Abstract
Discovering densely-populated regions in a dataset of data points is an essential task for density-based clustering. To do so, it is often necessary to calculate each data point’s local density in the dataset. Various definitions for the local density have been proposed in the literature. These definitions can be divided into two categories: Radius-based and k Nearest Neighbors-based. In this study, we find the commonality between these two types of definitions and propose a canonical form for the local density. With the canonical form, the pros and cons of the existing definitions can be better explored, and new definitions for the local density can be derived and investigated.
Highlights
We propose a canonical form for local density
The contribution function could be concontrolled with a radius e and an exponent m
A definition for local density could trolled with a radius and an exponent
Summary
The canonical form decomposes local density definition into three parts: The contribution set, contribution function, and integration operator. √ the kNN-based local density defined in [6,7] implicitly uses a radius equal to one and k, respectively. This canonical form facilitates exploring the pros and cons of these existing definitions for local density.
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