Association Analysis for Real-valued Data: Definitions and Application to Microarray Data

Date of Submission: 
March 3, 2008
Report Number: 
08-007
Report PDF: 
Abstract: 
The discovery of biclusters, which denote groups of items that show coherent values across a subset of all the transactions in a data set, is an important type of analysis performed on real-valued data sets in several domains, such as biology. Several algorithms have been proposed to find different types of biclusters in such data sets. However, the search schemes used by these algorithms are unable to search the space of all possible biclusters exhaustively. Pattern mining algorithms in association analysis also essentially produce biclusters as their result, since the patterns consist of items that are supported by a subset of all the transactions. However, a major limitation of the numerous techniques developed in association analysis is that they are only able to analyze data sets that are constituted of binary and/or categorical variables, and their application to real-valued data sets often involves some lossy transformation such as discretization or binarization of the attributes. In this paper, we propose a novel association analysis framework for exhaustively and efficiently mining range support patterns from such a data set. On one hand, this framework reduces the loss of information incurred by binarization- and discretization-based approaches, and on the other, it enables the exhaustive discovery of coherent biclusters. We compared the performance of our framework with two standard biclustering algorithms through the evaluation of the functional coherence on patterns/biclusters derived from microarray data. These experiments show that the real-valued patterns discovered by our framework are better enriched by small biologically interesting functional classes. We also demonstrate the complementarity between our framework and the commonly used biclustering algorithm ISA, using specific examples of patterns that are found and functions that are covered by the former but not the latter. The source code and data sets used in this paper are available at http://www.cs.umn.edu/vk/gaurav/rap.