Detecting clusters of different geometrical shapes in microarray gene expression data

MOTIVATION: Clustering has been used as a popular technique for finding groups of genes that show similar expression patterns under multiple experimental conditions. Many clustering methods have been proposed for clustering gene-expression data, including the hierarchical clustering, k-means clustering and self-organizing map (SOM). However, the conventional methods are limited to identify different shapes of clusters because they use a fixed distance norm when calculating the distance between genes. The fixed distance norm imposes a fixed geometrical shape on the clusters regardless of the actual data distribution. Thus, different distance norms are required for handling the different shapes of clusters. RESULTS: We present the Gustafson-Kessel (GK) clustering method for microarray gene-expression data. To detect clusters of different shapes in a dataset, we use an adaptive distance norm that is calculated by a fuzzy covariance matrix (F) of each cluster in which the eigenstructure of F is used as an indicator of the shape of the cluster. Moreover, the GK method is less prone to falling into local minima than the k-means and SOM because it makes decisions through the use of membership degrees of a gene to clusters. The algorithmic procedure is accomplished by the alternating optimization technique, which iteratively improves a sequence of sets of clusters until no further improvement is possible. To test the performance of the GK method, we applied the GK method and well-known conventional methods to three recently published yeast datasets, and compared the performance of each method using the Saccharomyces Genome Database annotations. The clustering results of the GK method are more significantly relevant to the biological annotations than those of the other methods, demonstrating its effectiveness and potential for clustering gene-expression data. AVAILABILITY: The software was developed using Java language, and can be executed on the platforms that JVM (Java Virtual Machine) is running. It is available from the authors upon request. SUPPLEMENTARY INFORMATION: Supplementary data are available at http://dragon.kaist.ac.kr/gk.     

Evaluation and comparison of gene clustering methods in microarray analysis

MOTIVATION: Microarray technology has been widely applied in biological and clinical studies for simultaneous monitoring of gene expression in thousands of genes. Gene clustering analysis is found useful for discovering groups of correlated genes potentially co-regulated or associated to the disease or conditions under investigation. Many clustering methods including hierarchical clustering, K-means, PAM, SOM, mixture model-based clustering and tight clustering have been widely used in the literature. Yet no comprehensive comparative study has been performed to evaluate the effectiveness of these methods. RESULTS: In this paper, six gene clustering methods are evaluated by simulated data from a hierarchical log-normal model with various degrees of perturbation as well as four real datasets. A weighted Rand index is proposed for measuring similarity of two clustering results with possible scattered genes (i.e. a set of noise genes not being clustered). Performance of the methods in the real data is assessed by a predictive accuracy analysis through verified gene annotations. Our results show that tight clustering and model-based clustering consistently outperform other clustering methods both in simulated and real data while hierarchical clustering and SOM perform among the worst. Our analysis provides deep insight to the complicated gene clustering problem of expression profile and serves as a practical guideline for routine microarray cluster analysis.     

Using Hierarchical Clustering and Dendrograms to Quantify the Clustering of Membrane Proteins

Cell biologists have developed methods to label membrane proteins with gold nanoparticles and then extract spatial point patterns of the gold particles from transmission electron microscopy images using image processing software. Previously, the resulting patterns were analyzed using the Hopkins statistic, which distinguishes nonclustered from modestly and highly clustered distributions, but is not designed to quantify the number or sizes of the clusters. Clusters were defined by the partitional clustering approach which required the choice of a distance. Two points from a pattern were put in the same cluster if they were closer than this distance. In this study, we present a new methodology based on hierarchical clustering to quantify clustering. An intrinsic distance is computed, which is the distance that produces the maximum number of clusters in the biological data, eliminating the need to choose a distance. To quantify the extent of clustering, we compare the clustering distance between the experimental data being analyzed with that from simulated random data. Results are then expressed as a dimensionless number, the clustering ratio that facilitates the comparison of clustering between experiments. Replacing the chosen cluster distance by the intrinsic clustering distance emphasizes densely packed clusters that are likely more important to downstream signaling events.     

Unsupervised clustering and centroid estimation using dynamic competitive learning

In this paper, an unsupervised learning algorithm is developed. Two versions of an artificial neural network, termed a differentiator, are described. It is shown that our algorithm is a dynamic variation of the competitive learning found in most unsupervised learning systems. These systems are frequently used for solving certain pattern recognition tasks such as pattern classification and k-means clustering. Using computer simulation, it is shown that dynamic competitive learning outperforms simple competitive learning methods in solving cluster detection and centroid estimation problems. The simulation results demonstrate that high quality clusters are detected by our method in a short training time. Either a distortion function or the minimum spanning tree method of clustering is used to verify the clustering results. By taking full advantage of all the information presented in the course of training in the differentiator, we demonstrate a powerful adaptive system capable of learning continuously changing patterns.     

Somatostatin selectively inhibits excitatory contractile pathways of the feline lower esophageal sphincter.

Intrinsic reflexes of the feline lower esophageal sphincter (LES) have been shown to be mediated by specific arrangements of excitatory peptidergic interneurons. Inhibition of intrinsic reflexes may also be mediated by neuropeptides. The specific aims of this study were: (1) to examine the effect of somatostatin (SOM) and vasoactive intestinal peptide (VIP) on basal LES tone, and (2) to determine if these transmitters exert selective inhibitory effects on excitatory contractile pathways. Intraluminal pressures were recorded from the LES, esophagus and fundus by a fixed perfused catheter assembly in anesthetized cats. Peptides were administered via the left gastric artery. SOM had no effect on basal LES pressure with doses ranging from 10(-9) to 10(-5) g/kg. VIP induced a dose-dependent inhibition of basal LES pressure. The maximal effective dose of VIP, 10(-6) g/kg, completely inhibited basal LES pressure (34.7 +/- 6.8 to 1.0 +/- 0.6 mmHg, P less than 0.001). We have previously shown that bombesin (BN) but not substance P (SP) or bethanechol contracts the LES via tetrodotoxin-sensitive pathways. BN at the D50 (5.10(-8) g/kg) increased LES pressure by 32.1 +/- 3.6 mmHg. SOM (10(-5) g/kg) decreased this BN response to 19.2 +/- 5.0 mmHg, P less than 0.05. In contrast, while the D50 of SP (5.10(-8) g/kg) gave a similar increase in LES pressure, 28.8 +/- 5.1 mmHg, this effect was not altered by SOM (23.8 +/- 6.7 mmHg, P greater than 0.10). SOM also had no effect on bethanechol-induced LES contractions (P greater than 0.10). VIP (10(-6) g/kg) totally inhibited the LES response to the D50 of BN, SP, and bethanechol. A submaximal dose of VIP (10(-7) g/kg) partially inhibited the contractile response of all three. Conclusions: (1) VIP, but not SOM, inhibits basal LES tone. (2) SOM selectively inhibits BN but not SP- or bethanechol-induced LES contraction. (3) VIP inhibits BN, SP and bethanechol-induced LES contractions. These studies suggest that somatostatin can selectively inhibit excitatory interneurons at the LES.     

Neural networks and cluster analysis for unsupervised classification of cultivated species of Tilia (Malvaceae)

A case study of the classification of 19 species of the genus Tilia (Malvaceae) using morphological data is presented. The value of a self‐organizing map (SOM) neural network when applied to this problem is compared with that of a standard cluster analysis method. An interpretation of the results and a discussion of traditional classification systems are provided in order to evaluate the practical usefulness of the SOM methodology. The SOM technique is shown to provide an easily understandable two‐dimensional topological map which enables simple linear separation of taxonomic groups. Good separation of traditional infrageneric groups in Tilia is achieved and suggestions about changes to the existing classification are provided. It is concluded that the SOM and cluster analysis methods, whilst both producing results similar to existing classifications, are most effective at different hierarchical levels. © 2009 The Linnean Society of London, Botanical Journal of the Linnean Society, 2009, 159 , 300–314.     

Clustering of the SOM easily reveals distinct gene expression patterns: results of a reanalysis of lymphoma study

Background  

A method to evaluate and analyze the massive data generated by series of microarray experiments is of utmost importance to reveal the hidden patterns of gene expression. Because of the complexity and the high dimensionality of microarray gene expression profiles, the dimensional reduction of raw expression data and the feature selections necessary for, for example, classification of disease samples remains a challenge. To solve the problem we propose a two-level analysis. First self-organizing map (SOM) is used. SOM is a vector quantization method that simplifies and reduces the dimensionality of original measurements and visualizes individual tumor sample in a SOM component plane. Next, hierarchical clustering and K-means clustering is used to identify patterns of gene expression useful for classification of samples.     

Complementary hierarchical clustering

When applying hierarchical clustering algorithms to cluster patient samples from microarray data, the clustering patterns generated by most algorithms tend to be dominated by groups of highly differentially expressed genes that have closely related expression patterns. Sometimes, these genes may not be relevant to the biological process under study or their functions may already be known. The problem is that these genes can potentially drown out the effects of other genes that are relevant or have novel functions. We propose a procedure called complementary hierarchical clustering that is designed to uncover the structures arising from these novel genes that are not as highly expressed. Simulation studies show that the procedure is effective when applied to a variety of examples. We also define a concept called relative gene importance that can be used to identify the influential genes in a given clustering. Finally, we analyze a microarray data set from 295 breast cancer patients, using clustering with the correlation-based distance measure. The complementary clustering reveals a grouping of the patients which is uncorrelated with a number of known prognostic signatures and significantly differing distant metastasis-free probabilities.     

Combining hierarchical clustering and self-organizing maps for exploratory analysis of gene expression patterns

Self-organizing maps (SOM) constitute an alternative to classical clustering methods because of its linear run times and superior performance to deal with noisy data. Nevertheless, the clustering obtained with SOM is dependent on the relative sizes of the clusters. Here, we show how the combination of SOM with hierarchical clustering methods constitutes an excellent tool for exploratory analysis of massive data like DNA microarray expression patterns.     

Averaged gene expressions for regression

Although averaging is a simple technique, it plays an important role in reducing variance. We use this essential property of averaging in regression of the DNA microarray data, which poses the challenge of having far more features than samples. In this paper, we introduce a two-step procedure that combines (1) hierarchical clustering and (2) Lasso. By averaging the genes within the clusters obtained from hierarchical clustering, we define supergenes and use them to fit regression models, thereby attaining concise interpretation and accuracy. Our methods are supported with theoretical justifications and demonstrated on simulated and real data sets.     

Partition decoupling for multi-gene analysis of gene expression profiling data

Background

Molecular dynamics (MD) simulations are powerful tools to investigate the conformational dynamics of proteins that is often a critical element of their function. Identification of functionally relevant conformations is generally done clustering the large ensemble of structures that are generated. Recently, Self-Organising Maps (SOMs) were reported performing more accurately and providing more consistent results than traditional clustering algorithms in various data mining problems. We present a novel strategy to analyse and compare conformational ensembles of protein domains using a two-level approach that combines SOMs and hierarchical clustering.

Results

The conformational dynamics of the α-spectrin SH3 protein domain and six single mutants were analysed by MD simulations. The Cα's Cartesian coordinates of conformations sampled in the essential space were used as input data vectors for SOM training, then complete linkage clustering was performed on the SOM prototype vectors. A specific protocol to optimize a SOM for structural ensembles was proposed: the optimal SOM was selected by means of a Taguchi experimental design plan applied to different data sets, and the optimal sampling rate of the MD trajectory was selected. The proposed two-level approach was applied to single trajectories of the SH3 domain independently as well as to groups of them at the same time. The results demonstrated the potential of this approach in the analysis of large ensembles of molecular structures: the possibility of producing a topological mapping of the conformational space in a simple 2D visualisation, as well as of effectively highlighting differences in the conformational dynamics directly related to biological functions.

Conclusions

The use of a two-level approach combining SOMs and hierarchical clustering for conformational analysis of structural ensembles of proteins was proposed. It can easily be extended to other study cases and to conformational ensembles from other sources.     

Molecular pattern discovery based on penalized matrix decomposition

A reliable and precise identification of the type of tumors is crucial to the effective treatment of cancer. With the rapid development of microarray technologies, tumor clustering based on gene expression data is becoming a powerful approach to cancer class discovery. In this paper, we apply the penalized matrix decomposition (PMD) to gene expression data to extract metasamples for clustering. The extracted metasamples capture the inherent structures of samples belong to the same class. At the same time, the PMD factors of a sample over the metasamples can be used as its class indicator in return. Compared with the conventional methods such as hierarchical clustering (HC), self-organizing maps (SOM), affinity propagation (AP) and nonnegative matrix factorization (NMF), the proposed method can identify the samples with complex classes. Moreover, the factor of PMD can be used as an index to determine the cluster number. The proposed method provides a reasonable explanation of the inconsistent classifications made by the conventional methods. In addition, it is able to discover the modules in gene expression data of conterminous developmental stages. Experiments on two representative problems show that the proposed PMD-based method is very promising to discover biological phenotypes.     

Hierarchical clustering of flow cytometry data for the study of conventional central chondrosarcoma

We have investigated the use of hierarchical clustering of flow cytometry data to classify samples of conventional central chondrosarcoma, a malignant cartilage forming tumor of uncertain cellular origin, according to similarities with surface marker profiles of several known cell types. Human primary chondrosarcoma cells, articular chondrocytes, mesenchymal stem cells, fibroblasts, and a panel of tumor cell lines from chondrocytic or epithelial origin were clustered based on the expression profile of eleven surface markers. For clustering, eight hierarchical clustering algorithms, three distance metrics, as well as several approaches for data preprocessing, including multivariate outlier detection, logarithmic transformation, and z‐score normalization, were systematically evaluated. By selecting clustering approaches shown to give reproducible results for cluster recovery of known cell types, primary conventional central chondrosacoma cells could be grouped in two main clusters with distinctive marker expression signatures: one group clustering together with mesenchymal stem cells (CD49b‐high/CD10‐low/CD221‐high) and a second group clustering close to fibroblasts (CD49b‐low/CD10‐high/CD221‐low). Hierarchical clustering also revealed substantial differences between primary conventional central chondrosarcoma cells and established chondrosarcoma cell lines, with the latter not only segregating apart from primary tumor cells and normal tissue cells, but clustering together with cell lines from epithelial lineage. Our study provides a foundation for the use of hierarchical clustering applied to flow cytometry data as a powerful tool to classify samples according to marker expression patterns, which could lead to uncover new cancer subtypes. J. Cell. Physiol. 225: 601–611, 2010. © 2010 Wiley‐Liss, Inc.     

On an improved clustering algorithm based on node density for WSN routing protocol

To better collect data in context to balance energy consumption, wireless sensor networks (WSN) need to be divided into clusters. The division of clusters makes the network become a hierarchical organizational structure, which plays the role of balancing the network load and prolonging the life cycle of the system. In clustering routing algorithm, the pros and cons of clustering algorithm directly affect the result of cluster division. In this paper, an algorithm for selecting cluster heads based on node distribution density and allocating remaining nodes is proposed for the defects of cluster head random election and uneven clustering in the traditional LEACH protocol clustering algorithm in WSN. Experiments show that the algorithm can realize the rapid selection of cluster heads and division of clusters, which is effective for node clustering and is conducive to equalizing energy consumption.

     

Incorporating biological knowledge into distance-based clustering analysis of microarray gene expression data

MOTIVATION: Because co-expressed genes are likely to share the same biological function, cluster analysis of gene expression profiles has been applied for gene function discovery. Most existing clustering methods ignore known gene functions in the process of clustering. RESULTS: To take advantage of accumulating gene functional annotations, we propose incorporating known gene functions into a new distance metric, which shrinks a gene expression-based distance towards 0 if and only if the two genes share a common gene function. A two-step procedure is used. First, the shrinkage distance metric is used in any distance-based clustering method, e.g. K-medoids or hierarchical clustering, to cluster the genes with known functions. Second, while keeping the clustering results from the first step for the genes with known functions, the expression-based distance metric is used to cluster the remaining genes of unknown function, assigning each of them to either one of the clusters obtained in the first step or some new clusters. A simulation study and an application to gene function prediction for the yeast demonstrate the advantage of our proposal over the standard method.     

An unsupervised hierarchical dynamic self-organizing approach to cancer class discovery and marker gene identification in microarray data

MOTIVATION: Current Self-Organizing Maps (SOMs) approaches to gene expression pattern clustering require the user to predefine the number of clusters likely to be expected. Hierarchical clustering methods used in this area do not provide unique partitioning of data. We describe an unsupervised dynamic hierarchical self-organizing approach, which suggests an appropriate number of clusters, to perform class discovery and marker gene identification in microarray data. In the process of class discovery, the proposed algorithm identifies corresponding sets of predictor genes that best distinguish one class from other classes. The approach integrates merits of hierarchical clustering with robustness against noise known from self-organizing approaches. RESULTS: The proposed algorithm applied to DNA microarray data sets of two types of cancers has demonstrated its ability to produce the most suitable number of clusters. Further, the corresponding marker genes identified through the unsupervised algorithm also have a strong biological relationship to the specific cancer class. The algorithm tested on leukemia microarray data, which contains three leukemia types, was able to determine three major and one minor cluster. Prediction models built for the four clusters indicate that the prediction strength for the smaller cluster is generally low, therefore labelled as uncertain cluster. Further analysis shows that the uncertain cluster can be subdivided further, and the subdivisions are related to two of the original clusters. Another test performed using colon cancer microarray data has automatically derived two clusters, which is consistent with the number of classes in data (cancerous and normal). AVAILABILITY: JAVA software of dynamic SOM tree algorithm is available upon request for academic use. SUPPLEMENTARY INFORMATION: A comparison of rectangular and hexagonal topologies for GSOM is available from http://www.mame.mu.oz.au/mechatronics/journalinfo/Hsu2003supp.pdf     

Clustering huge data sets for parametric PET imaging

A new preprocessing clustering technique for quantification of kinetic PET data is presented. A two-stage clustering process, which combines a precluster and a classic hierarchical cluster analysis, provides data which are clustered according to a distance measure between time activity curves (TACs). The resulting clustered mean TACs can be used directly for estimation of kinetic parameters at the cluster level, or to span a vector space that is used for subsequent estimation of voxel level kinetics. The introduction of preclustering significantly reduces the overall time for clustering of multiframe kinetic data. The efficiency and superiority of the preclustering scheme combined with thresholding is validated by comparison of the results for clustering both with and without preclustering for FDG-PET brain data of 13 healthy subjects.     

Generative topographic mapping applied to clustering and visualization of motor unit action potentials

The identification and visualization of clusters formed by motor unit action potentials (MUAPs) is an essential step in investigations seeking to explain the control of the neuromuscular system. This work introduces the generative topographic mapping (GTM), a novel machine learning tool, for clustering of MUAPs, and also it extends the GTM technique to provide a way of visualizing MUAPs. The performance of GTM was compared to that of three other clustering methods: the self-organizing map (SOM), a Gaussian mixture model (GMM), and the neural-gas network (NGN). The results, based on the study of experimental MUAPs, showed that the rate of success of both GTM and SOM outperformed that of GMM and NGN, and also that GTM may in practice be used as a principled alternative to the SOM in the study of MUAPs. A visualization tool, which we called GTM grid, was devised for visualization of MUAPs lying in a high-dimensional space. The visualization provided by the GTM grid was compared to that obtained from principal component analysis (PCA).     

A dynamically growing self-organizing tree (DGSOT) for hierarchical clustering gene expression profiles

MOTIVATION: The increasing use of microarray technologies is generating large amounts of data that must be processed in order to extract useful and rational fundamental patterns of gene expression. Hierarchical clustering technology is one method used to analyze gene expression data, but traditional hierarchical clustering algorithms suffer from several drawbacks (e.g. fixed topology structure; mis-clustered data which cannot be reevaluated). In this paper, we introduce a new hierarchical clustering algorithm that overcomes some of these drawbacks. RESULT: We propose a new tree-structure self-organizing neural network, called dynamically growing self-organizing tree (DGSOT) algorithm for hierarchical clustering. The DGSOT constructs a hierarchy from top to bottom by division. At each hierarchical level, the DGSOT optimizes the number of clusters, from which the proper hierarchical structure of the underlying dataset can be found. In addition, we propose a new cluster validation criterion based on the geometric property of the Voronoi partition of the dataset in order to find the proper number of clusters at each hierarchical level. This criterion uses the Minimum Spanning Tree (MST) concept of graph theory and is computationally inexpensive for large datasets. A K-level up distribution (KLD) mechanism, which increases the scope of data distribution in the hierarchy construction, was used to improve the clustering accuracy. The KLD mechanism allows the data misclustered in the early stages to be reevaluated at a later stage and increases the accuracy of the final clustering result. The clustering result of the DGSOT is easily displayed as a dendrogram for visualization. Based on a yeast cell cycle microarray expression dataset, we found that our algorithm extracts gene expression patterns at different levels. Furthermore, the biological functionality enrichment in the clusters is considerably high and the hierarchical structure of the clusters is more reasonable. AVAILABILITY: DGSOT is available upon request from the authors.