Mean Square Residue Biclustering with Missing Data and Row Inversions
Cheng and Church proposed a greedy deletion-addition algorithm to find a given number of k biclusters, whose mean squared residues (MSRs) are below certain thresholds and the missing values in the matrix are replaced with random numbers. In our previous paper we introduced the dual biclustering method with quadratic optimization to missing data and row inversions.
In this paper, we modified the dual biclustering method with quadratic optimization and added three new features. First, we introduce ”row status” for each row in a bicluster where we add and also delete rows from biclusters based on their status in order to find min MSR. We compare our results with Cheng and Church’s approach where they inverse rows while adding them to the biclusters. We select the row or the negated row not only at addition, but also at deletion and show improvement. Second, we give a prove for the theorem introduced by Cheng and Church in . Since, missing data often occur in the given data matrices for biclustering, usually, missing data are filled by random numbers. However, we show that ignoring the missing data is a better approach and avoids additional noise caused by randomness. Since, an ideal bicluster is a bicluster with an H value of zero, our results show a significant decrease of H value of the biclusters with lesser noise compared to original dual biclustering and Cheng and Church method.
KeywordsBiclustering Mean Square Residue
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- 2.Baldi, P., Hatfield, G.W.: DNA Microarrays and Gene Expression. In: From Experiments to Data Analysis and Modelling. Cambridge Univ. Press, Cambridge (2002)Google Scholar
- 3.Bertsimas, D., Tsitsiklis, J.: Introduction to Linear Optimization. Athena ScientificGoogle Scholar
- 4.Cheng, Y., Church, G.: Biclustering of Expression Data. In: Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology (ISMB), pp. 93–103. AAAI Press, Menlo Park (2000)Google Scholar
- 6.Papadimitriou, C.H., Steiglitz, K.: Combinatorial optimization: algorithms and complexity, p. 2982. Prentice-Hall, Inc., Upper Saddle RiverGoogle Scholar
- 8.Shamir, R., Lecture notes, http://www.cs.tau.ac.il/~rshamir/ge/05/scribes/lec04.pdf
- 11.Yang, J., Wang, H., Wang, W., Yu, P.: Enhanced biclustering on gene expression data. In: Proceedings of the 3rd IEEE Conference on Bioinformatics and Bioengineering (BIBE), pp. 321–327 (2003)Google Scholar
- 12.Zhang, Y., Zha, H., Chu, C.H.: A time-series biclustering algorithm for revealing co-regulated genes. In: Proc. Int. Symp. Information and Technology: Coding and Computing (ITCC 2005), Las Vegas, USA, pp. 32–37 (2005)Google Scholar
- 13.Zhou, J., Khokhar, A.A.: ParRescue: Scalable Parallel Algorithm and Implementation for Biclustering over Large Distributed Datasets. In: 26th IEEE International Conference on Distributed Computing Systems, ICDCS 2006 (2006)Google Scholar
- 16.Yang, J., Wang, W., Wang, H., Yu, P.S.: Enhanced biclustering on expression data. In: Proceedings of the 3rd IEEE Conference on Bioinformatics and Bioengineering (BIBE 2003), pp. 321–327 (2003)Google Scholar