Skeleton Clustering: Dimension-Free Density-Aided Clustering

ABSTRACT

We introduce a density-aided clustering method called Skeleton Clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density measures that are less dependent on the dimension but have intuitive geometric interpretations. The clustering framework constructs a concise representation of the given data as an intermediate step and can be thought of as a combination of prototype methods, density-based clustering, and hierarchical clustering. We show by theoretical analysis and empirical studies that the skeleton clustering leads to reliable clusters in multivariate and high-dimensional scenarios. Supplementary materials for this article are available online.

KEYWORDS:

• Density estimation
• Density-based clustering
• High-dimensional clustering
• k-means clustering

Supplementary Materials

The supplementary materials contain additional theoretical results, the proofs, and additional empirical results. R code implementation is also included.

Disclosure Statement

The authors report there are no competing interests to declare.

Funding

Yen-Chi Chen is supported by NSF DMS-195278, 2112907, 2141808, and NIH U24-AG072122. Zeyu Wei is supported by NSF DMS-2112907.

Additional information

Funding

Yen-Chi Chen is supported by NSF DMS-195278, 2112907, 2141808, and NIH U24-AG072122. Zeyu Wei is supported by NSF DMS-2112907.