Published online 20 March 2006
V1 Comp methods and X1 microarray |
Microarray missing data imputation based on a set theoretic framework and biological knowledge
1Department of Electronic Engineering, City University of Hong Kong 83 Tat Chee Avenue, Kowloon, Hong Kong 2Department of Computer Science and Engineering, The Chinese University of Hong Kong Shatin, Hong Kong 3School of Electrical and Information Engineering, University of Sydney NSW 2006, Australia
*To whom correspondence should be addressed. Tel: 852 26098419; Fax: 852 26035024; Email: wcliew{at}cse.cuhk.edu.hk
Received October 31, 2005. Revised February 22, 2006. Accepted February 22, 2006.
Gene expressions measured using microarrays usually suffer from the missing value problem. However, in many data analysis methods, a complete data matrix is required. Although existing missing value imputation algorithms have shown good performance to deal with missing values, they also have their limitations. For example, some algorithms have good performance only when strong local correlation exists in data while some provide the best estimate when data is dominated by global structure. In addition, these algorithms do not take into account any biological constraint in their imputation. In this paper, we propose a set theoretic framework based on projection onto convex sets (POCS) for missing data imputation. POCS allows us to incorporate different types of a priori knowledge about missing values into the estimation process. The main idea of POCS is to formulate every piece of prior knowledge into a corresponding convex set and then use a convergence-guaranteed iterative procedure to obtain a solution in the intersection of all these sets. In this work, we design several convex sets, taking into consideration the biological characteristic of the data: the first set mainly exploit the local correlation structure among genes in microarray data, while the second set captures the global correlation structure among arrays. The third set (actually a series of sets) exploits the biological phenomenon of synchronization loss in microarray experiments. In cyclic systems, synchronization loss is a common phenomenon and we construct a series of sets based on this phenomenon for our POCS imputation algorithm. Experiments show that our algorithm can achieve a significant reduction of error compared to the KNNimpute, SVDimpute and LSimpute methods.
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