Bioinformatics Advance Access published online on January 12, 2005
Bioinformatics, doi:10.1093/bioinformatics/bti251
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1 Department of BioSystems and Advanced Information Technology Research Center, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea
* To whom correspondence should be addressed.
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. 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 data set, 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 self-organizing map 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 data sets, 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 data are available at http://dragon.kaist.ac.kr/gk.
Received August 13, 2004
Revised December 16, 2004
Accepted December 23, 2004
Article
Detecting clusters of different geometrical shapes in microarray gene expression data
2 Department of BioSystems and Advanced Information Technology Research Center, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea; Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology, 373-1 Guseong-dong, Yuseong-gu, Daejeon, 305-701, Korea
Doheon Lee, E-mail: dhlee{at}bisl.kaist.ac.kr
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