In cluster analyses, setting the scale parameter which is implicitly related to the complexity of the data distribution is an important issue; different scale values lead to different results and hence cause different interpretation. In this study, we discuss a framework of multi-scale clustering, where clustering is done with multiple scale values and then the obtained results are compiled into a visually appropriate form to observe overall structures of the clusters. For such purpose, a brick view method is proposed in this study. The construction of a brick view diagram consists of a reindexing procedure of clusters obtained with various scale values and a sorting procedure of samples so as to minimize the distortion defined based on the multiple clustering results. Although some popular clustering methods, such as K-means, spherical K-means, and hierarchical clustering, have been used within the multi-scale framework, we introduce mean-shift clustering based on the kernel density estimation for directional data. We evaluate our approach and existing hierarchical clustering by using an artificial data set and a real data set of gene expression profiles. The results show global structures of distributions can be observed well and in a stable manner, in the brick view diagram.
['Shigeyuki Oba', 'Kikuya Kato', 'Shin Ishii']
Multi-scale clustering for gene expression profiling data