Adaptive Nonparametric Clustering

Kirill Efimov, Larisa Adamyan and Vladimir Spokoiny

No 2018-018, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

Abstract: This paper presents a new approach to non-parametric cluster analysis called Adaptive Weights Clustering (AWC). The idea is to identify the clustering structure by checking at different points and for dierent scales on departure from local homogeneity. The proposed procedure describes the clustering structure in terms of weights wij each of them measures the degree of local inhomogeneity for two neighbor local clusters using statistical tests of "no gap" between them. The procedure starts from very local scale, then the parameter of locality grows by some factor at each step. The method is fully adaptive and does not require to specify the number of clusters or their structure. The clustering results are not sensitive to noise and outliers, the procedure is able to recover dierent clusters with sharp edges or manifold structure. The method is scalable and computationally feasible. An intensive numerical study shows a state-of-the-art performance of the method in various articial examples and applications to text data. Our theoretical study states optimal sensitivity of AWC to local inhomogeneity.

Keywords: adaptive weights; clustering; gap coecient; manifold clustering (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (19)

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