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Volume 11 (2011), Pages 2051-2061
Research Article

Nonlinear Model-Based Method for Clustering Periodically Expressed Genes

1School of Information, Beijing Wuzi University, No.1 Fuhe Street, Tongzhou District, Beijing 101149, China
2Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Dr., Saskatoon, SK, S7N 5A9, Canada
3Division of Biomedical Engineering, University of Saskatchewan, 57 Campus Dr., Saskatoon, SK, S7N 5A9, Canada

Received 15 September 2011; Accepted 15 October 2011

Academic Editor: Akhmad Sabarudin

Copyright © 2011 Li-Ping Tian 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.


Clustering periodically expressed genes from their time-course expression data could help understand the molecular mechanism of those biological processes. In this paper, we propose a nonlinear model-based clustering method for periodically expressed gene profiles. As periodically expressed genes are associated with periodic biological processes, the proposed method naturally assumes that a periodically expressed gene dataset is generated by a number of periodical processes. Each periodical process is modelled by a linear combination of trigonometric sine and cosine functions in time plus a Gaussian noise term. A two stage method is proposed to estimate the model parameter, and a relocation-iteration algorithm is employed to assign each gene to an appropriate cluster. A bootstrapping method and an average adjusted Rand index (AARI) are employed to measure the quality of clustering. One synthetic dataset and two biological datasets were employed to evaluate the performance of the proposed method. The results show that our method allows the better quality clustering than other clustering methods (e.g., k-means) for periodically expressed gene data, and thus it is an effective cluster analysis method for periodically expressed gene data.