Model order selection for bio-molecular data clustering

Abstract

Background: Cluster analysis has been widely applied for investigating structure in bio-molecular data. A drawback of most clustering algorithms is that they cannot automatically detect the "natural" number of clusters underlying the data, and in many cases we have no enough "a priori" biological knowledge to evaluate both the number of clusters as well as their validity. Recently several methods based on the concept of stability have been proposed to estimate the "optimal" number of clusters, but despite their successful application to the analysis of complex bio-molecular data, the assessment of the statistical significance of the discovered clustering solutions and the detection of multiple structures simultaneously present in high-dimensional bio-molecular data are still major problems.

A stability-based algorithm to validate hierarchical clusters of genes

“…Using the algorithm described in Section 2 and the standard average-linkage algorithm with Euclidean distance to perform the hierarchical clusterings, we iterated 50 random projections from the original 14-dimensional space to a lower 10-dimensional space, using Bernoulli random projections (Bertoni and Valentini, 2007).…”

“…Considering that clusters of genes may show a hierarchical multi-level organisation (Bertoni and Valentini, 2007), we could reduce the computational complexity by examining a linear number of clusters, computed by a hierarchical clustering algorithm.…”

Probabilistic modeling and machine learning in structural and systems biology

“…Three of the papers are particularly focused in this task. Yoon et al [5] introduce a robust preprocessing method for treating missing values in gene expression data, and Bertoni and Valentini [6] decide the number of clusters based on stability against fluctuations caused by random projections. In the only paper on metabonomics, Vehtari et al [7] introduce a full-Bayesian way of modeling the mapping between NMR spectra and clinical variables.…”

Normality-based validation for crisp clustering

“…Nevertheless, Gaussian mixtures assume a probabilistic (fuzzy) model for the data, and so these approaches can not be directly applied to the validation of a crisp partition. Finally, some recent techniques based on stability criteria measure the reproducibility of clustering solutions on a second sample [27,28,29]. They have been applied to cluster validation mainly for gene expression data sets.…”