Discovering clusters from a dataset with different shapes, density, and scales is a known challenging problem in data clustering. In this paper, we propose the RElative COre MErge (RECOME) clustering algorithm. The core of RECOME is a novel density measure, i.e., Relative @math nearest Neighbor Kernel Density (RNKD). RECOME identifies core objects with unit RNKD, and partitions non-core objects into atom clusters by successively following higher-density neighbor relations toward core objects. Core objects and their corresponding atom clusters are then merged through @math -reachable paths on a KNN graph. Furthermore, we discover that the number of clusters computed by RECOME is a step function of the @math parameter with jump discontinuity on a small collection of values. A jump discontinuity discovery (JDD) method is proposed using a variant of the Dijkstra's algorithm. RECOME is evaluated on three synthetic datasets and six real datasets. Experimental results indicate that RECOME is able to discover clusters with different shapes, density and scales. It achieves better clustering results than established density-based clustering methods on real datasets. Moreover, JDD is shown to be effective to extract the jump discontinuity set of parameter @math for all tested dataset, which can ease the task of data exploration and parameter tuning.
Kernel density is a well-known alternative to cut-off density. Kernel density is continuous and is less sensitive to parameter selection. However, traditional kernel density methods face the same difficulty as DBSCAN when dealing with complex datasets that contain clusters with different densities @cite_4 , and tend to confuse low-density clusters with noise. Consequently, KNN kernel density has been applied to handle such situations @cite_2 . The proposed RNKD estimation is inspired by the KNN kernel density with further improvement allowing the inclusion of low-density clusters.
@cite_4 @cite_2
1979896142 2133326466
Density-based clustering algorithms for multivariate data often have difficulties with high-dimensional data and clusters of very different densities. A new density-based clustering algorithm, called KNNCLUST, is presented in this paper that is able to tackle these situations. It is based on the combination of nonparametric k-nearest-neighbor (KNN) and kernel (KNN-kernel) density estimation. The KNN-kernel density estimation technique makes it possible to model clusters of different densities in high-dimensional data sets. Moreover, the number of clusters is identified automatically by the algorithm. KNNCLUST is tested using simulated data and applied to a multispectral compact airborne spectrographic imager (CASI)_image of a floodplain in the Netherlands to illustrate the characteristics of the method. Kernel density estimation is the most widely-used practical method for accurate nonparametric density estimation. However, long-standing worst-case theoretical results showing that its performance worsens exponentially with the dimension of the data have quashed its application to modern high-dimensional datasets for decades. In practice, it has been recognized that often such data have a much lower-dimensional intrinsic structure. We propose a small modification to kernel density estimation for estimating probability density functions on Riemannian submanifolds of Euclidean space. Using ideas from Riemannian geometry, we prove the consistency of this modified estimator and show that the convergence rate is determined by the intrinsic dimension of the submanifold. We conclude with empirical results demonstrating the behavior predicted by our theory.