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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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. We consider the problem of identifying a sparse set of relevant columns and rows in a large data matrix with highly corrupted entries. This problem of identifying groups from a collection of bipartite variables such as proteins and drugs, biological species and gene sequences, malware and signatures, etc is commonly referred to as biclustering or co-clustering. Despite its great practical relevance, and although several ad-hoc methods are available for biclustering, theoretical analysis of the problem is largely non-existent. The problem we consider is also closely related to structured multiple hypothesis testing, an area of statistics that has recently witnessed a flurry of activity. We make the following contributions 1. We prove lower bounds on the minimum signal strength needed for successful recovery of a bicluster as a function of the noise variance, size of the matrix and bicluster of interest. 2. We show that a combinatorial procedure based on the scan statistic achieves this optimal limit. 3. We characterize the SNR required by several computationally tractable procedures for biclustering including element-wise thresholding, column row average thresholding and a convex relaxation approach to sparse singular vector decomposition. 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. Mining matrices to find relevant biclusters, subsets of rows exhibiting a coherent pattern over a subset of columns, is a critical task for a wide-set of biomedical and social applications. Since biclustering is a challenging combinatorial optimization task, existing approaches place restrictions on the allowed structure, coherence and quality of biclusters. Biclustering approaches relying on pattern mining (PM) allow an exhaustive yet efficient space exploration together with the possibility to discover flexible structures of biclusters with parameterizable coherency and noise-tolerance. Still, state-of-the-art contributions are dispersed and the potential of their integration remains unclear.This work proposes a structured and integrated view of the contributions of state-of-the-art PM-based biclustering approaches, makes available a set of principles for a guided definition of new PM-based biclustering approaches, and discusses their relevance for applications in pattern recognition. Empirical evidence shows that these principles guarantee the robustness, efficiency and flexibility of PM-based biclustering. HighlightsPattern mining (PM) searches enable flexible, exhaustive and efficient biclusteringIntegration of existing dispersed PM-inspired contributions for biclustering.Principles for guided design and evaluation of new PM-based biclustering approachesPM-based biclustering solutions have parameterizable coherency and quality.