Biclustering involves the simultaneous clustering of objects and their attributes, thus defining local two-way clustering models. Recently, efficient algorithms were conceived to enumerate all biclusters in real-valued datasets. In this case, the solution composes a complete set of maximal and non-redundant biclusters. However, the ability to enumerate biclusters revealed a challenging scenario: in noisy datasets, each true bicluster may become highly fragmented and with a high degree of overlapping. It prevents a direct analysis of the obtained results. To revert the fragmentation, we propose here two approaches for properly aggregating the whole set of enumerated biclusters: one based on single linkage and the other directly exploring the rate of overlapping. Both proposals were compared with each other and with the actual state-of-the-art in several experiments, and they not only significantly reduced the number of biclusters but also consistently increased the quality of the solution.
Triclustering was proposed by Haczar & Nadif @cite_15 as a biclustering ensemble algorithm. First, they transform each bicluster into a binary matrix. After that, they propose a triclustering algorithm to find the @math most relevant biclusters. As they were able to improve the biological relevance of biclustering for microarray data @cite_0 , we will use this method as a contender in this paper. One major point in ensemble is that we want to combine the results reinforcing the biclusters that seem to be important for several components, and discarding the ones that may come from noise. Due to the way the triclustering algorithm handles the optimization step, non-maximal biclusters can interfere in the final results. Bicluster aggregation is slightly different from bicluster ensemble. While on ensemble tasks we discard biclusters that seem unimportant and combine the ones that contribute the most for the solution, in bicluster aggregation we never discard any bicluster. Given this characteristic, the bicluster ensemble solution is expected to show a high with an impacted (see Section ), as it eliminates biclusters.
@cite_0 @cite_15
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Biclustering is become undoubtedly a current tool for micro array data analysis. Its objective is to identify a set of biclusters, i.e. sub matrices of the original data matrix, presenting a particular pattern. A large number of biclustering methods have already been proposed for gene expression data. Based on ensemble methods, w e propose a new approach improving the performance of all existing biclustering algorithms. Further, we show that the ensemble biclustering can be seen as a problem of binary triclustering and propose an algorithm to solve it. The results on three public micro array datasets show that the ensemble approach produces better biclusters than single approach. Several biclustering algorithms have been proposed in different fields of microarray data analysis. We present a new approach that improves their performance in using the ensemble methods. An ensemble biclustering is considered and formalized by a problem of binary triclustering. We propose a simple and efficient algorithm to solve it. To illustrate the interest of our ensemble approach, numerical experiments are performed on both artificial and real datasets with two biclustering algorithms commonly used in bioinformatics.