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PubMed2005

Self-organizing topological tree for online vector quantization and data clustering.

The self-organizing Maps (SOM) introduced by Kohonen implement two important operations: vector quantization (VQ) and a topology-preserving mapping. In this paper, an online self-organizing topological tree (SOTT) with faster learning is proposed. A new learning rule delivers the efficiency and topology preservation, which is superior of other structures of SOMs. The computational complexity of the proposed SOTT is O(log N) rather than O(N) as for the basic SOM. The experimental results demonstrate that the reconstruction performance of SOTT is comparable to the full-search SOM and its computation time is much shorter than the full-search SOM and other vector quantizers. In addition, SOTT delivers the hierarchical mapping of codevectors and the progressive transmission and decoding property, which are rarely supported by other vector quantizers at the same time. To circumvent the shortcomings of clustering performance of classical partition clustering algorithms, a hybrid clustering algorithm that fully exploit the online learning and multiresolution characteristics of SOTT is devised. A new linkage metric is proposed which can be updated online to accelerate the time consuming agglomerative hierarchical clustering stage. Besides the enhanced clustering performance, due to the online learning capability, the memory requirement of the proposed SOTT hybrid clustering algorithm is independent of the size of the data set, making it attractive for large database.

Algorithms↗
PubMed2004

Supervised cluster analysis for microarray data based on multivariate Gaussian mixture.

MOTIVATION: Grouping genes having similar expression patterns is called gene clustering, which has been proved to be a useful tool for extracting underlying biological information of gene expression data. Many clustering procedures have shown success in microarray gene clustering; most of them belong to the family of heuristic clustering algorithms. Model-based algorithms are alternative clustering algorithms, which are based on the assumption that the whole set of microarray data is a finite mixture of a certain type of distributions with different parameters. Application of the model-based algorithms to unsupervised clustering has been reported. Here, for the first time, we demonstrated the use of the model-based algorithm in supervised clustering of microarray data. RESULTS: We applied the proposed methods to real gene expression data and simulated data. We showed that the supervised model-based algorithm is superior over the unsupervised method and the support vector machines (SVM) method. AVAILABILITY: The program written in the SAS language implementing methods I-III in this report is available upon request. The software of SVMs is available in the website http://svm.sdsc.edu/cgi-bin/nph-SVMsubmit.cgi

Algorithms↗
PubMed2006

Evaluation of stability of k-means cluster ensembles with respect to random initialization.

Many clustering algorithms, including cluster ensembles, rely on a random component. Stability of the results across different runs is considered to be an asset of the algorithm. The cluster ensembles considered here are based on k-means clusterers. Each clusterer is assigned a random target number of clusters, k and is started from a random initialization. Here, we use 10 artificial and 10 real data sets to study ensemble stability with respect to random k, and random initialization. The data sets were chosen to have a small number of clusters (two to seven) and a moderate number of data points (up to a few hundred). Pairwise stability is defined as the adjusted Rand index between pairs of clusterers in the ensemble, averaged across all pairs. Nonpairwise stability is defined as the entropy of the consensus matrix of the ensemble. An experimental comparison with the stability of the standard k-means algorithm was carried out for k from 2 to 20. The results revealed that ensembles are generally more stable, markedly so for larger k. To establish whether stability can serve as a cluster validity index, we first looked at the relationship between stability and accuracy with respect to the number of clusters, k. We found that such a relationship strongly depends on the data set, varying from almost perfect positive correlation (0.97, for the glass data) to almost perfect negative correlation (-0.93, for the crabs data). We propose a new combined stability index to be the sum of the pairwise individual and ensemble stabilities. This index was found to correlate better with the ensemble accuracy. Following the hypothesis that a point of stability of a clustering algorithm corresponds to a structure found in the data, we used the stability measures to pick the number of clusters. The combined stability index gave best results.

Algorithms↗
PubMed2005

Combining multiple clusterings using evidence accumulation.

We explore the idea of evidence accumulation (EAC) for combining the results of multiple clusterings. First, a clustering ensemble--a set of object partitions, is produced. Given a data set (n objects or patterns in d dimensions), different ways of producing data partitions are: 1) applying different clustering algorithms and 2) applying the same clustering algorithm with different values of parameters or initializations. Further, combinations of different data representations (feature spaces) and clustering algorithms can also provide a multitude of significantly different data partitionings. We propose a simple framework for extracting a consistent clustering, given the various partitions in a clustering ensemble. According to the EAC concept, each partition is viewed as an independent evidence of data organization, individual data partitions being combined, based on a voting mechanism, to generate a new n x n, similarity matrix between the n patterns. The final data partition of the n patterns is obtained by applying a hierarchical agglomerative clustering algorithm on this matrix. We have developed a theoretical framework for the analysis of the proposed clustering combination strategy and its evaluation, based on the concept of mutual information between data partitions. Stability of the results is evaluated using bootstrapping techniques. A detailed discussion of an evidence accumulation-based clustering algorithm, using a split and merge strategy based on the K-means clustering algorithm, is presented. Experimental results of the proposed method on several synthetic and real data sets are compared with other combination strategies, and with individual clustering results produced by well-known clustering algorithms.

Algorithms↗
PubMed2000

Cluster update algorithm and recognition

We present a fast and robust cluster update algorithm that is especially efficient in implementing the task of image segmentation using the method of superparamagnetic clustering. We apply it to a Potts model with spin interactions that are are defined by gray-scale differences within the image. Motivated by biological systems, we introduce the concept of neural inhibition to the Potts model realization of the segmentation problem. Including the inhibition term in the Hamiltonian results in enhanced contrast and thereby significantly improves segmentation quality. As a second benefit we can, after equilibration, directly identify the image segments as the clusters formed by the clustering algorithm. To construct a subsequent spin configuration the algorithm performs the standard steps of (i) forming clusters and of (ii) updating the spins in a cluster simultaneously. As opposed to standard algorithms, however, we share the interaction energy between the two steps. Thus, the update probabilities are not independent of the interaction energies. As a consequence, we observe an acceleration of the relaxation by a factor of 10 compared to the Swendson and Wang [Phys. Rev. Lett. 58, 86 (1987)] procedure.

Journal Article↗
PubMed2005

General C-means clustering model.

Partitional clustering is an important part of cluster analysis. Based on various theories, numerous clustering algorithms have been developed, and new clustering algorithms continue to appear in the literature. It is known that Occam's razor plays a pivotal role in data-based models, and partitional clustering is categorized as a data-based model. However, no relation had previously been discovered between Occam's razor and partitional clustering, as we discuss in this paper. The three main contributions of this paper can be summarized as follows: 1) According to a novel definition of the mean, a unifying generative framework for partitional clustering algorithms, called a general c-means clustering model (GCM), is presented and studied. 2) Based on the local optimality test of the GCM, the connection between Occam's razor and partitional clustering is established for the first time. As its application, a comprehensive review of the existing objective function-based clustering algorithms is presented based on GCM. 3) Under a common assumption about partitional clustering, a theoretical guide for devising and implementing clustering algorithm is discovered. These conclusions are verified by numerical experimental results.

Algorithms↗
PubMed2006

An approach for clustering gene expression data with error information.

BACKGROUND: Clustering 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. RESULTS: In 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. CONCLUSION: The 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.

Algorithms↗
PubMedDate not supplied

Robust growing neural gas algorithm with application in cluster analysis.

We propose a novel robust clustering algorithm within the Growing Neural Gas (GNG) framework, called Robust Growing Neural Gas (RGNG) network.The Matlab codes are available from . By incorporating several robust strategies, such as outlier resistant scheme, adaptive modulation of learning rates and cluster repulsion method into the traditional GNG framework, the proposed RGNG network possesses better robustness properties. The RGNG is insensitive to initialization, input sequence ordering and the presence of outliers. Furthermore, the RGNG network can automatically determine the optimal number of clusters by seeking the extreme value of the Minimum Description Length (MDL) measure during network growing process. The resulting center positions of the optimal number of clusters represented by prototype vectors are close to the actual ones irrespective of the existence of outliers. Topology relationships among these prototypes can also be established. Experimental results have shown the superior performance of our proposed method over the original GNG incorporating MDL method, called GNG-M, in static data clustering tasks on both artificial and UCI data sets.

Algorithms↗
PubMed1995

Prediction of protein three-dimensional structures in insertion and deletion regions: a procedure for searching data bases of representative protein fragments using geometric scoring criteria.

The prediction of protein structure in insertion/deletion regions (referred to as indels) is an important part of protein model building by homology. Here we combine cluster analysis with data base search procedures. Initially, data bases of representative protein fragments are constructed using two different clustering algorithms. In the HCAPD (hierarchical clustering after preliminary division) approach, all protein fragments are divided into classes with similar anchor region structures (a protein fragment consists of two anchoring regions and a central region). Within these classes the fragments are further clustered using a hierarchical cluster algorithm. The DCANN (deterministic clustering by assignment of all nearest neighbours) approach is a variant of the k-nearest neighbours cluster algorithm. Only geometric scoring criteria are used for data base searching. The main advantage of a non-redundant data base is the ability to provide structurally different fragments during the search process, which leads to an improvement in structure prediction. Both methods have been tested on 71 insertions and 74 deletions with lengths between one and eight residues.

Algorithms↗
PubMed2006

Applying Robust Directional Similarity based Clustering approach RDSC to classification of gene expression data.

Despite the fact that the classification of gene expression data from a cDNA microarrays has been extensively studied, nowadays a robust clustering method, which can estimate an appropriate number of clusters and be insensitive to its initialization has not yet been developed. In this work, a novel Robust Clustering approach, RDSC, based on the new Directional Similarity measure is presented. This new approach RDSC, which integrates the Directional Similarity based Clustering Algorithm, DSC, with the Agglomerative Hierarchical Clustering Algorithm, AHC, exhibits its robustness to initialization and its capability to determine the appropriate number of clusters reasonably. RDSC has been successfully employed to both artificial and benchmarking gene expression datasets. Our experimental results demonstrate its distinctive superiority over the conventional method Kmeans and the two typical directional clustering algorithms SPKmeans and moVMF.

Algorithms↗
PubMed1980

A new algorithm for clustering lymphocyte typing sera.

An algorithm is presented for clustering antisera by computer. It has two novel features: the leading serum to which all other sera in the cluster are compared is chosen as the most centrally located serum in the cluster; the similarity between two sera is defined from the 2 X 2 table of serum reactions as s = 2a/(2a + b + c). This similarity index is a better measure of the similarity between two sera than conventional measures of similarity such as the correlation coefficient. Finally, the identification of cluster and serum subsets provides a more complete analysis of cross-reactivity and multispecificity, and suggests which absorptions might yield monospecific typing sera. A computer program which performs this serum cluster analysis is available upon request.

Blood Grouping and Crossmatching↗
PubMed2004

Incremental genetic K-means algorithm and its application in gene expression data analysis.

BACKGROUND: In recent years, clustering algorithms have been effectively applied in molecular biology for gene expression data analysis. With the help of clustering algorithms such as K-means, hierarchical clustering, SOM, etc, genes are partitioned into groups based on the similarity between their expression profiles. In this way, functionally related genes are identified. As the amount of laboratory data in molecular biology grows exponentially each year due to advanced technologies such as Microarray, new efficient and effective methods for clustering must be developed to process this growing amount of biological data. RESULTS: In this paper, we propose a new clustering algorithm, Incremental Genetic K-means Algorithm (IGKA). IGKA is an extension to our previously proposed clustering algorithm, the Fast Genetic K-means Algorithm (FGKA). IGKA outperforms FGKA when the mutation probability is small. The main idea of IGKA is to calculate the objective value Total Within-Cluster Variation (TWCV) and to cluster centroids incrementally whenever the mutation probability is small. IGKA inherits the salient feature of FGKA of always converging to the global optimum. C program is freely available at http://database.cs.wayne.edu/proj/FGKA/index.htm. CONCLUSIONS: Our experiments indicate that, while the IGKA algorithm has a convergence pattern similar to FGKA, it has a better time performance when the mutation probability decreases to some point. Finally, we used IGKA to cluster a yeast dataset and found that it increased the enrichment of genes of similar function within the cluster.

Algorithms↗
PubMed2002

Supervised clustering of genes.

BACKGROUND: We focus on microarray data where experiments monitor gene expression in different tissues and where each experiment is equipped with an additional response variable such as a cancer type. Although the number of measured genes is in the thousands, it is assumed that only a few marker components of gene subsets determine the type of a tissue. Here we present a new method for finding such groups of genes by directly incorporating the response variables into the grouping process, yielding a supervised clustering algorithm for genes. RESULTS: An empirical study on eight publicly available microarray datasets shows that our algorithm identifies gene clusters with excellent predictive potential, often superior to classification with state-of-the-art methods based on single genes. Permutation tests and bootstrapping provide evidence that the output is reasonably stable and more than a noise artifact. CONCLUSIONS: In contrast to other methods such as hierarchical clustering, our algorithm identifies several gene clusters whose expression levels clearly distinguish the different tissue types. The identification of such gene clusters is potentially useful for medical diagnostics and may at the same time reveal insights into functional genomics.

Algorithms↗
PubMed2002

The advantage of functional prediction based on clustering of yeast genes and its correlation with non-sequence based classifications.

Sequence similarity is probably the most widely used tool to infer functional linkage between proteins. The fully sequenced, much researched, genome of Saccharomyces cerevisiae gives us on opportunity to compare and statistically quantify computational methods based on sequence similarity, which aim to detect such linkage. In addition, the amount of data regarding Saccharomyces Cerevisiae genes and proteins, which is not directly based on sequence is rapidly increasing. Consequently, it allows investigation of the connections and correlation between classification based on these types of data and that based solely on sequence similarity. In this work we start with a simple clustering algorithm to cluster genes based on the BLAST E-score of their similarity. We analyze how well one can infer function from these clusters and for how many of the genes that are currently unknown one can suggest a prediction. Given these parameters, we show that even a simple algorithm achieves better results than simply considering the BLAST output of matching genes. In the second part of the paper, we show that there is a highly significant correlation (p-value < 10(-4) for the vast majority of the experiments) between the aforementioned clusters and other types of classifications. Namely, we show that a pair of genes being clustered together is correlated with these genes having similar expression patterns in DNA array experiments and with the encoded proteins being involved in protein-protein interactions. Although this correlation is highly significant, it is, of course, not strong enough to be, by itself, a tool for predicting co-regulation of genes or interaction of proteins. We discuss possible explanations for this correlation. Furthermore, the statistical evaluation of these results should be considered when developing tools that are aimed at making such predictions.

Algorithms↗
PubMed2002

Visualization and evaluation of clusters for exploratory analysis of gene expression data.

Clustering algorithms have been shown to be useful to explore large-scale gene expression profiles. Visualization and objective evaluation of clusters are two important considerations when users are selecting different clustering algorithms, but they are often overlooked. The developments of a framework and software tools that implement comprehensive data visualization and objective measures of cluster quality are crucial. In this paper, we describe a theoretical framework and formalizations for consistently developing clustering algorithms. A new clustering algorithm was developed within the proposed framework. We demonstrate that a theoretically sound principle can be uniformly applied to the developments of cluster-optimization function, comprehensive data-visualization strategy, and objective cluster-evaluation measures as well as actual implementation of the principle. Cluster consistency and quality measures of the algorithm are rigorously evaluated against those of popular clustering algorithms for gene expression data analysis (K-means and self-organizing maps), in four data sets, yielding promising results.

Algorithms↗
PubMed2001

Model-based clustering and data transformations for gene expression data.

MOTIVATION: Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated by a finite mixture of underlying probability distributions such as multivariate normal distributions. The issues of selecting a 'good' clustering method and determining the 'correct' number of clusters are reduced to model selection problems in the probability framework. Gaussian mixture models have been shown to be a powerful tool for clustering in many applications. RESULTS: We benchmarked the performance of model-based clustering on several synthetic and real gene expression data sets for which external evaluation criteria were available. The model-based approach has superior performance on our synthetic data sets, consistently selecting the correct model and the number of clusters. On real expression data, the model-based approach produced clusters of quality comparable to a leading heuristic clustering algorithm, but with the key advantage of suggesting the number of clusters and an appropriate model. We also explored the validity of the Gaussian mixture assumption on different transformations of real data. We also assessed the degree to which these real gene expression data sets fit multivariate Gaussian distributions both before and after subjecting them to commonly used data transformations. Suitably chosen transformations seem to result in reasonable fits. AVAILABILITY: MCLUST is available at http://www.stat.washington.edu/fraley/mclust. The software for the diagonal model is under development. CONTACT: kayee@cs.washington.edu. SUPPLEMENTARY INFORMATION: http://www.cs.washington.edu/homes/kayee/model.

Algorithms↗
PubMed2004

Gene Ontology friendly biclustering of expression profiles.

The soundness of clustering in the analysis of gene expression profiles and gene function prediction is based on the hypothesis that genes with similar expression profiles may imply strong correlations with their functions in the biological activities. Gene Ontology (GO) has become a well accepted standard in organizing gene function categories. Different gene function categories in GO can have very sophisticated relationships, such as 'part of' and 'overlapping'. Until now, no clustering algorithm can generate gene clusters within which the relationships can naturally reflect those of gene function categories in the GO hierarchy. The failure in resembling the relationships may reduce the confidence of clustering in gene function prediction. In this paper, we present a new clustering technique, Smart Hierarchical Tendency Preserving clustering (SHTP-clustering), based on a bicluster model, Tendency Preserving cluster (TP-Cluster). By directly incorporating Gene Ontology information into the clustering process, the SHTP-clustering algorithm yields a TP-cluster tree within which any subtree can be well mapped to a part of the GO hierarchy. Our experiments on yeast cell cycle data demonstrate that this method is efficient and effective in generating the biological relevant TP-Clusters.

Algorithms↗
PubMed2003

Scoring clustering solutions by their biological relevance.

MOTIVATION: A central step in the analysis of gene expression data is the identification of groups of genes that exhibit similar expression patterns. Clustering gene expression data into homogeneous groups was shown to be instrumental in functional annotation, tissue classification, regulatory motif identification, and other applications. Although there is a rich literature on clustering algorithms for gene expression analysis, very few works addressed the systematic comparison and evaluation of clustering results. Typically, different clustering algorithms yield different clustering solutions on the same data, and there is no agreed upon guideline for choosing among them. RESULTS: We developed a novel statistically based method for assessing a clustering solution according to prior biological knowledge. Our method can be used to compare different clustering solutions or to optimize the parameters of a clustering algorithm. The method is based on projecting vectors of biological attributes of the clustered elements onto the real line, such that the ratio of between-groups and within-group variance estimators is maximized. The projected data are then scored using a non-parametric analysis of variance test, and the score's confidence is evaluated. We validate our approach using simulated data and show that our scoring method outperforms several extant methods, including the separation to homogeneity ratio and the silhouette measure. We apply our method to evaluate results of several clustering methods on yeast cell-cycle gene expression data. AVAILABILITY: The software is available from the authors upon request.

Algorithms↗