Paper:

# An Algorithm for Recomputing Concepts in Microarray Data Analysis by Biological Lattice

## Hidenobu Hashikami^{*}, Takanari Tanabata^{**}, Fumiaki Hirose^{***},

Nur Hasanah^{*}, Kazuhito Sawase^{*}, and Hajime Nobuhara^{*}

^{*}Department of Intelligent Interaction Technologies, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba Science City, Ibaraki 305-8573, Japan

^{**}Gene Discovery Research Group, RIKEN Center for Sustainable Resource Science, 3-1-1 Koyadai, Tsukuba, Ibaraki 305-0074, Japan

^{***}Functional Transgenic Crops Research Unit, National Institute of Agrobiological Sciences (NIAS), 2-1-2 Kannondai, Tsukuba, Ibaraki 305-8602, Japan

A data-analytic system is proposed for microarray gene expression data based on Formal Concept Analysis (FCA). The purpose of the system is to systematically organize data and to build a complete lattice that analyzes complex relations among genes and give biological interpretation of microarray data. In the system, formal concept analysis handles complex relations, so the microarray data is binarized by setting up a threshold. When change occurs in a conventional algorithm, formal concepts that are nodes of the lattice were calculated from the beginning, but the calculation is inefficient. This paper proposes a new algorithm that has two phase of matrix detection and updating concepts to efficiently update only altered concepts from previously generated concepts. Experiments on run time show that the algorithm takes an average of 0.94 seconds to process real microarray data containing of 43,734 genes and 6 gene expression values.

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