Related papers: Stability of Density-Based Clustering
We consider quantizing an $Ld$-dimensional sample, which is obtained by concatenating $L$ vectors from datasets of $d$-dimensional vectors, to a $d$-dimensional cluster center. The distortion measure is the weighted sum of $r$th powers of…
Assessing how adequate clusters fit a dataset and finding an optimum number of clusters is a difficult process. A membership matrix and the degree of membership matrix is suggested to determine the homogeneity of a cluster fit. Maximisation…
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…
We consider a network design and expansion problem, where we need to make a capacity investment now, such that uncertain future demand can be satisfied as closely as possible. To use a robust optimization approach, we need to construct an…
The clustering of a data set is one of the core tasks in data analytics. Many clustering algorithms exhibit a strong contrast between a favorable performance in practice and bad theoretical worst-cases. Prime examples are least-squares…
Application of K-Means algorithm is restricted by the fact that the number of clusters should be known beforehand. Previously suggested methods to solve this problem are either ad hoc or require parametric assumptions and complicated…
Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat…
In presence of long range dispersal, epidemics spread in spatially disconnected regions known as clusters. Here, we characterize exactly their statistical properties in a solvable model, in both the supercritical (outbreak) and critical…
The cumulant correlators, $C_{pq}$, are statistical quantities that generalise the better-known $S_p$ parameters; the former are obtained from the two-point probability distribution function of the density fluctuations while the latter…
Despite the inherent lack of a ground truth in clustering, a broad consensus is overall acknowledged in defining the concept of cluster in the continuous setting. Conversely, this remains controversial in the presence of categorical data.…
Dirichlet process mixtures are flexible non-parametric models, particularly suited to density estimation and probabilistic clustering. In this work we study the posterior distribution induced by Dirichlet process mixtures as the sample size…
We propose the DPSM method, a density-based node clustering approach that automatically determines the number of clusters and can be applied in both data space and graph space. Unlike traditional density-based clustering methods, which…
The roles of different nodes within a network are often understood through centrality analysis, which aims to quantify the capacity of a node to influence, or be influenced by, other nodes via its connection topology. Many different…
Suppose a researcher observes individuals within a county within a state. Given concerns about correlation across individuals, it is common to group observations into clusters and conduct inference treating observations across clusters as…
Semi-supervised learning (SSL) assumes that neighbor points lie in the same category (neighbor assumption), and points in different clusters belong to various categories (cluster assumption). Existing methods usually rely on similarity…
Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are…
Many young star clusters appear to be fractal, i.e. they appear to be concentrated in a nested hierarchy of clusters within clusters. We present a new algorithm for statistically analysing the distribution of stars to quantify the level of…
Scatterplots are used for a variety of visual analytics tasks, including cluster identification, and the visual encodings used on a scatterplot play a deciding role on the level of visual separation of clusters. For visualization designers,…
Clustering provides a common means of identifying structure in complex data, and there is renewed interest in clustering as a tool for the analysis of large data sets in many fields. A natural question is how many clusters are appropriate…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…