Automated graph-based fuzzy density peak clustering to detect high-dimensional discrete structures of arbitrary shapes

• Density-based clustering methods are prominent clustering approaches to discover discrete structures buried in high-dimensional (HD) data in terms of density variations. Among them is the well-known Density Peak Clustering (DPC) proposed by Rodriguez and Laio (2014) that performs fairly well in detecting clusters with nonlinear shapes and varying densities. However, it has several shortcomings that it does not learn about the nonlinear shapes of the underlying HD data, is lack of a probabilistic framework to handle overlapping clusters, and is not fully automated.Here we develop comprehensive generalizations of DPC, termed Graph-based Fuzzy Density Peak Clustering (GF-DPC), to circumvent these limitations. In GF-DPC, graph-based methods are employed to robustly estimate densities and capture nonlinearities in the HD data that enhances its power in detecting clusters with arbitrary shapes. Furthermore, a fuzzy extension is introduced that returns a probabilistic assignment of data points to the detected clusters. Finally, the identification of cluster centers and the number of clusters are automated and generalized in terms of fuzzy clustering validation index. The superior performances of GF-DPC compared to other well-known fuzzy clustering methods in discovering clusters with arbitrary shapes, densities, separations and overlapping are demonstrated using both intuitive examples and real datasets.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

Density based clustering

Fuzzy clustering

Graph distance

Automatic validation

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