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BioMed Research International
Volume 2015 (2015), Article ID 918954, 10 pages
Research Article

-Profiles: A Nonlinear Clustering Method for Pattern Detection in High Dimensional Data

1Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA
2School of Software Engineering, Tongji University, Shanghai 200092, China
3The Advanced Institute of Translational Medicine and Department of Gastroenterology, Shanghai Tenth People’s Hospital, Tongji University, Shanghai 200092, China
4Department of Biostatistics and Bioinformatics, Emory University, Atlanta, GA 30322, USA

Received 5 November 2014; Accepted 18 December 2014

Academic Editor: Fang-Xiang Wu

Copyright © 2015 Kai Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


With modern technologies such as microarray, deep sequencing, and liquid chromatography-mass spectrometry (LC-MS), it is possible to measure the expression levels of thousands of genes/proteins simultaneously to unravel important biological processes. A very first step towards elucidating hidden patterns and understanding the massive data is the application of clustering techniques. Nonlinear relations, which were mostly unutilized in contrast to linear correlations, are prevalent in high-throughput data. In many cases, nonlinear relations can model the biological relationship more precisely and reflect critical patterns in the biological systems. Using the general dependency measure, Distance Based on Conditional Ordered List (DCOL) that we introduced before, we designed the nonlinear -profiles clustering method, which can be seen as the nonlinear counterpart of the -means clustering algorithm. The method has a built-in statistical testing procedure that ensures genes not belonging to any cluster do not impact the estimation of cluster profiles. Results from extensive simulation studies showed that -profiles clustering not only outperformed traditional linear -means algorithm, but also presented significantly better performance over our previous General Dependency Hierarchical Clustering (GDHC) algorithm. We further analyzed a gene expression dataset, on which -profile clustering generated biologically meaningful results.