A Clustering Algorithm Based on an Ensemble of Dissimilarities: An Application in the Bioinformatics Domain

Abstract

Clustering algorithms such as k-means depend heavily on choosing an appropriate distance metric that reflect accurately the object proximities. A wide range of dissimilarities may be defined that often lead to different clustering results. Choosing the best dissimilarity is an ill-posed problem and learning a general distance from the data is a complex task, particularly for high dimensional problems. Therefore, an appealing approach is to learn an ensemble of dissimilarities. In this paper, we have developed a semi-supervised clustering algorithm that learns a linear combination of dissimilarities considering incomplete knowledge in the form of pairwise constraints. The minimization of the loss function is based on a robust and efficient quadratic optimization algorithm. Besides, a regularization term is considered that controls the complexity of the distance metric learned avoiding overfitting. The algorithm has been applied to the identification of tumor samples using the gene expression profiles, where domain experts provide often incomplete knowledge in the form of pairwise constraints. We report that the algorithm proposed outperforms a standard semi-supervised clustering technique available in the literature and clustering results based on a single dissimilarity. The improvement is particularly relevant for applications with high level of noise.