Feature Screening in Large Scale Cluster Analysis

Mais trabalhos sobre clustering.

Feature Screening in Large Scale Cluster Analysis – Trambak Banerjee, Gourab Mukherjee, Peter Radchenko

Abstract: We propose a novel methodology for feature screening in clustering massive datasets, in which both the number of features and the number of observations can potentially be very large. Taking advantage of a fusion penalization based convex clustering criterion, we propose a very fast screening procedure that efficiently discards non-informative features by first computing a clustering score corresponding to the clustering tree constructed for each feature, and then thresholding the resulting values. We provide theoretical support for our approach by establishing uniform non-asymptotic bounds on the clustering scores of the “noise” features. These bounds imply perfect screening of non-informative features with high probability and are derived via careful analysis of the empirical processes corresponding to the clustering trees that are constructed for each of the features by the associated clustering procedure. Through extensive simulation experiments we compare the performance of our proposed method with other screening approaches, popularly used in cluster analysis, and obtain encouraging results. We demonstrate empirically that our method is applicable to cluster analysis of big datasets arising in single-cell gene expression studies.

Conclusions: We propose COSCI, a novel feature screening method for large scale cluster analysis problems that are characterized by both large sample sizes and high dimensionality of the observations. COSCI efficiently ranks the candidate features in a non-parametric fashion and, under mild regularity conditions, is robust to the distributional form of the true noise coordinates. We establish theoretical results supporting ideal feature screening properties of our proposed procedure and provide a data driven approach for selecting the screening threshold parameter. Extensive simulation experiments and real data studies demonstrate encouraging performance of our proposed approach. An interesting topic for future research is extending our marginal screening method by means of utilizing multivariate objective criteria, which are more potent in detecting multivariate cluster information among marginally unimodal features. Preliminary analysis of the corresponding `2 fusion penalty based criterion, which, unlike the `1 based approach used in this paper, is non-separable across dimensions, suggests that this criterion can provide a way to move beyond marginal screening.

Feature Screening in Large Scale Cluster Analysis

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