Related papers: Stability of Density-Based Clustering
Urban structure detection is a basic task in urban geography. Clustering is a core technology to detect the patterns of urban spatial structure, urban functional region, and so on. In big data era, diverse urban sensing datasets recording…
By virtue of their high galaxy space densities and their large spatial separations, clusters are efficient and accurate tracers of the large-scale density and velocity fields. Substantial progress has been made over the past decade in the…
We introduce a consistent estimator for the homology (an algebraic structure representing connected components and cycles) of level sets of both density and regression functions. Our method is based on kernel estimation. We apply this…
This paper deals with nonparametric estimation of conditional den-sities in mixture models in the case when additional covariates are available. The proposed approach consists of performing a prelim-inary clustering algorithm on the…
This study contributes to the body of work on instabilities in the homogeneous cooling system focusing on clustering in the multiphase gas-particle system. The critical system size for the onset of instability, $L^*_c$, is studied via three…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
The correct identification of clusters is crucial for an accurate monitoring of the spread of a disease and also in many other natural, social and physical phenomena which exhibit an epidemic structure. Nevertheless, even when an accurate…
Clustering is an important phenomenon in turbulent flows laden with inertial particles. Although this process has been studied extensively, there are still open questions about both the fundamental physics and the reconciliation of…
Data clustering with uneven distribution in high level noise is challenging. Currently, HDBSCAN is considered as the SOTA algorithm for this problem. In this paper, we propose a novel clustering algorithm based on what we call graph of…
This paper proposes a novel, nonparametric, interpoint distance-based measure to investigate whether there exist any groups in a set of given data, and if so then, how many groups are prevailing in total. It is a cluster accuracy index…
We tackle the problem of the estimation of the level sets L_f({\lambda}) of the density f of a random vector X supported on a smooth manifold M\subsetR^d , from an iid sample of X. To do that we introduce a kernel-based estimator f^n,h ,…
We provide a definition for class density that can be used to measure the aggregate similarity of the samples within each of the classes in a high-dimensional, unstructured dataset. We then put forth several candidate methods for…
The R package pdfCluster performs cluster analysis based on a nonparametric estimate of the density of the observed variables. After summarizing the main aspects of the methodology, we describe the features and the usage of the package, and…
We investigate the dependence of cluster abundance $n(>M,r_{cl})$, i.e., the number density of clusters with mass larger than $M$ within radius $r_{cl}$, on scale parameter $r_{cl}$. Using numerical simulations of clusters in the CDM…
This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our…
Determining the number of clusters present in a dataset is an important problem in cluster analysis. Conventional clustering techniques generally assume this parameter to be provided up front. %user supplied. %Recently, robustness of any…
Since the appearance of the classical paper of Lifshitz almost half a century ago, linear stability analysis of cosmological models is textbook knowledge. Until recently, however, little was known about the behavior of higher than linear…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…
Clustering is an underspecified task: there are no universal criteria for what makes a good clustering. This is especially true for relational data, where similarity can be based on the features of individuals, the relationships between…