Significance Test of Clusters in Gene Expression Profile Data
Clustering is a popular technique used in gene expression analyses. However, conventionally well-used clustering methods often produce variety in results depending on, e.g., initial algorithmic condition. Due to this instability, analysis results may be questionable. For example [3], although B-cell lymphomas had been classified into two distinct classes using hierarchical clustering, another analysis by a different clustering method failed to find these classes [1, 2]. In spite of such instability, the preprocessing or visualization of data by a clustering technique is still important for gene expression analyses. For utilizing technique with certain reliability, it is required to develop not only a stable method but also a method to evaluate quantitatively the reliability of the clustering results. In this report, we propose a quantitative evaluation method of clusters, which determines whether a data group, seemingly a cluster, constructs a statistically significant cluster. In particular, we propose a statistical test examining the existence possibility of a cluster within a parametric model of background noise. A seeming cluster is expressed by a window function represented by characteristic parameters. This statistical test can be extended to examining of feature spaces; we also propose a significance test of feature subspace extracted from PCA analysis.