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In gene expression data analysis, the problems of cancer classification and gene selection are closely related. Successfully selecting informative genes will significantly improve the classification performance. To identify informative genes from a large number of candidate genes, various methods have been proposed. However, the gene expression data may include some important correlation structures, and some of the genes can be divided into different groups based on their biological pathways. Many existing methods do not take into consideration the exact correlation structure within the data. Therefore, from both the knowledge discovery and biological perspectives, an ideal gene selection method should take this structural information into account. Moreover, the better generalization performance can be obtained by discovering correlation structure within data. In order to discover structure information among data and improve learning performance, we propose a structured penalized logistic regression model which simultaneously performs feature selection and model learning for gene expression data analysis. An efficient coordinate descent algorithm has been developed to optimize the model. The numerical simulation studies demonstrate that our method is able to select the highly correlated features. In addition, the results from real gene expression datasets show that the proposed method performs competitively with respect to previous approaches. [ABSTRACT FROM AUTHOR]

Traditional cluster ensemble approaches have several limitations. (1) Few make use of prior knowledge provided by experts. (2) It is difficult to achieve good performance in high-dimensional datasets. (3) All of the weight values of the ensemble members are equal, which ignores different contributions from different ensemble members. (4) Not all pairwise constraints contribute to the final result. In the face of this situation, we propose double weighting semi-supervised ensemble clustering based on selected constraint projection(DCECP) which applies constraint weighting and ensemble member weighting to address these limitations. Specifically, DCECP first adopts the random subspace technique in combination with the constraint projection procedure to handle high-dimensional datasets. Second, it treats prior knowledge of experts as pairwise constraints, and assigns different subsets of pairwise constraints to different ensemble members. An adaptive ensemble member weighting process is designed to associate different weight values with different ensemble members. Third, the weighted normalized cut algorithm is adopted to summarize clustering solutions and generate the final result. Finally, nonparametric statistical tests are used to compare multiple algorithms on real-world datasets. Our experiments on 15 high-dimensional datasets show that DCECP performs better than most clustering algorithms. [ABSTRACT FROM AUTHOR]

The objective of cluster structure ensemble is to find a unified cluster structure from multiple cluster structures obtained from different datasets. Unfortunately, not all the cluster structures contribute to the unified cluster structure. This paper investigates the problem of how to select the suitable cluster structures in the ensemble which will be summarized to a more representative cluster structure. Specifically, the cluster structure is first represented by a mixture of Gaussian distributions, the parameters of which are estimated using the expectation–maximization algorithm. Then, several distribution-based distance functions are designed to evaluate the similarity between two cluster structures. Based on the similarity comparison results, we propose a new approach, which is referred to as the distribution-based cluster structure ensemble (DCSE) framework, to find the most representative unified cluster structure. We then design a new technique, the distribution-based cluster structure selection strategy (DCSSS), to select a subset of cluster structures. Finally, we propose using a distribution-based normalized hypergraph cut algorithm to generate the final result. In our experiments, a nonparametric test is adopted to evaluate the difference between DCSE and its competitors. We adopt 20 real-world datasets obtained from the University of California, Irvine and knowledge extraction based on evolutionary learning repositories, and a number of cancer gene expression profiles to evaluate the performance of the proposed methods. The experimental results show that: 1) DCSE works well on the real-world datasets and 2) DCSE based on DCSSS can further improve the performance of the algorithm. [ABSTRACT FROM PUBLISHER]

Traditional cluster ensemble approaches have three limitations: ($1$ ) They do not make use of prior knowledge of the datasets given by experts. ($2$ ) Most of the conventional cluster ensemble methods cannot obtain satisfactory results when handling high dimensional data. ( $3$) All the ensemble members are considered, even the ones without positive contributions. In order to address the limitations of conventional cluster ensemble approaches, we first propose an incremental semi-supervised clustering ensemble framework (ISSCE) which makes use of the advantage of the random subspace technique, the constraint propagation approach, the proposed incremental ensemble member selection process, and the normalized cut algorithm to perform high dimensional data clustering. The random subspace technique is effective for handling high dimensional data, while the constraint propagation approach is useful for incorporating prior knowledge. The incremental ensemble member selection process is newly designed to judiciously remove redundant ensemble members based on a newly proposed local cost function and a global cost function, and the normalized cut algorithm is adopted to serve as the consensus function for providing more stable, robust, and accurate results. Then, a measure is proposed to quantify the similarity between two sets of attributes, and is used for computing the local cost function in ISSCE. Next, we analyze the time complexity of ISSCE theoretically. Finally, a set of nonparametric tests are adopted to compare multiple semi-supervised clustering ensemble approaches over different datasets. The experiments on 18 real-world datasets, which include six UCI datasets and 12 cancer gene expression profiles, confirm that ISSCE works well on datasets with very high dimensionality, and outperforms the state-of-the-art semi-supervised clustering ensemble approaches. [ABSTRACT FROM PUBLISHER]

Tumor clustering is one of the important techniques for tumor discovery from cancer gene expression profiles, which is useful for the diagnosis and treatment of cancer. While different algorithms have been proposed for tumor clustering, few make use of the expert’s knowledge to better the performance of tumor discovery. In this paper, we first view the expert’s knowledge as constraints in the process of clustering, and propose a feature selection based semi-supervised cluster ensemble framework (FS-SSCE) for tumor clustering from bio-molecular data. Compared with traditional tumor clustering approaches, the proposed framework FS-SSCE is featured by two properties: (1) The adoption of feature selection techniques to dispel the effect of noisy genes. (2) The employment of the binate constraint based K-means algorithm to take into account the effect of experts’ knowledge. Then, a double selection based semi-supervised cluster ensemble framework (DS-SSCE) which not only applies the feature selection technique to perform gene selection on the gene dimension, but also selects an optimal subset of representative clustering solutions in the ensemble and improve the performance of tumor clustering using the normalized cut algorithm. DS-SSCE also introduces a confidence factor into the process of constructing the consensus matrix by considering the prior knowledge of the data set. Finally, we design a modified double selection based semi-supervised cluster ensemble framework (MDS-SSCE) which adopts multiple clustering solution selection strategies and an aggregated solution selection function to choose an optimal subset of clustering solutions. The results in the experiments on cancer gene expression profiles show that ($\rm i$) FS-SSCE, DS-SSCE and MDS-SSCE are suitable for performing tumor clustering from bio-molecular data. ( $\rm ii$) MDS-SSCE outperforms a number of state-of-the-art tumor clustering approaches on most of the data sets. [ABSTRACT FROM PUBLISHER]

Similarity measurement is one of the most important stages in the process of cancer discovery from gene expression data. Traditional distance functions, such as the Euclidean distance, the correlation coefficient measure, the cosine distance, and so on, are selected to quantify the similarity between two cancer samples. However, these measures do not take into account the properties of cancer samples and do not consider the relationships among the genes in gene expression data. In order to explore the properties of cancer samples and the relationships among genes, we design a new similarity measure called representative distance (RD) to identify cancer samples in gene expression data. Specifically, RD does not compute the distance between two cancer samples using all the genes, but only calculates the similarity using representative genes selected by the affinity propagation algorithm. Then, a similarity matrix is constructed based on the representative distance. Finally, the spectral clustering algorithm is adopted to partition the similarity matrix, and discover the biological meaningful samples. To our knowledge, this is the first time in which the representative distance is applied to class discovery for gene expression data. Experiments on real cancer datasets indicate that our similarity measure can i) outperform most of the traditional distance measures, ii) identify cancer samples correctly in most of the datasets. [ABSTRACT FROM PUBLISHER]

In order to perform successful diagnosis and treatment of cancer, discovering, and classifying cancer types correctly is essential. One of the challenging properties of class discovery from cancer data sets is that cancer gene expression profiles not only include a large number of genes, but also contains a lot of noisy genes. In order to reduce the effect of noisy genes in cancer gene expression profiles, we propose two new consensus clustering frameworks, named as triple spectral clustering-based consensus clustering (SC^3) and double spectral clustering-based consensus clustering (SC^2Ncut) in this paper, for cancer discovery from gene expression profiles. SC^3 integrates the spectral clustering (SC) algorithm multiple times into the ensemble framework to process gene expression profiles. Specifically, spectral clustering is applied to perform clustering on the gene dimension and the cancer sample dimension, and also used as the consensus function to partition the consensus matrix constructed from multiple clustering solutions. Compared with SC^3, SC^2Ncut adopts the normalized cut algorithm, instead of spectral clustering, as the consensus function. Experiments on both synthetic data sets and real cancer gene expression profiles illustrate that the proposed approaches not only achieve good performance on gene expression profiles, but also outperforms most of the existing approaches in the process of class discovery from these profiles. [ABSTRACT FROM PUBLISHER]

Feature selection is widely established as one of the fundamental computational techniques in mining microarray data. Due to the lack of categorized information in practice, unsupervised feature selection is more practically important but correspondingly more difficult. Motivated by the cluster ensemble techniques, which combine multiple clustering solutions into a consensus solution of higher accuracy and stability, recent efforts in unsupervised feature selection proposed to use these consensus solutions as oracles. However, these methods are dependent on both the particular cluster ensemble algorithm used and the knowledge of the true cluster number. These methods will be unsuitable when the true cluster number is not available, which is common in practice. In view of the above problems, a new unsupervised feature ranking method is proposed to evaluate the importance of the features based on consensus affinity. Different from previous works, our method compares the corresponding affinity of each feature between a pair of instances based on the consensus matrix of clustering solutions. As a result, our method alleviates the need to know the true number of clusters and the dependence on particular cluster ensemble approaches as in previous works. Experiments on real gene expression data sets demonstrate significant improvement of the feature ranking results when compared to several state-of-the-art techniques. [ABSTRACT FROM PUBLISHER]

Highlights • we develop a new formulation for MTL based on the decomposition of the coeffcient matrix into a Hadamard (element-wise) product of two matrices. Comparing with conventional MTL methods and EL, the advantages of the proposed approach can be summarized as follows: (1) It is capable of capturing the competitive structure among tasks. (2) Unimportant features which are common across the tasks can be removed from the final model. Moreover, we propose to employ an alternating optimization method to iteratively estimate the coeffcients of the two components in the SpEL objective function. • We also provide an analysis of the proposed model based on the element- wise product decomposition framework to highlight its advantage. • We conduct experimental studies on both synthetic and real data in different application domains which include handwritten digit data and gene expression analysis. The experimental results demonstrate the effectiveness of the proposed model, and suggest potential applications of the proposed method. Abstract Multi-task learning (MTL) aims to enhance generalization performance by exploring the inherent structures across tasks. Most existing MTL methods are based on the assumption that the tasks are positively correlated, and utilize the shared structures among tasks to improve learning performance. By contrast, there also exist competitive structure (negative relationships) among tasks in some real-world applications, and conventional MTL methods which explore shared structures across tasks may lead to unsatisfactory performance in this setting. Another challenge, especially in a high dimensional setting, is to exclude irrelevant features (sparse structure) from the final model. For this purpose, this work propose a new method, which is referred to as Sparse Exclusive Lasso (SpEL) for multi-task learning. The proposed SpEL is able to capture the competitive relationship among tasks (competitive structure), while remove unimportant features which are common across the tasks from the final model (sparse structure). Experimental studies on synthetic and real data indicate that the proposed method can significantly improve learning performance by identifying sparse and task-competitive structures simultaneously. [ABSTRACT FROM AUTHOR]

Abstract: Cluster ensemble approaches make use of a set of clustering solutions which are derived from different data sources to gain a more comprehensive and significant clustering result over conventional single clustering approaches. Unfortunately, not all the clustering solutions in the ensemble contribute to the final result. In this paper, we focus on the clustering solution selection strategy in the cluster ensemble, and propose to view clustering solutions as features such that suitable feature selection techniques can be used to perform clustering solution selection. Furthermore, a hybrid clustering solution selection strategy (HCSS) is designed based on a proposed weighting function, which combines several feature selection techniques for the refinement of clustering solutions in the ensemble. Finally, a new measure is designed to evaluate the effectiveness of clustering solution selection strategies. The experimental results on both UCI machine learning datasets and cancer gene expression profiles demonstrate that HCSS works well on most of the datasets, obtains more desirable final results, and outperforms most of the state-of-the-art clustering solution selection strategies. [Copyright &y& Elsevier]