Clustering Microarrays with Predictive Weighted Ensembles

Abstract

Cluster ensembles seek a consensus across many individual partitions and the resulting solution is usually stable. Cluster ensembles are well suited to the analysis of DNA microarrays, where the tremendous size of the dataset can thwart the discovery of stable groups.Post processing cluster ensembles, where each individual partition is weighted according to its relative accuracy improves the performance of the ensemble whilst maintaining its stability. However, weighted cluster ensembles remain relatively unexplored, primarily because there are no common means of assessing the accuracy of individual clustering solutions. This paper describes a technique of creating weighted cluster ensembles suitable for use with microarray datasets. A regression technique is used to obtain individual cluster solutions. Each solution is then weighted according to its predictive accuracy. The consensus partition is obtained using a novel modification to the traditional k-means algorithm which further enforces the predictability of the solution. An estimate of the natural number of clusters can also be obtained using the modified k-means algorithm. Furthermore, a valuable byproduct of this weighted ensemble approach is a variable importance list. The methodology is applied on two well-known microarray datasets with promising results.

Predictive weighting for cluster ensembles

“…To make the procedure more amenable for use with large datasets, a partition of the datasets could be considered in the manner of Smyth and Coomans [27]. For example, the first subset would be used to train the individual trees, the second subset would be used to calculate the lasso weights, and the third subset could be used as a test subset.…”

Weighted Clustering Ensemble: A Review

“…When p is too large, the response space dimension can be reduced via either principal component analysis or factor analysis. In Smyth and Coomans (2007) The similarity function is defined as…”

SC³: Triple Spectral Clustering-Based Consensus Clustering Framework for Class Discovery from Cancer Gene Expression Profiles

“…There are a number of different consensus clustering approaches which can be divided into two categories based on their emphases [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33]. The approaches [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] in the first category designed new consensus clustering techniques, and applied them to cancer gene expression profiles. For example, Duboit et al [18], [19] applied a prediction-based resampling consensus clustering approach named Clest to perform class discovery from four cancer microarray data sets.…”

“…They [23] also designed a new cluster ensemble approach based on the perturbation technique and the neural gas algorithm to perform clustering analysis on cancer data sets, and proposed a new cluster validity index to identify the number of cancer subtypes. Smyth and Coomans [24] presented a weighted consensus clustering approach by considering the relative accuracy of each clustering solution, and applied it to perform cluster analysis on cancer gene expression profiles. Valentini and Bertoni [25], [26], [27] introduced the randomized map-based consensus clustering approach, and applied it to discover the meaningful clusters from the gene expression profiles.…”

“…There are a number of cluster validity indices that could be used in the first stage, such as the Akaike Information Criterion (AIC) [52], the Minimum Description Length criterion (MDL) [53], the Bayesian Information Criterion (BIC) [54], the Silhouette Index (SI) [55], the Davies-Bouldin index (DBI) [56], the Dunn index (DI) [57], the Gap statistic [58], and so on. Different kinds of clustering algorithms could be applied to microarray data at the second stage of class discovery, such as the self-organizing feature maps [1], the two-way clustering method [2], hierarchical clustering [4], spectral clustering [47], [48], [49], [50], [51], consensus clustering approaches [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], and so on. Our proposed triple spectral clustering-based consensus clustering framework mainly focuses on the improvement of the second stage of class discovery, which assigns data samples to their corresponding clusters as correctly as possible.…”