title: Fuzzy ensemble clustering based on random projections for DNA microarray data analysis.
abstract: OBJECTIVE
  Two major problems related 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.
  
  
  METHODS
  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 clustering.
  
  
  CONCLUSIONS
  We applied our proposed fuzzy ensemble methods to the gene expression analysis of leukemia, lymphoma, adenocarcinoma and melanoma patients, and we compared the results with other state of the art ensemble methods. Results show that in some cases, taking into account the natural fuzziness of the data, we can improve the discovery of classes of patients defined at bio-molecular level. The reduction of the dimension of the data, achieved through random projections techniques, is well-suited to the characteristics of high-dimensional gene expression data, thus resulting in improved performance with respect to single fuzzy k-means and with respect to ensemble methods based on resampling techniques. Moreover, we show that the analysis of the accuracy and diversity of the base fuzzy clusterings can be useful to explain the advantages and the limitations of the proposed fuzzy ensemble approach.
authors.affiliation: DSI, Dipartimento di Scienze dell' Informazione, Università degli Studi di Milano, Via Comelico 39, 20135 Milano, Italy. avogadri@dsi.unimi.it
authors.forename: Roberto
authors.initials: R
authors.lastname: Avogadri
authors.forename: Giorgio
authors.initials: G
authors.lastname: Valentini
mesh_terms: D000465:Algorithms; D016000:Cluster Analysis; D017143:Fuzzy Logic; D015870:Gene Expression; D006801:Humans; D009369:Neoplasms / Q000235:genetics; D020411:Oligonucleotide Array Sequence Analysis