Clustering Of Gene Expression Data Research Articles

ERG Deletions Define a Novel Subtype of B-Progenitor Acute Lymphoblastic Leukemia.

In a previous gene expression profiling study of acute lymphoblastic leukemia (ALL), we identified a novel subtype of B-progenitor ALL (4.9% of 284 cases) with a unique gene expression profile, aberrant expression of CD2 and the absence of recurring cytogenetic abnormalities (Cancer Cell 2002; 1:133). Efforts to identify rearrangement or mutation of many of the top-ranked genes in the novel expression signature failed to identify a causative lesion. To further investigate the genetic basis of this subtype, we performed integrated genomic analysis of 277 ALL cases. Affymetrix 250k Sty and Nsp SNP microarrays were used in all cases, and Affymetrix U133A gene expression profiles were obtained on 183 of the cases. Unsupervised clustering of gene expression data identified 16 cases of the novel subtype, including all of the 14 previously defined cases. Remarkably, focal mono-allelic deletions of the ETS family member ERG (v-ets erythroblastosis virus E26 oncogene homolog) were detected by genome-wide copy number analysis in 11/16 (69%) of the novel cases, but not in any other ALL subtype. Extensive analysis failed to reveal evidence of translocations involving the altered ERG allele, indicating that these are intragenic deletions limited to ERG. The ERG deletions involved a subset of exons (ERG isoform 1 exons 3–7 or 3–9) resulting in the expression of internally deleted ERG transcripts with altered reading frames predicted to produce a prematurely truncated N-terminal protein fragment. However, using an alternative translational start site 5′ to exon 10, the transcripts also encode a ∼28kDa C-terminal ERG fragment that contains the entire C-terminal ETS DNA-binding and transactivation domains, but lacks all N-terminal domains. Importantly, western blot analysis of primary leukemic blasts revealed expression of only the 28kDa C-terminal ERG protein, along with full length ERG expressed from the retained wild type allele. Remarkably, the C-terminal ERG protein was also detected in 4 of 5 novel ALL cases that lacked detectable ERG deletions, but not in any other ALL subtype. In luciferase reporter assays, this aberrant ERG protein acts as a competitive inhibitor of wild type ERG. Analysis of a second cohort of 35 B-progenitor ALL cases lacking recurring cytogenetic abnormalities identified two cases with ERG deletions and a third expressing the aberrant ERG protein, all of which had the novel gene expression profile. Sequencing of ERG in 252 ALL cases identified only one case with an ERG mutation that resulted in a frameshift in the ETS domain. This case did not share the novel signature nor express the aberrant C-terminal ERG protein. Finally, in an analysis of 37 acute leukemia cell lines, the B-progenitor ALL line NALM-6 was found to harbor a focal, internally truncating ERG deletion, expressed the aberrant ERG protein, and shared the novel gene expression profile, thus identifying it as a model of this novel ALL subtype. These data establish focal ERG deletions as the genetic lesion underlying a novel subtype of ALL, and have expanded the genetic mechanisms that lead to the dysregulation of ERG from chromosomal translocations that result in enhanced transcriptional activity, to deletions that generate dominant negative forms of the transcription factor.

Consensus Clustering of Gene Expression Data and its Application to Gene Function Prediction

Predicting functions of genes is an important issue in biology. Clustering gene expression profiles has been widely used for gene function prediction, but most clustering methods are unstable and sensitive to input parameters such as starting values and number of clusters. In this article, we develop a novel consensus clustering method to address the instability issue and thus improve the performance of clustering methods. The biological function of an unannotated gene is predicted based on the most enriched functional category in its consensus cluster. The MIPS gene annotations are used to evaluate the predictive performance. It is shown that the consensus clustering-based classification method has a significantly better predictive performance than a previously used clustering-based classification method while performing as well as support vector machines (SVMs). In addition to the obvious applicability of consensus clustering to unsupervised learning, the method's advantages in supervised learning include its being a multiclass classifier that can be trained much faster than SVMs, its generality to include any of the many existing clustering algorithms, and its flexibility to be integrated with other predictive models built with other types of data, suggesting its potential for further improved performance. As a concrete example, we consider its combined use with protein-protein interaction data for gene function prediction. It is shown that the combined analysis has a significantly higher predictive accuracy and a much broader functional coverage than using either data source alone.

An improved algorithm for clustering gene expression data

Recent advancements in microarray technology allows simultaneous monitoring of the expression levels of a large number of genes over different time points. Clustering is an important tool for analyzing such microarray data, typical properties of which are its inherent uncertainty, noise and imprecision. In this article, a two-stage clustering algorithm, which employs a recently proposed variable string length genetic scheme and a multiobjective genetic clustering algorithm, is proposed. It is based on the novel concept of points having significant membership to multiple classes. An iterated version of the well-known Fuzzy C-Means is also utilized for clustering. The significant superiority of the proposed two-stage clustering algorithm as compared to the average linkage method, Self Organizing Map (SOM) and a recently developed weighted Chinese restaurant-based clustering method (CRC), widely used methods for clustering gene expression data, is established on a variety of artificial and publicly available real life data sets. The biological relevance of the clustering solutions are also analyzed.

Clustering of time-course gene expression data using functional data analysis

Clustering of gene expression data collected across time is receiving growing attention in the biological literature since time-course experiments allow one to understand dynamic biological processes and identify genes governed by the same processes. It is believed that genes demonstrating similar expression profiles over time might give an informative insight into how underlying biological mechanisms work. In this paper, we propose a method based on functional data analysis (FNDA) to cluster time-dependent gene expression profiles. Consideration of clustering problems using the FNDA setting provides ways to take time dependency into account by using basis function expansion to describe the partially observed curves. We also discuss how to choose the number of bases in the basis function expansion in FNDA. A synthetic cycle data and a real data are used to demonstrate the proposed method and some comparisons between the proposed and existing approaches using the adjusted Rand indices are made.

Clustering gene expression data using a novel model of self-organizing map

Clustering is an important technique for analyzing gene expression data. The self-organizing map is one of the most useful clustering algorithms. However, its applicability is limited by the fact that some knowledge about the data is required prior to clustering. This paper introduces a novel model of self-organizing map (SOM) called growing hierarchical self-organizing map (GHSOM) to cluster gene expression data. The training and growth processes of GHSOM are entirely data driven, requiring no prior knowledge or estimates for parameter specification, thus help find not only the appropriate number of clusters but also the hierarchical relations in the data set. Compared with other clustering algorithms, GHSOM has better accuracy. To validate the results, a novel validation technique is used, known as figure of merit (FOM).

Evaluation of gene-expression clustering via mutual information distance measure.

BackgroundThe definition of a distance measure plays a key role in the evaluation of different clustering solutions of gene expression profiles. In this empirical study we compare different clustering solutions when using the Mutual Information (MI) measure versus the use of the well known Euclidean distance and Pearson correlation coefficient.ResultsRelying on several public gene expression datasets, we evaluate the homogeneity and separation scores of different clustering solutions. It was found that the use of the MI measure yields a more significant differentiation among erroneous clustering solutions. The proposed measure was also used to analyze the performance of several known clustering algorithms. A comparative study of these algorithms reveals that their "best solutions" are ranked almost oppositely when using different distance measures, despite the found correspondence between these measures when analysing the averaged scores of groups of solutions.ConclusionIn view of the results, further attention should be paid to the selection of a proper distance measure for analyzing the clustering of gene expression data.

Integrating Functional Knowledge during Sample Clustering for Microarray Data using Unsupervised Decision Trees

Clustering of microarray gene expression data is performed routinely, for genes as well as for samples. Clustering of genes can exhibit functional relationships between genes; clustering of samples on the other hand is important for finding e.g. disease subtypes, relevant patient groups for stratification or related treatments. Usually this is done by first filtering the genes for high-variance under the assumption that they carry most of the information needed for separating different sample groups. If this assumption is violated, important groupings in the data might be lost. Furthermore, classical clustering methods do not facilitate the biological interpretation of the results. Therefore, we propose to methodologically integrate the clustering algorithm with prior biological information. This is different from other approaches as knowledge about classes of genes can be directly used to ease the interpretation of the results and possibly boost clustering performance. Our approach computes dendrograms that resemble decision trees with gene classes used to split the data at each node which can help to find biologically meaningful differences between the sample groups. We have tested the proposed method both on simulated and real data and conclude its usefulness as a complementary method, especially when assumptions of few differentially expressed genes along with an informative mapping of genes to different classes are met.

Including probe-level uncertainty in model-based gene expression clustering.

BackgroundClustering is an important analysis performed on microarray gene expression data since it groups genes which have similar expression patterns and enables the exploration of unknown gene functions. Microarray experiments are associated with many sources of experimental and biological variation and the resulting gene expression data are therefore very noisy. Many heuristic and model-based clustering approaches have been developed to cluster this noisy data. However, few of them include consideration of probe-level measurement error which provides rich information about technical variability.ResultsWe augment a standard model-based clustering method to incorporate probe-level measurement error. Using probe-level measurements from a recently developed Affymetrix probe-level model, multi-mgMOS, we include the probe-level measurement error directly into the standard Gaussian mixture model. Our augmented model is shown to provide improved clustering performance on simulated datasets and a real mouse time-course dataset.ConclusionThe performance of model-based clustering of gene expression data is improved by including probe-level measurement error and more biologically meaningful clustering results are obtained.

A new molecular breast cancer subclass defined from a large scale real-time quantitative RT-PCR study

BackgroundCurrent histo-pathological prognostic factors are not very helpful in predicting the clinical outcome of breast cancer due to the disease's heterogeneity. Molecular profiling using a large panel of genes could help to classify breast tumours and to define signatures which are predictive of their clinical behaviour.MethodsTo this aim, quantitative RT-PCR amplification was used to study the RNA expression levels of 47 genes in 199 primary breast tumours and 6 normal breast tissues. Genes were selected on the basis of their potential implication in hormonal sensitivity of breast tumours. Normalized RT-PCR data were analysed in an unsupervised manner by pairwise hierarchical clustering, and the statistical relevance of the defined subclasses was assessed by Chi2 analysis. The robustness of the selected subgroups was evaluated by classifying an external and independent set of tumours using these Chi2-defined molecular signatures.ResultsHierarchical clustering of gene expression data allowed us to define a series of tumour subgroups that were either reminiscent of previously reported classifications, or represented putative new subtypes. The Chi2 analysis of these subgroups allowed us to define specific molecular signatures for some of them whose reliability was further demonstrated by using the validation data set. A new breast cancer subclass, called subgroup 7, that we defined in that way, was particularly interesting as it gathered tumours with specific bioclinical features including a low rate of recurrence during a 5 year follow-up.ConclusionThe analysis of the expression of 47 genes in 199 primary breast tumours allowed classifying them into a series of molecular subgroups. The subgroup 7, which has been highlighted by our study, was remarkable as it gathered tumours with specific bioclinical features including a low rate of recurrence. Although this finding should be confirmed by using a larger tumour cohort, it suggests that gene expression profiling using a minimal set of genes may allow the discovery of new subclasses of breast cancer that are characterized by specific molecular signatures and exhibit specific bioclinical features.

Transcriptional Profiling of the Nuclear Factor-κB Pathway Identifies a Subgroup of Primary Lymphoma of the Central Nervous System With Low BCL10 Expression

Recent studies point to a role of nuclear factor (NF)-kappaB signaling in a subset of diffuse large B cell lymphomas. We have analyzed the expression of 21 genes encoding NF-kappaB family members, upstream modulators, and targets in 32 primary central nervous system lymphomas (PCNSLs) by quantitative reverse transcriptase-polymerase chain reaction (RT-PCR). Compared with nonmalignant germinal center centroblasts, expression of BCL10, REL, IAP1, and TRAF1 was significantly lower in PCNSLs, whereas that of BAX, BCLXL, BCL2, MALT1, CARD9, CARD10, CARD11, CARD14, CCND2, cFLIP, RELA, RELB, NFKB1, NFKB2, and IRF4 was higher. Hierarchical clustering of gene expression data revealed two distinct subgroups of PCNSLs, which were characterized by significantly different transcriptional levels, predominantly of BCL10, but also of REL and IAP1. Thus, these quantitative RT-PCR data with expression of genes of the NF-kappaB family as well as NF-kappaB-regulated genes together with immunohistochemical detection of nuclear RELA and REL indicate activation of the NF-kappaB pathway in PCNSLs, which may contribute to their high proliferative activity and the low level of apoptosis.

Simultaneous clustering of gene expression data with clinical chemistry and pathological evaluations reveals phenotypic prototypes

BackgroundCommonly employed clustering methods for analysis of gene expression data do not directly incorporate phenotypic data about the samples. Furthermore, clustering of samples with known phenotypes is typically performed in an informal fashion. The inability of clustering algorithms to incorporate biological data in the grouping process can limit proper interpretation of the data and its underlying biology.ResultsWe present a more formal approach, the modk-prototypes algorithm, for clustering biological samples based on simultaneously considering microarray gene expression data and classes of known phenotypic variables such as clinical chemistry evaluations and histopathologic observations. The strategy involves constructing an objective function with the sum of the squared Euclidean distances for numeric microarray and clinical chemistry data and simple matching for histopathology categorical values in order to measure dissimilarity of the samples. Separate weighting terms are used for microarray, clinical chemistry and histopathology measurements to control the influence of each data domain on the clustering of the samples. The dynamic validity index for numeric data was modified with a category utility measure for determining the number of clusters in the data sets. A cluster's prototype, formed from the mean of the values for numeric features and the mode of the categorical values of all the samples in the group, is representative of the phenotype of the cluster members. The approach is shown to work well with a simulated mixed data set and two real data examples containing numeric and categorical data types. One from a heart disease study and another from acetaminophen (an analgesic) exposure in rat liver that causes centrilobular necrosis.ConclusionThe modk-prototypes algorithm partitioned the simulated data into clusters with samples in their respective class group and the heart disease samples into two groups (sick and buff denoting samples having pain type representative of angina and non-angina respectively) with an accuracy of 79%. This is on par with, or better than, the assignment accuracy of the heart disease samples by several well-known and successful clustering algorithms. Following modk-prototypes clustering of the acetaminophen-exposed samples, informative genes from the cluster prototypes were identified that are descriptive of, and phenotypically anchored to, levels of necrosis of the centrilobular region of the rat liver. The biological processes cell growth and/or maintenance, amine metabolism, and stress response were shown to discern between no and moderate levels of acetaminophen-induced centrilobular necrosis. The use of well-known and traditional measurements directly in the clustering provides some guarantee that the resulting clusters will be meaningfully interpretable.

Intrinsic androgen-dependent gene expression patterns revealed by comparison of genital fibroblasts from normal males and individuals with complete and partial androgen insensitivity syndrome

BackgroundTo better understand the molecular programs of normal and abnormal genital development, clear-cut definition of androgen-dependent gene expression patterns, without the influence of genotype (46, XX vs. 46, XY), is warranted. Previously, we have identified global gene expression profiles in genital-derived fibroblasts that differ between 46, XY males and 46, XY females with complete androgen insensitivity syndrome (CAIS) due to inactivating mutations of the androgen receptor (AR). While these differences could be due to cell autonomous changes in gene expression induced by androgen programming, recent work suggests they could also be influenced by the location from which the fibroblasts were harvested (topology). To minimize the influence of topology, we compared gene expression patterns of fibroblasts derived from identical urogenital anlagen: the scrotum in normally virilized 46, XY males and the labia majora from completely feminized 46, XY individuals with CAIS.Results612 transcripts representing 440 unique genes differed significantly in expression levels between scrotum and CAIS labia majora, suggesting the effects of androgen programming. While some genes coincided with those we had identified previously (TBX3, IGFBP5, EGFR, CSPG2), a significant number did not, implying that topology had influenced gene expression in our previous experiments. Supervised clustering of gene expression data derived from a large set of fibroblast cultures from individuals with partial AIS revealed that the new, topology controlled data set better classified the specimens.ConclusionInactivating mutations of the AR, in themselves, appear to induce lasting changes in gene expression in cultured fibroblasts, independent of topology and genotype. Genes identified are likely to be relevant candidates to decipher androgen-dependent normal and abnormal genital development.

Clustering of gene expression data: performance and similarity analysis

BackgroundDNA Microarray technology is an innovative methodology in experimental molecular biology, which has produced huge amounts of valuable data in the profile of gene expression. Many clustering algorithms have been proposed to analyze gene expression data, but little guidance is available to help choose among them. The evaluation of feasible and applicable clustering algorithms is becoming an important issue in today's bioinformatics research.ResultsIn this paper we first experimentally study three major clustering algorithms: Hierarchical Clustering (HC), Self-Organizing Map (SOM), and Self Organizing Tree Algorithm (SOTA) using Yeast Saccharomyces cerevisiae gene expression data, and compare their performance. We then introduce Cluster Diff, a new data mining tool, to conduct the similarity analysis of clusters generated by different algorithms. The performance study shows that SOTA is more efficient than SOM while HC is the least efficient. The results of similarity analysis show that when given a target cluster, the Cluster Diff can efficiently determine the closest match from a set of clusters. Therefore, it is an effective approach for evaluating different clustering algorithms.ConclusionHC methods allow a visual, convenient representation of genes. However, they are neither robust nor efficient. The SOM is more robust against noise. A disadvantage of SOM is that the number of clusters has to be fixed beforehand. The SOTA combines the advantages of both hierarchical and SOM clustering. It allows a visual representation of the clusters and their structure and is not sensitive to noises. The SOTA is also more flexible than the other two clustering methods. By using our data mining tool, Cluster Diff, it is possible to analyze the similarity of clusters generated by different algorithms and thereby enable comparisons of different clustering methods.

Extension of the mixture of factor analyzers model to incorporate the multivariate t-distribution

Mixtures of factor analyzers enable model-based density estimation to be undertaken for high-dimensional data, where the number of observations n is small relative to their dimension p. However, this approach is sensitive to outliers as it is based on a mixture model in which the multivariate normal family of distributions is assumed for the component error and factor distributions. An extension to mixtures of t-factor analyzers is considered, whereby the multivariate t-family is adopted for the component error and factor distributions. An EM-based algorithm is developed for the fitting of mixtures of t-factor analyzers. Its application is demonstrated in the clustering of some microarray gene-expression data.

BioNMF: a versatile tool for non-negative matrix factorization in biology.

BackgroundIn the Bioinformatics field, a great deal of interest has been given to Non-negative matrix factorization technique (NMF), due to its capability of providing new insights and relevant information about the complex latent relationships in experimental data sets. This method, and some of its variants, has been successfully applied to gene expression, sequence analysis, functional characterization of genes and text mining. Even if the interest on this technique by the bioinformatics community has been increased during the last few years, there are not many available simple standalone tools to specifically perform these types of data analysis in an integrated environment.ResultsIn this work we propose a versatile and user-friendly tool that implements the NMF methodology in different analysis contexts to support some of the most important reported applications of this new methodology. This includes clustering and biclustering gene expression data, protein sequence analysis, text mining of biomedical literature and sample classification using gene expression. The tool, which is named bioNMF, also contains a user-friendly graphical interface to explore results in an interactive manner and facilitate in this way the exploratory data analysis process.ConclusionbioNMF is a standalone versatile application which does not require any special installation or libraries. It can be used for most of the multiple applications proposed in the bioinformatics field or to support new research using this method. This tool is publicly available at .

Interactive Gene Clustering—A Case Study of Breast Cancer Microarray Data

We present a new approach to clustering and visualization of the DNA microarray gene expression data. We utilize the self-organizing map (SOM) framework for handling (dis)similarities between genes in terms of their expression characteristics. We rely on appropriately defined distances between ranked genes-attributes, also capable of handling missing values. As a case study, we consider breast cancer data and the gene ESR1, whose expression alterations, appearing for many of the tumor subtypes, have been already observed to be correlated with some other significant genes. Preliminary results positively verify applicability of our approach, although further development is definitely needed. They suggest that it may be very effective when used by the domain experts. The algorithmic toolkit is enriched with GUI enabling the users to interactively support the SOM optimization process. Its effectiveness is achieved by drag&drop techniques allowing for the cluster modification according to the expert knowledge or intuition.

Incorporating gene functions as priors in model-based clustering of microarray gene expression data

Cluster analysis of gene expression profiles has been widely applied to clustering genes for gene function discovery. Many approaches have been proposed. The rationale is that the genes with the same biological function or involved in the same biological process are more likely to co-express, hence they are more likely to form a cluster with similar gene expression patterns. However, most existing methods, including model-based clustering, ignore known gene functions in clustering. To take advantage of accumulating gene functional annotations, we propose incorporating known gene functions as prior probabilities in model-based clustering. In contrast to a global mixture model applicable to all the genes in the standard model-based clustering, we use a stratified mixture model: one stratum corresponds to the genes of unknown function while each of the other ones corresponding to the genes sharing the same biological function or pathway; the genes from the same stratum are assumed to have the same prior probability of coming from a cluster while those from different strata are allowed to have different prior probabilities of coming from the same cluster. We derive a simple EM algorithm that can be used to fit the stratified model. A simulation study and an application to gene function prediction demonstrate the advantage of our proposal over the standard method. weip@biostat.umn.edu

An approach for clustering gene expression data with error information.

BackgroundClustering of gene expression patterns is a well-studied technique for elucidating trends across large numbers of transcripts and for identifying likely co-regulated genes. Even the best clustering methods, however, are unlikely to provide meaningful results if too much of the data is unreliable. With the maturation of microarray technology, a wealth of research on statistical analysis of gene expression data has encouraged researchers to consider error and uncertainty in their microarray experiments, so that experiments are being performed increasingly with repeat spots per gene per chip and with repeat experiments. One of the challenges is to incorporate the measurement error information into downstream analyses of gene expression data, such as traditional clustering techniques.ResultsIn this study, a clustering approach is presented which incorporates both gene expression values and error information about the expression measurements. Using repeat expression measurements, the error of each gene expression measurement in each experiment condition is estimated, and this measurement error information is incorporated directly into the clustering algorithm. The algorithm, CORE (Clustering Of Repeat Expression data), is presented and its performance is validated using statistical measures. By using error information about gene expression measurements, the clustering approach is less sensitive to noise in the underlying data and it is able to achieve more accurate clusterings. Results are described for both synthetic expression data as well as real gene expression data from Escherichia coli and Saccharomyces cerevisiae.ConclusionThe additional information provided by replicate gene expression measurements is a valuable asset in effective clustering. Gene expression profiles with high errors, as determined from repeat measurements, may be unreliable and may associate with different clusters, whereas gene expression profiles with low errors can be clustered with higher specificity. Results indicate that including error information from repeat gene expression measurements can lead to significant improvements in clustering accuracy.

Clustering on the Unit Hypersphere using von Mises-Fisher Distributions

Several large scale data mining applications, such as text categorization and gene expression analysis, involve high-dimensional data that is also inherently directional in nature. Often such data is L2 normalized so that it lies on the surface of a unit hypersphere. Popular models such as (mixtures of) multi-variate Gaussians are inadequate for characterizing such data. This paper proposes a generative mixture-model approach to clustering directional data based on the von Mises-Fisher (vMF) distribution, which arises naturally for data distributed on the unit hypersphere. In particular, we derive and analyze two variants of the Expectation Maximization (EM) framework for estimating the mean and concentration parameters of this mixture. Numerical estimation of the concentration parameters is non-trivial in high dimensions since it involves functional inversion of ratios of Bessel functions. We also formulate two clustering algorithms corresponding to the variants of EM that we derive. Our approach provides a theoretical basis for the use of cosine similarity that has been widely employed by the information retrieval community, and obtains the spherical kmeans algorithm (kmeans with cosine similarity) as a special case of both variants. Empirical results on clustering of high-dimensional text and gene-expression data based on a mixture of vMF distributions show that the ability to estimate the concentration parameter for each vMF component, which is not present in existing approaches, yields superior results, especially for difficult clustering tasks in high-dimensional spaces.

GenClust: a genetic algorithm for clustering gene expression data.

BackgroundClustering is a key step in the analysis of gene expression data, and in fact, many classical clustering algorithms are used, or more innovative ones have been designed and validated for the task. Despite the widespread use of artificial intelligence techniques in bioinformatics and, more generally, data analysis, there are very few clustering algorithms based on the genetic paradigm, yet that paradigm has great potential in finding good heuristic solutions to a difficult optimization problem such as clustering.ResultsGenClust is a new genetic algorithm for clustering gene expression data. It has two key features: (a) a novel coding of the search space that is simple, compact and easy to update; (b) it can be used naturally in conjunction with data driven internal validation methods. We have experimented with the FOM methodology, specifically conceived for validating clusters of gene expression data. The validity of GenClust has been assessed experimentally on real data sets, both with the use of validation measures and in comparison with other algorithms, i.e., Average Link, Cast, Click and K-means.ConclusionExperiments show that none of the algorithms we have used is markedly superior to the others across data sets and validation measures; i.e., in many cases the observed differences between the worst and best performing algorithm may be statistically insignificant and they could be considered equivalent. However, there are cases in which an algorithm may be better than others and therefore worthwhile. In particular, experiments for GenClust show that, although simple in its data representation, it converges very rapidly to a local optimum and that its ability to identify meaningful clusters is comparable, and sometimes superior, to that of more sophisticated algorithms. In addition, it is well suited for use in conjunction with data driven internal validation measures and, in particular, the FOM methodology.