Fuzzy ensemble clustering based on random
projections for DNA microarray data analysis
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Objective: Two major problems relatared the unsupervised analysis of gene expression data are represented by the accuracy and reliability of the discovered clusters, and by the biological fact that the boundaries between classes of patients or classes of functionally related genes are sometimes not clearly deﬁned. The main goal of this work consists in the exploration of new strategies and in the development of new clustering methods to improve the accuracy and robustness of clustering results, taking into account the uncertainty underlying the assignment of examples to clusters in the context of gene expression data analysis. Methodology: We propose a fuzzy ensemble clustering approach both to improve the accuracy of clustering results and to take into account the inherent fuzziness of biological and bio-medical gene expression data. We applied random projections that obey the Johnson-Lindenstrauss lemma to obtain several instances of lower dimensional gene expression data from the original high-dimensional ones, approximately preserving the information and the metric structure of the original data. Then we adopt a double fuzzy approach to obtain a consensus ensemble clustering, by ﬁrst applying a fuzzy k-means algorithm to the diﬀerent instances of the projected low-dimensional data and then by using a fuzzy t-norm to combine the multiple clusterings. Several variants of the fuzzy ensemble clustering algorithms are proposed, according to diﬀerent techniques to combine the base clusterings and to obtain the ﬁnal consensus
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