Towards improving fuzzy clustering using support vector machine: Application to gene expression data

Recent advancement in microarray technology permits monitoring of the expression levels of a large set of genes across a number of time points simultaneously. For extracting knowledge from such huge volume of microarray gene expression data, computational analysis is required. Clustering is one of the important data mining tools for analyzing such microarray data to group similar genes into clusters. Researchers have proposed a number of clustering algorithms in this purpose. In this article, an attempt has been made in order to improve the performance of fuzzy clustering by combining it with support vector machine (SVM) classifier. A recently proposed real-coded variable string length genetic algorithm based clustering technique and an iterated version of fuzzy C-means clustering have been utilized in this purpose. The performance of the proposed clustering scheme has been compared with that of some well-known existing clustering algorithms and their SVM boosted versions for one simulated and six real life gene expression data sets. Statistical significance test based on analysis of variance (ANOVA) followed by posteriori Tukey-Kramer multiple comparison test has been conducted to establish the statistical significance of the superior performance of the proposed clustering scheme. Moreover biological significance of the clustering solutions have been established.     

非负矩阵分解在微阵列数据分类和聚类发现中的应用

基因芯片是微阵列技术的典型代表,它具有高通量的特性和同时检测全部基因组基因表达水平的能力。应用微阵列芯片的一个主要目的是基因表达模式的发现,即在基因组水平发现功能相似,生物学过程相关的基因簇;或者将样本分类,发现样本的各种亚型。例如根据基因表达水平对癌症样本进行分类,发现疾病的分子亚型。非负矩阵分解NMF方法是一种非监督的、非正交的、基于局部表示的矩阵分解方法。近年来这种方法被越来越多地应用在微阵列数据的分类分析和聚类发现中。系统地介绍了非负矩阵分解的原理、算法和应用,分解结果的生物学解释,分类结果的质量评估和基于NMF算法的分类软件。总结并评估了NMF方法在微阵列数据分类和聚类发现应用中的表现。     

Cluster analysis for gene expression data: a survey

DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity for an enhanced understanding of functional genomics. However, the large number of genes and the complexity of biological networks greatly increases the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. A very rich literature on cluster analysis has developed over the past three decades. Many conventional clustering algorithms have been adapted or directly applied to gene expression data, and also new algorithms have recently been proposed specifically aiming at gene expression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. In particular, we divide cluster analysis for gene expression data into three categories. Then, we present specific challenges pertinent to each clustering category and introduce several representative approaches. We also discuss the problem of cluster validation in three aspects and review various methods to assess the quality and reliability of clustering results. Finally, we conclude this paper and suggest the promising trends in this field.     

Improvement of new automatic differential fuzzy clustering using SVM classifier for microarray analysis

In recent year, the problem of clustering in microarray data has been gaining significant attention. However most of the clustering methods attempt to find the group of genes where the number of cluster is known a priori. This fact motivated us to develop a new real-coded improved differential evolution based automatic fuzzy clustering algorithm which automatically evolves the number of clusters as well as the proper partitioning of a gene expression data set. To improve the result further, the clustering method is integrated with a support vector machine, a well-known technique for supervised learning. A fraction of the gene expression data points selected from different clusters based on their proximity to the respective centers, is used for training the SVM. The clustering assignments of the remaining gene expression data points are thereafter determined using the trained classifier. The performance of the proposed clustering technique has been demonstrated on five gene expression data sets by comparing it with the differential evolution based automatic fuzzy clustering, variable length genetic algorithm based fuzzy clustering and well known Fuzzy C-Means algorithm. Statistical significance test has been carried out to establish the statistical superiority of the proposed clustering approach. Biological significance test has also been carried out using a web based gene annotation tool to show that the proposed method is able to produce biologically relevant clusters of genes. The processed data sets and the matlab version of the software are available at http://bio.icm.edu.pl/～darman/IDEAFC-SVM/.     

基因表达数据的聚类分析研究进展

基因表达数据的爆炸性增长迫切需求自动、有效的数据分析工具. 目前聚类分析已成为分析基因表达数据获取生物学信息的有力工具. 为了更好地挖掘基因表达数据, 近年来提出了许多改进的传统聚类算法和新聚类算法. 本文首先简单介绍了基因表达数据的获取和表示, 之后系统地介绍了近年来应用在基因表达数据分析中的聚类算法. 根据聚类目标的不同将算法分为基于基因的聚类、基于样本的聚类和两路聚类, 并对每类算法介绍了其生物学的含义及其难点, 详细讨论了各种算法的基本原理及优缺点. 最后总结了当前的基因表达数据的聚类分析方法,并对发展趋势作了进一步的展望.     

An evolutionary clustering algorithm for gene expression microarray data analysis

Clustering is concerned with the discovery of interesting groupings of records in a database. Many algorithms have been developed to tackle clustering problems in a variety of application domains. In particular, some of them have been used in bioinformatics research to uncover inherent clusters in gene expression microarray data. In this paper, we show how some popular clustering algorithms have been used for this purpose. Based on experiments using simulated and real data, we also show that the performance of these algorithms can be further improved. For more effective clustering of gene expression microarray data, which is typically characterized by a lot of noise, we propose a novel evolutionary algorithm called evolutionary clustering (EvoCluster). EvoCluster encodes an entire cluster grouping in a chromosome so that each gene in the chromosome encodes one cluster. Based on such encoding scheme, it makes use of a set of reproduction operators to facilitate the exchange of grouping information between chromosomes. The fitness function that the EvoCluster adopts is able to differentiate between how relevant a feature value is in determining a particular cluster grouping. As such, instead of just local pairwise distances, it also takes into consideration how clusters are arranged globally. Unlike many popular clustering algorithms, EvoCluster does not require the number of clusters to be decided in advance. Also, patterns hidden in each cluster can be explicitly revealed and presented for easy interpretation even by casual users. For performance evaluation, we have tested EvoCluster using both simulated and real data. Experimental results show that it can be very effective and robust even in the presence of noise and missing values. Also, when correlating the gene expression microarray data with DNA sequences, we were able to uncover significant biological binding sites (both previously known and unknown) in each cluster discovered by EvoCluster.     

基因表达数据中的局部模式挖掘研究综述

基因微阵列(DNA microarray)是实验分子生物学中的一个重要突破,其使得研究者可以同时监测多个基因在多个实验条件下表达水平的变化,进而为发现基因协同表达网络、研制药物、预防疾病等提供技术支持.研究者们提出了大量的聚类算法来分析基因表达数据,但是标准的聚类算法(单向聚类)只能发现少量的知识.因为基因不可能在所有实验条件下共表达,也不可能展示出相同的表达水平,但是可能参与多种遗传通路.在这种情况下,双聚类方法应运而生.这样就将基因表达数据的分析从整体模式转向局部模式,从而改变了只根据数据的全部对象或属性将数据聚类的局面.主要从局部模式的定义、局部模式类型与标准、局部模式的挖掘与查询等方面进行了梳理.介绍了基因表达数据中局部模式挖掘当前的研究现状与进展,详细总结了基于定量和定性的局部模式挖掘标准以及相关的挖掘系统,分析了存在的问题,并深入探讨了未来的研究方向.     

Gene clustering for time-series microarray with production outputs

The identification of coexpressed genes from microarray data is a challenging problem in bioinformatics and computational biology. The objective of this study is to obtain knowledge about the most important genes and clusters related to production outputs of real-world time-series microarray data in the industrial microbiology area. Each sample in the microarray data experiment is complemented with the measurement of the corresponding production and growth values. A novel aspect of this research refers to considering the relation of coexpression patterns with the measured outputs to guide the biological interpretation of results. Shape-based clustering models are developed using the pattern of gene expression values over time and further incorporating knowledge about the correlation between the change in the gene expression level and the output value. Experiments are performed for time-series microarray of bacteria, and an analysis from a biological perspective is carried out. The obtained results confirm the existence of relationships between output variables and gene expressions. Moreover, the shape-based clustering methods show promising results, being able to guide metabolic engineering actions with the identification of potential targets.     

openModeller: a generic approach to species’ potential distribution modelling

Species’ potential distribution modelling is the process of building a representation of the fundamental ecological requirements for a species and extrapolating these requirements into a geographical region. The importance of being able to predict the distribution of species is currently highlighted by issues like global climate change, public health problems caused by disease vectors, anthropogenic impacts that can lead to massive species extinction, among other challenges. There are several computational approaches that can be used to generate potential distribution models, each achieving optimal results under different conditions. However, the existing software packages available for this purpose typically implement a single algorithm, and each software package presents a new learning curve to the user. Whenever new software is developed for species’ potential distribution modelling, significant duplication of effort results because many feature requirements are shared between the different packages. Additionally, data preparation and comparison between algorithms becomes difficult when using separate software applications, since each application has different data input and output capabilities. This paper describes a generic approach for building a single computing framework capable of handling different data formats and multiple algorithms that can be used in potential distribution modelling. The ideas described in this paper have been implemented in a free and open source software package called openModeller. The main concepts of species’ potential distribution modelling are also explained and an example use case illustrates potential distribution maps generated by the framework.     

Simulated annealing based automatic fuzzy clustering combined with ANN classification for analyzing microarray data

Microarray technology has made it possible to monitor the expression levels of many genes simultaneously across a number of experimental conditions. Fuzzy clustering is an important tool for analyzing microarray gene expression data. In this article, a real-coded Simulated Annealing (VSA) based fuzzy clustering method with variable length configuration is developed and combined with popular Artificial Neural Network (ANN) based classifier. The idea is to refine the clustering produced by VSA using ANN classifier to obtain improved clustering performance. The proposed technique is used to cluster three publicly available real life microarray data sets. The superior performance of the proposed technique has been demonstrated by comparing with some widely used existing clustering algorithms. Also statistical significance test has been conducted to establish the statistical significance of the superior performance of the proposed clustering algorithm. Finally biological relevance of the clustering solutions are established.     

Binary matrix factorization for analyzing gene expression data

The advent of microarray technology enables us to monitor an entire genome in a single chip using a systematic approach. Clustering, as a widely used data mining approach, has been used to discover phenotypes from the raw expression data. However traditional clustering algorithms have limitations since they can not identify the substructures of samples and features hidden behind the data. Different from clustering, biclustering is a new methodology for discovering genes that are highly related to a subset of samples. Several biclustering models/methods have been presented and used for tumor clinical diagnosis and pathological research. In this paper, we present a new biclustering model using Binary Matrix Factorization (BMF). BMF is a new variant rooted from non-negative matrix factorization (NMF). We begin by proving a new boundedness property of NMF. Two different algorithms to implement the model and their comparison are then presented. We show that the microarray data biclustering problem can be formulated as a BMF problem and can be solved effectively using our proposed algorithms. Unlike the greedy strategy-based algorithms, our proposed algorithms for BMF are more likely to find the global optima. Experimental results on synthetic and real datasets demonstrate the advantages of BMF over existing biclustering methods. Besides the attractive clustering performance, BMF can generate sparse results (i.e., the number of genes/features involved in each biclustering structure is very small related to the total number of genes/features) that are in accordance with the common practice in molecular biology.     

MicroClAn: Microarray clustering analysis

Evaluating clustering results is a fundamental task in microarray data analysis, due to the lack of enough biological knowledge to know in advance the true partition of genes. Many quality indexes for gene clustering evaluation have been proposed. A critical issue in this domain is to compare and aggregate quality indexes to select the best clustering algorithm and the optimal parameter setting for a dataset. Furthermore, due to the huge amount of data generated by microarray experiments and the requirement of external resources such as ontologies to compute biological indexes, another critical issue is the performance decline in term of execution time. Thus, the distributed computation of algorithms and quality indexes becomes essential. Addressing these issues, this paper presents the MicroClAn framework, a distributed system to evaluate and compare clustering algorithms using the most exploited quality indexes. The best solution is selected through a two-step ranking aggregation of the ranks produced by quality indexes. A new index oriented to the biological validation of microarray clustering results is also introduced. Several scheduling strategies integrated in the framework allow to distribute tasks in the grid environment to optimize the completion time. Experimental results show the effectiveness of our aggregation strategy in identifying the best rank among different clustering algorithms. Moreover, our framework achieves good performance in terms of completion time with few computational resources.     

A Novel Approach to Revealing Positive and Negative Co-Regulated Genes

As explored by biologists, there is a real and emerging need to identify co-regulated gene clusters, which include both positive and negative regulated gene clusters. However, the existing pattern-based and tendency-based clustering approaches are only designed for finding positive regulated gene clusters. In this paper, a new subspace clustering model called g-Cluster is proposed for gene expression data. The proposed model has the following advantages： 1） find both positive and negative co-regulated genes in a shot, 2） get away from the restriction of magnitude transformation relationship among co-regulated genes, and 3） guarantee quality of clusters and significance of regulations using a novel similarity measurement gCode and a user-specified regulation threshold δ, respectively. No previous work measures up to the task which has been set. Moreover, MDL technique is introduced to avoid insignificant g-Clusters generated. A tree structure, namely GS-tree, is also designed, and two algorithms combined with efficient pruning and optimization strategies to identify all qualified g-Clusters. Extensive experiments are conducted on real and synthetic datasets. The experimental results show that 1） the algorithm is able to find an amount of co-regulated gene clusters missed by previous models, which are potentially of high biological significance, and 2） the algorithms are effective and efficient, and outperform the existing approaches.     

Dynamic range-based distance measure for microarray expressions and a fast gene-ordering algorithm.

This investigation deals with a new distance measure for genes using their microarray expressions and a new algorithm for fast gene ordering without clustering. This distance measure is called "Maxrange distance," where the distance between two genes corresponding to a particular type of experiment is computed using a normalization factor, which is dependent on the dynamic range of the gene expression values of that experiment. The new gene-ordering method called "Minimal Neighbor" is based on the concept of nearest neighbor heuristic involving O(n2) time complexity. The superiority of this distance measure and the comparability of the ordering algorithm have been extensively established on widely studied microarray data sets by performing statistical tests. An interesting application of this ordering algorithm is also demonstrated for finding useful groups of genes within clusters obtained from a nonhierarchical clustering method like the self-organizing map.     

Bifurcation Analysis of Railway Vehicles

To identify the long-time behaviour of nonlinear dynamical systems with respect to the influence of one or more system parameters, numerical bifurcation analysis is an ideal computer-aided method. The objective of the paper is to describe a software environment for such an analysis that is based on the principles of path-following or continuation. A specific viewpoint is the application to ‘realistic’, i.e. detailed and complex simulation models of railway vehicles following a multibody system approach. Stationary as well as periodic behaviour is considered. Three major topics are of primary interest: The integration of a bifurcation software into a software package for the simulation of arbitrary mechanical systems; the direct calculation of periodic solutions (limit cycles); and the handling of differential algebraic equations (DAEs). The algorithms are applied finally to the ‘realistic’ simulation model of a high-speed railway passenger car.     

Mining microarray gene expression data with unsupervised possibilistic clustering and proximity graphs

Gene expression data generated by DNA microarray experiments provide a vast resource of medical diagnostic and disease understanding. Unfortunately, the large amount of data makes it hard, sometimes even impossible, to understand the correct behavior of genes. In this work, we develop a possibilistic approach for mining gene microarray data. Our model consists of two steps. In the first step, we use possibilistic clustering to partition the data into groups (or clusters). The optimal number of clusters is evaluated automatically from the data using the Information Entropy as a validity measure. In the second step, we select from each computed cluster the most representative genes and model them as a graph called a proximity graph. This set of graphs (or hyper-graph) will be used to predict the function of new and previously unknown genes. Experimental results using real-world data sets reveal a good performance and a high prediction accuracy of our model.     

Analysis and Visualization of Gene Expression Microarray Data in Human Cancer Using Self-Organizing Maps

cDNA microarrays permit massively parallel gene expression analysis and have spawned a new paradigm in the study of molecular biology. One of the significant challenges in this genomic revolution is to develop sophisticated approaches to facilitate the visualization, analysis, and interpretation of the vast amounts of multi-dimensional gene expression data. We have applied self-organizing map (SOM) in order to meet these challenges. In essence, we utilize U-matrix and component planes in microarray data visualization and introduce general procedure for assessing significance for a cluster detected from U-matrix. Our case studies consist of two data sets. First, we have analyzed a data set containing 13,824 genes in 14 breast cancer cell lines. In the second case we show an example of the SOM in drug treatment of prostate cancer cells. Our results indicate that (1) SOM is capable of helping finding certain biologically meaningful clusters, (2) clustering algorithms could be used for finding a set of potential predictor genes for classification purposes, and (3) comparison and visualization of the effects of different drugs is straightforward with the SOM. In summary, the SOM provides an excellent format for visualization and analysis of gene microarray data, and is likely to facilitate extraction of biologically and medically useful information.     

基于聚类和微粒群优化的基因选择新方法

鉴于传统的基因选择方法会选出大量冗余基因从而导致较低的样本预测准确率,提出一种基于聚类和微粒群优化的基因选择算法。首先采用聚类算法将基因分成固定数目的簇;然后,采用极限学习机作为分类器进行簇中的特征基因分类性能评价,得到一个备选基因库;最后,采用基于微粒群优化和极限学习机的缠绕法从备选基因库中选择具有最大分类率、最小数目的基因子集。所选出的基因具有良好的分类性能。在两个公开的微阵列数据集上的实验结果表明,相对于一些经典的方法,新方法能够以较少的基因获得更高的分类性能。     

An interactive approach to mining gene expression data

Effective identification of coexpressed genes and coherent patterns in gene expression data is an important task in bioinformatics research and biomedical applications. Several clustering methods have recently been proposed to identify coexpressed genes that share similar coherent patterns. However, there is no objective standard for groups of coexpressed genes. The interpretation of co-expression heavily depends on domain knowledge. Furthermore, groups of coexpressed genes in gene expression data are often highly connected through a large number of "intermediate" genes. There may be no clear boundaries to separate clusters. Clustering gene expression data also faces the challenges of satisfying biological domain requirements and addressing the high connectivity of the data sets. In this paper, we propose an interactive framework for exploring coherent patterns in gene expression data. A novel coherent pattern index is proposed to give users highly confident indications of the existence of coherent patterns. To derive a coherent pattern index and facilitate clustering, we devise an attraction tree structure that summarizes the coherence information among genes in the data set. We present efficient and scalable algorithms for constructing attraction trees and coherent pattern indices from gene expression data sets. Our experimental results show that our approach is effective in mining gene expression data and is scalable for mining large data sets.     

Measuring gene similarity by means of the classification distance

Microarray technology provides a simple way for collecting huge amounts of data on the expression level of thousands of genes. Detecting similarities among genes is a fundamental task, both to discover previously unknown gene functions and to focus the analysis on a limited set of genes rather than on thousands of genes. Similarity between genes is usually evaluated by analyzing their expression values. However, when additional information is available (e.g., clinical information), it may be beneficial to exploit it. In this paper, we present a new similarity measure for genes, based on their classification power, i.e., on their capability to separate samples belonging to different classes. Our method exploits a new gene representation that measures the classification power of each gene and defines the classification distance as the distance between gene classification powers. The classification distance measure has been integrated in a hierarchical clustering algorithm, but it may be adopted also by other clustering algorithms. The result of experiments runs on different microarray datasets supports the intuition of the proposed approach.