# Mean Square Residue Biclustering with Missing Data and Row Inversions

• Stefan Gremalschi
• Gulsah Altun
• Irina Astrovskaya
• Alexander Zelikovsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5542)

## Abstract

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 [4]. 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.

## Keywords

Biclustering Mean Square Residue

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## Authors and Affiliations

• Stefan Gremalschi
• 1
• Gulsah Altun
• 2
• Irina Astrovskaya
• 1
• Alexander Zelikovsky
• 1
1. 1.Department of Computer ScienceGeorgia State UniversityAtlanta
2. 2.Department of Reproductive MedicineUniversity of CaliforniaSan Diego