-based drug discovery methods can overcome this limitation. This kind of method, such as the Integrative Penalized Matrix Decomposition (iPaD) method, identifies the drug-pathway associations by taking the lasso-type penalty on the regularization term. Moreover, instead of imposing the L1-norm regularization, the L2,1-Integrative Penalized Matrix Decomposition (L2,1-iPaD) method imposes the L2,1-norm penalty on the regularization term. In this paper, based on the iPaD and L2,1-iPaD methods, we propose a novel method named L1L2,1-iPaD (L1L2,1-Integrative Penalized Matrix Decomposition), which takes the sum of the L1-norm and L2,1-norm penalties on the regularization term. Besides, we perform permutation test to assess the significance of the identified drug-pathway association pairs and compute the P-values. Compared with the existing methods, our method can identify more drug-pathway association pairs which have been validated in the CancerResource database. In order to identify drug-pathway associations which are not validated in the CancerResource database, we retrieve published papers to prove these associations. The results on two real datasets prove that our method can achieve better enrichment for identified association pairs than the iPaD and L2,1-iPaD methods.

Gene Extraction Based on Sparse Singular Value Decomposition

In this paper, we develop a new feature extraction method based on sparse singular value decomposition (SSVD). We apply SSVD algorithm to select the characteristic genes from Colorectal Cancer (CRC) genomic dataset, and then the differentially expressed genes obtained are evaluated by the tools based on Gene Ontology. As a gene extraction method, SSVD is also compared with some existing feature extraction methods such as independent component analysis (ICA), the p-norm robust feature extraction (PREE) and sparse principal component analysis (SPCA). The experimental results show that SSVD method outperforms the existing algorithms.

Performance Analysis of Non-negative Matrix Factorization Methods on TCGA Data.

Non-negative Matrix Factorization (NMF) is recognized as one of fundamentally important and highly popular methods for clustering and feature selection, and many related methods have been proposed so far. Nevertheless, their performances, especially on real data, are still unclear due to few studies focusing on their comparison. This study aims at a assessment study of several representative methods from clustering and feature selection, including NMF, GNMF, MD-NMF, L2,1NMF, LNMF, Convex-NMF and Semi-NMF, on the data of the Cancer Genome Atlas (TCGA), which is one of current research hotspot of bioinformatics. Specifically, three data types of four cancers are either separately or integratedly decomposed as the coefficient matrices and the basis matrices by these NMF methods. The coefficient matrices are evaluated by accuracies of clustered samples and the basis matrices are assessed by p-values of selected genes. Experiment results not only show merits and limitations of compared NMF methods, which may provide guidelines for applying them and proposing novel NMF methods, but also reveal several clues for the exploration of related cancers.

Robust and Efficient Biomolecular Clustering of Tumor Based on

High dimensionality has become a typical feature of biomolecular data. In this paper, a novel dimension reduction method named p-norm singular value decomposition (PSVD) is proposed to seek the low-rank approximation matrix to the biomolecular data. To enhance the robustness to outliers, the Lp-norm is taken as the error function and the Schatten p-norm is used as the regularization function in the optimization model. To evaluate the performance of PSVD, the Kmeans clustering method is then employed for tumor clustering based on the low-rank approximation matrix. Extensive experiments are carried out on five gene expression data sets including two benchmark data sets and three higher dimensional data sets from the cancer genome atlas. The experimental results demonstrate that the PSVD-based method outperforms many existing methods. Especially, it is experimentally proved that the proposed method is more efficient for processing higher dimensional data with good robustness, stability, and superior time performance.

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Tumor clustering based on biomolecular data plays a very important role for cancer classifications discovery. To further improve the robustness, stability and accuracy of tumor clustering, we develop a novel dimension reduction method named p-norm singular value decomposition (PSVD) to seek a low-rank approximation matrix to the bimolecular data. To enhance the robustness to outliers, the Lp-norm is taken as the error function and the Schatten p-norm is used as the regularization function in our optimization model. To evaluate the performance of PSVD, Kmeans clustering method is then employed for tumor clustering based on the low-rank approximation matrix. The extensive experiments are performed on gene expression dataset and cancer genome dataset respectively. All experimental results demonstrate that the PSVD-based method outperforms many existing methods. Especially it is experimentally proved that the proposed method is efficient for processing higher dimensional data with good robustness and superior time performance.

-Norm Singular Value Decomposition

Robust Principal Component Analysis (RPCA) is an efficient method in the selection of differentially expressed genes. However, nuclear norm minimizes all singular values simultaneously, so it may not be the best solution to replace the low-rank function. In this paper, the truncated nuclear norm is introduced. And a new method named Truncated nuclear norm regularized Robust Principal Component Analysis (TRPCA) is proposed. The method decomposes the observation matrix of genomic data into a low-rank matrix and a sparse matrix. The differentially expressed genes can be selected according to the sparse matrix. The experimental results on the The Cancer Genome Atlas (TCGA) data illustrate that the TRPCA method outperforms other state-of-the-art methods in the selection of differentially expressed genes.

A p-norm singular value decomposition method for robust tumor clustering

Recently, feature extraction and dimensionality reduction have become fundamental tools for many data mining tasks, especially for processing high-dimensional data such as genome data. In this paper, a new feature extraction method based on sparse singular value decomposition (SSVD) is developed. SSVD algorithm is applied to extract differentially expressed genes from two different genome datasets that are all from The Cancer Genome Atlas (TCGA), and then the extracted genes are evaluated by the tools based on Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) pathway enrichment analysis. As a gene extraction method, SSVD is also compared with some existing feature extraction methods such as independent component analysis, the p-norm robust feature extraction and sparse principal component analysis. The experimental GO analysis results show that SSVD method outperforms the competitive algorithms. The KEGG analysis results demonstrate the genes which participate in the pathways in cancer. The elaborate experiments prove that SSVD is an effective feature selection method compared with the competitive methods. The KEGG analysis results may provide a meaningful reference to carry out further study for professionals in the field of biomedical science.

Differentially expressed genes selection via Truncated Nuclear Norm Regularization

Tumor clustering is becoming a powerful method in cancer class discovery. In this community, non-negative matrix factorization (NMF) has shown its advantages, such as the accuracy and robustness of the representation, over other conventional clustering techniques. Though NMF has shown its efficiency in tumor clustering, there is a considerable room for improvement in clustering accuracy and robustness. In this paper, gene selection and explicitly enforcing sparseness are introduced into clustering process. The independent component analysis (ICA) is employed to select a subset of genes. The unsupervised methods NMF and its extensions, sparse NMF (SNMF) and NMF with sparseness constraint (NMFSC), are then used for tumor clustering on the subset of genes selected by ICA. The experimental results demonstrate the efficiency of the proposed scheme.