BSig: evaluating the statistical significance of biclustering solutions

Statistical evaluation of biclustering solutions is essential to guarantee the absence of spurious relations and to validate the high number of scientific statements inferred from unsupervised data analysis without a proper statistical ground. Most biclustering methods rely on merit functions to discover biclusters with specific homogeneity criteria. However, strong homogeneity does not guarantee the statistical significance of biclustering solutions. Furthermore, although some biclustering methods test the statistical significance of specific types of biclusters, there are no methods to assess the significance of flexible biclustering models. This work proposes a method to evaluate the statistical significance of biclustering solutions. It integrates state-of-the-art statistical views on the significance of local patterns and extends them with new principles to assess the significance of biclusters with additive, multiplicative, symmetric, order-preserving and plaid coherencies. The proposed statistical tests provide the unprecedented possibility to minimize the number of false positive biclusters without incurring on false negatives, and to compare state-of-the-art biclustering algorithms according to the statistical significance of their outputs. Results on synthetic and real data support the soundness and relevance of the proposed contributions, and stress the need to combine significance and homogeneity criteria to guide the search for biclusters.     

A probabilistic relaxation labeling framework for reducing the noise effect in geometric biclustering of gene expression data

Biclustering is an important method in DNA microarray analysis which can be applied when only a subset of genes is co-expressed in a subset of conditions. Unlike standard clustering analyses, biclustering methodology can perform simultaneous classification on two dimensions of genes and conditions in a microarray data matrix. However, the performance of biclustering algorithms is affected by the inherent noise in data, types of biclusters and computational complexity. In this paper, we present a geometric biclustering method based on the Hough transform and the relaxation labeling technique. Unlike many existing biclustering algorithms, we first consider the biclustering patterns through geometric interpretation. Such a perspective makes it possible to unify the formulation of different types of biclusters as hyperplanes in spatial space and facilitates the use of a generic plane finding algorithm for bicluster detection. In our algorithm, the Hough transform is employed for hyperplane detection in sub-spaces to reduce the computational complexity. Then sub-biclusters are combined into larger ones under the probabilistic relaxation labeling framework. Our simulation studies demonstrate the robustness of the algorithm against noise and outliers. In addition, our method is able to extract biologically meaningful biclusters from real microarray gene expression data.     

Biclustering of human cancer microarray data using co-similarity based co-clustering

Biclustering of gene expression data aims at finding localized patterns in a subspace. A bicluster (sometimes called a co-cluster), in the context of gene expression data, is a set of genes that exhibit similar expression intensity under a subset of experimental features (conditions). Most biclustering algorithms proposed in the literature aim at finding sub-matrices that exhibit some sort of coherence by selecting an initial sub-matrix and iteratively adding or subtracting rows and columns. These algorithms are generally dependent on the initial, hard selection of the gene and condition clusters respectively. In this work, we adapt a recently proposed approach for clustering textual data to find biclusters in gene expression data. Our proposed technique is based on the concept of co-similarity between genes (and between conditions) that exploits weighted higher order paths in a bipartite graph representation of the gene expression data. Therefore, we build statistical relations between genes and between conditions by comparing all genes and conditions before finally extracting biclusters from the data. We show that the proposed technique is able to find meaningful non-overlapping biclusters both on synthetically generated data as well as real cancer data. Our results indicate that the proposed technique is resistant to noise in the data and can successfully retrieve biclusters even in the presence of relatively large amount of noise. We also analyze our results with respect to the discovered genes and observe that our extracted biclusters are supported by biological evidences, such as enrichment of gene functions and biological processes.     

Using the bagging approach for biclustering of gene expression data

Several methods have been proposed for microarray data analysis that enables to identify groups of genes with similar expression profiles only under a subset of examples. We propose to improve the performance of these biclustering methods by adapting the approach of bagging to biclustering problems. The principle consists in generating a set of biclusters and aggregating the results. Our method has been tested with success on both synthetic and real datasets.     

Biclustering meets triadic concept analysis

Biclustering numerical data became a popular data-mining task at the beginning of 2000’s, especially for gene expression data analysis and recommender systems. A bicluster reflects a strong association between a subset of objects and a subset of attributes in a numerical object/attribute data-table. So-called biclusters of similar values can be thought as maximal sub-tables with close values. Only few methods address a complete, correct and non-redundant enumeration of such patterns, a well-known intractable problem, while no formal framework exists. We introduce important links between biclustering and Formal Concept Analysis (FCA). Indeed, FCA is known to be, among others, a methodology for biclustering binary data. Handling numerical data is not direct, and we argue that Triadic Concept Analysis (TCA), the extension of FCA to ternary relations, provides a powerful mathematical and algorithmic framework for biclustering numerical data. We discuss hence both theoretical and computational aspects on biclustering numerical data with triadic concept analysis. These results also scale to n-dimensional numerical datasets.     

Gene interaction – An evolutionary biclustering approach

DNA Microarray experiments form a powerful tool for studying gene expression patterns, in large scale. Sharing of the regulatory mechanism among genes, in an organism, is predominantly responsible for their co-expression. Biclustering aims at finding a subset of similarly expressed genes under a subset of experimental conditions. A small number of genes participate in a cellular process of interest. Again, a gene may be simultaneously involved in a number of cellular processes. In cellular environment, genes interact among themselves to produce enzymes, metabolites, proteins, etc. responsible for a particular function(s).In this study, a simple and novel correlation-based approach is proposed to extract gene interaction networks from biclusters in microarray data. Local search strategy is employed to add (remove) relevant (irrelevant) genes for finer tuning, in multi-objective biclustering framework. Preprocessing is done to preserve strongly correlated gene interaction pairs. Experimental results on time-series gene expression data from Yeast are biologically validated using benchmark databases and literature.     

BicFinder: a biclustering algorithm for microarray data analysis

In the context of microarray data analysis, biclustering allows the simultaneous identification of a maximum group of genes that show highly correlated expression patterns through a maximum group of experimental conditions (samples). This paper introduces a heuristic algorithm called BicFinder (The BicFinder software is available at: ) for extracting biclusters from microarray data. BicFinder relies on a new evaluation function called Average Correspondence Similarity Index (ACSI) to assess the coherence of a given bicluster and utilizes a directed acyclic graph to construct its biclusters. The performance of BicFinder is evaluated on synthetic and three DNA microarray datasets. We test the biological significance using a gene annotation web-tool to show that our proposed algorithm is able to produce biologically relevant biclusters. Experimental results show that BicFinder is able to identify coherent and overlapping biclusters.     

Random walk biclustering for microarray data

A biclustering algorithm, based on a greedy technique and enriched with a local search strategy to escape poor local minima, is proposed. The algorithm starts with an initial random solution and searches for a locally optimal solution by successive transformations that improve a gain function. The gain function combines the mean squared residue, the row variance, and the size of the bicluster. Different strategies to escape local minima are introduced and compared. Experimental results on several microarray data sets show that the method is able to find significant biclusters, also from a biological point of view.     

基于逻辑运算的离散人工蜂群优化双聚类算法

基因表达数据是由DNA微阵列实验产生的大规模数据矩阵,双聚类算法是挖掘数据矩阵中具有较高相关性的子矩阵,能有效地提取生物学信息。针对当前多目标双聚类优化算法易于陷入早熟和局部最优解等问题,论文提出了基于逻辑运算的离散人工蜂群优化双聚类算法(LOABCB算法),一方面引入人工蜂群算法增强双聚类的全局寻优能力,另一方面通过逻辑运算邻域搜索策略寻找最优双聚类,提高搜索效率。采用基因表达数据的酵母细胞数据集进行实验,结果表明论文算法能够获得实验效果优的具有生物意义的双聚类。     

Biclustering of expression data with evolutionary computation

Microarray techniques are leading to the development of sophisticated algorithms capable of extracting novel and useful knowledge from a biomedical point of view. In this work, we address the biclustering of gene expression data with evolutionary computation. Our approach is based on evolutionary algorithms, which have been proven to have excellent performance on complex problems, and searches for biclusters following a sequential covering strategy. The goal is to find biclusters of maximum size with mean squared residue lower than a given /spl delta/. In addition, we pay special attention to the fact of looking for high-quality biclusters with large variation, i.e., with a relatively high row variance, and with a low level of overlapping among biclusters. The quality of biclusters found by our evolutionary approach is discussed and the results are compared to those reported by Cheng and Church, and Yang et al. In general, our approach, named SEBI, shows an excellent performance at finding patterns in gene expression data.     

Scatter search-based identification of local patterns with positive and negative correlations in gene expression data

This paper presents a scatter search approach based on linear correlations among genes to find biclusters, which include both shifting and scaling patterns and negatively correlated patterns contrarily to most of correlation-based algorithms published in the literature. The methodology established here for comparison is based on a priori biological information stored in the well-known repository Gene Ontology (GO). In particular, the three existing categories in GO, Biological Process, Cellular Components and Molecular Function, have been used. The performance of the proposed algorithm has been compared to other benchmark biclustering algorithms, specifically a group of classical biclustering algorithms and two algorithms that use correlation-based merit functions. The proposed algorithm outperforms the benchmark algorithms and finds patterns based on negative correlations. Although these patterns contain important relationship among genes, they are not found by most of biclustering algorithms. The experimental study also shows the importance of the size in a bicluster in addition to the value of its correlation. In particular, the size of a bicluster has an influence over its enrichment in a GO term.     

从基因表达数据中挖掘最大的行常量双聚类*

双聚类方法是当前分析基因表达数据的一个重要研究方向,其挖掘目标是发现哪些基因在哪些实验条件下具有相似的表达水平或者关系密切.目前已提出了许多双聚类算法来挖掘不同类型的双聚类,然而其大部分挖掘效率不高.鉴于此,提出了一个新颖的挖掘算法——MRCluster,其主要是用来从原始的基因表达数据中挖掘最大的行常量双聚类模式.就其挖掘效率来说,它采用的是基于Apriori原则的基因扩展深度优先的挖掘策略,并且在挖掘过程中引入了一些新颖的剪枝技术来提高效率.将MRCluster和一个行常量双聚类模式挖掘方法RAP(range support pattern)算法进行比较,从实验结果上可以看出,相比RAP算法,MRCluster算法对在原始的基因表达数据中挖掘最大的行常量双聚类模式具有更好的效率.因此,MRCluster算法能够有效地从原始的基因表达数据中挖掘最大的行常量双聚类.     

Experimental correlation analysis of bicluster coherence measures and gene ontology information

Biclustering algorithms have become popular tools for gene expression data analysis. They can identify local patterns defined by subsets of genes and subsets of samples, which cannot be detected by traditional clustering algorithms. In spite of being useful, biclustering is an NP-hard problem. Therefore, the majority of biclustering algorithms look for biclusters optimizing a pre-established coherence measure. Many heuristics and validation measures have been proposed for biclustering over the last 20 years. However, there is a lack of an extensive comparison of bicluster coherence measures on practical scenarios. To deal with this lack, this paper experimentally analyzes 17 bicluster coherence measures and external measures calculated from information obtained in the gene ontologies. In this analysis, results were produced by 10 algorithms from the literature in 19 gene expression datasets. According to the experimental results, a few pairs of strongly correlated coherence measures could be identified, which suggests redundancy. Moreover, the pairs of strongly correlated measures might change when dealing with normalized or non-normalized data and biclusters enriched by different ontologies. Finally, there was no clear relation between coherence measures and assessment using information from gene ontology.     

面向微阵列基因数据的基于PA指标双向聚类算法

针对目前双聚类算法很少考虑所得聚类结果整体的划分质量问题,提出一种基于PA指标的双聚类算法。该算法选定一种衡量所有簇划分效果的PA指标来构造双聚类的模型,运用启发式贪心策略,通过迭代增删行列的方式挖掘出划分效果较高的几个双聚类。将所提算法与CC、FLOC算法进行算法性能的比较。实验结果表明,该算法能获得更好的结果。这说明该算法更能挖掘出具备既有统计意义又有生物意义的局部模式。     

采用多样性选择的量子粒子群双向聚类算法

双向聚类已成为分析基因表达数据的一种重要工具,可以同时从基因和条件两个方向寻找具有相同表达波动的簇。但双向聚类是一种多目标优化的局部搜索算法,处理繁杂的基因数据时容易陷入局部最优。为提高算法的全局搜索能力,提出了一种多样性选择的量子粒子群双向聚类算法（Diversify-Optional QPSO,DOQPSO）。算法首先采用DOQPSO处理基因数据,然后用改进的FLOC算法进行贪心迭代寻找双向聚类,以求得更为理想的结果。算法通过实验仿真,并与FLOC算法和QPSO算法进行比较,结果证明DOQPSO双向聚类算法具有更好的全局寻优能力,且聚类效果更佳。     

CoBi: Pattern Based Co-Regulated Biclustering of Gene Expression Data

Co-regulation is a common phenomenon in gene expression. Finding positively and negatively co-regulated gene clusters from gene expression data is a real need. Existing techniques based on global similarity are unable to detect true up- and down-regulated gene clusters. This paper presents an expression pattern based biclustering technique, CoBi, for grouping both positively and negatively regulated genes from microarray expression data. Regulation pattern and similarity in degree of fluctuation are accounted for while computing similarity between two genes. Unlike traditional biclustering techniques, which use greedy iterative approaches, it uses a BiClust tree that needs single pass over the entire dataset to find a set of biologically relevant biclusters. Biclusters determined from different gene expression datasets by the technique show highly enriched functional categories.     

A new measure for gene expression biclustering based on non-parametric correlation

Background

One of the emerging techniques for performing the analysis of the DNA microarray data known as biclustering is the search of subsets of genes and conditions which are coherently expressed. These subgroups provide clues about the main biological processes. Until now, different approaches to this problem have been proposed. Most of them use the mean squared residue as quality measure but relevant and interesting patterns can not be detected such as shifting, or scaling patterns. Furthermore, recent papers show that there exist new coherence patterns involved in different kinds of cancer and tumors such as inverse relationships between genes which can not be captured.

Results

The proposed measure is called Spearman's biclustering measure (SBM) which performs an estimation of the quality of a bicluster based on the non-linear correlation among genes and conditions simultaneously. The search of biclusters is performed by using a evolutionary technique called estimation of distribution algorithms which uses the SBM measure as fitness function. This approach has been examined from different points of view by using artificial and real microarrays. The assessment process has involved the use of quality indexes, a set of bicluster patterns of reference including new patterns and a set of statistical tests. It has been also examined the performance using real microarrays and comparing to different algorithmic approaches such as Bimax, CC, OPSM, Plaid and xMotifs.

Conclusions

SBM shows several advantages such as the ability to recognize more complex coherence patterns such as shifting, scaling and inversion and the capability to selectively marginalize genes and conditions depending on the statistical significance.     

基于加权均方残差的改进双聚类算法*

现有的双聚类算法缺乏发现具有重叠结构双聚类的能力,无法有效发现基因表达数据中隐藏的相应双聚类结构,并且在增删条件过程中均未考虑条件重要性对双聚类结果的影响.针对上述问题,文中提出基于加权均方残差的改进双聚类算法.首先利用重叠率和隶属度控制的模糊划分将基因集划分为初始双聚类,然后在最小化目标函数过程中迭代修改各双簇中条件的权重,最后利用加权的均方残差添加符合条件的基因,删除优化的双聚类中一致波动性不好的基因,得到最终的双聚类集.实验表明,文中算法不仅能生成具有共表达水平大小不同的双簇,并且能将重叠率控制在合理范围内.     

Multi-objective evolutionary biclustering of gene expression data

Biclustering or simultaneous clustering of both genes and conditions have generated considerable interest over the past few decades, particularly related to the analysis of high-dimensional gene expression data in information retrieval, knowledge discovery, and data mining. The objective is to find sub-matrices, i.e., maximal subgroups of genes and subgroups of conditions where the genes exhibit highly correlated activities over a range of conditions. Since these two objectives are mutually conflicting, they become suitable candidates for multi-objective modeling. In this study, a novel multi-objective evolutionary biclustering framework is introduced by incorporating local search strategies. A new quantitative measure to evaluate the goodness of the biclusters is developed. The experimental results on benchmark datasets demonstrate better performance as compared to existing algorithms available in literature.