Entropic Approach to Multiscale Clustering Analysis

Entropic Approach to Multiscale Clustering Analysis

Recently, a novel method has been introduced to estimate the statistical significance of clustering in the direction distribution of objects. The method involves a multiscale procedure, based on the Kullback–Leibler divergence and the Gumbel statistics of extreme values, providing high discrimination power, even in presence of strong background isotropic contamination. It is shown that the meth...

Unsupervised Clustering Analysis: a Multiscale Complex Networks Approach

Unsupervised clustering, also known as natural clustering, stands for the classification of data according to their similarities. Here we study this problem from the perspective of complex networks. Mapping the description of data similarities to graphs, we propose to extend two multiresolution modularity based algorithms to the finding of modules (clusters) in general data sets producing a mul...

Entropic-Genetic Clustering

This paper addresses the clustering problem given the similarity matrix of a dataset. By representing this matrix as a weighted graph we transform this problem to a graph clustering/partitioning problem which aims at identifying groups of strongly inter-connected vertices. We define two distinct criteria with the aim of simultaneously minimizing the cut size and obtaining balanced clusters. The...

An Entropic Approach to the Analysis of Time Series

K-server via Multiscale Entropic Regularization

We present an O((log k)2)-competitive randomized algorithm for the k-server problem on hierarchically separated trees (HSTs). This is the first o(k)-competitive randomized algorithm for which the competitive ratio is independent of the size of the underlying HST. Our algorithm is designed in the framework of online mirror descent where the mirror map is a multiscale entropy. When combined with ...