Penalized and weighted K-means for clustering with scattered objects and prior information in high-throughput biological data

Motivation: Cluster analysis is one of the most important data mining tools for investigating high-throughput biological data. The existence of many scattered objects that should not be clustered has been found to hinder performance of most traditional clustering algorithms in such a high- dimensional complex situation. Very often, additional prior knowledge from databases or previous experiments is also available in the analysis. Excluding scattered objects and incorporating existing prior information are desirable to enhance the clustering performance. Results: In this article, a class of loss functions is proposed for cluster analysis and applied in high- throughput genomic and proteomic data. Two major extensions from K-means are involved: penalization and weighting. The additive penalty term is used to allow a set of scattered objects without being clustered. Weights are introduced to account for prior information of preferred or prohibited cluster patterns to be identified. Their relationship with the classification likelihood of Gaussian mixture models is explored. Incorporation of good prior information is also shown to improve the global optimization issue in clustering. Applications of the proposed method on simulated data as well as high- throughput data sets from tandem mass spectrometry (MS/MS) and microarray experiments are presented. Our results demonstrate its superior performance over most existing methods and its computational simplicity and extensibility in the application of large complex biological data sets.