Related papers: Dynamics and self-similarity in min-driven cluster…
In this paper, we develop a Mean Field Games approach to Cluster Analysis. We consider a finite mixture model, given by a convex combination of probability density functions, to describe the given data set. We interpret a data point as an…
An automatic procedure to perform sub-clustering on large samples is presented. At each iteration, the most diverse cluster is sub-clustered, and the global diversity of the new classification is compared to the previous one. The process…
A new maximum approximate likelihood (ML) estimation algorithm for the mixture of Kent distribution is proposed. The new algorithm is constructed via the BSLM (block successive lower-bound maximization) framework and incorporates manifold…
This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance…
We introduce a simple model of active transport for an ensemble of particles driven by an external shear flow. Active refers to the fact that the flow of the particles is modified by the distribution of particles itself. The model consists…
The totally asymmetric simple exclusion process in discrete time is considered on finite rings with fixed number of particles. A translation-invariant version of the backward-ordered sequential update is defined for periodic boundary…
The usual Langevin approach to describe systems driven by noise fails to describe the long time behavior of systems with multiple attractors. The solution of the associated linear Fokker-Planck equation is always unique, even though it…
In this paper we consider the clustering coefficient and clustering function in a random graph model proposed by Krioukov et al.~in 2010. In this model, nodes are chosen randomly inside a disk in the hyperbolic plane and two nodes are…
We study gravitational clustering of mass points in three dimensions with random initial positions and periodic boundary conditions (no expansion) by numerical simulations. Correlation properties are well defined in the system and a sort of…
In this paper we introduce and discuss kinetic equations for the evolution of the probability distribution of the number of particles in a population subject to binary interactions. The microscopic binary law of interaction is assumed to be…
The $k$-means method is an iterative clustering algorithm which associates each observation with one of $k$ clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
We consider the approach to self-similarity (or dynamical scaling) in Smoluchowski's coagulation equations for the solvable kernels K(x,y)=2, x+y and xy. We prove the uniform convergence of densities to the self-similar solution with…
Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of…
In this paper we formulate in general terms an approach to prove strong consistency of the Empirical Risk Minimisation inductive principle applied to the prototype or distance based clustering. This approach was motivated by the Divisive…
The persistence probability, $P_C(t)$, of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. In the mean-field the problem…
We revisit Pollard's classical result on consistency for $k$-means clustering in Euclidean space, with a focus on extensions in two directions: first, to problems where the data may come from interesting geometric settings (e.g., Riemannian…
This paper introduces a novel data clustering algorithm based on Langevin dynamics, where the associated potential is constructed directly from the data. To introduce a self-consistent potential, we adopt the potential model from the…
The problem of clustering a set of points moving on the line consists of the following: given positive integers n and k, the initial position and the velocity of n points, find an optimal k-clustering of the points. We consider two…
This note outlines a method for clustering time series based on a statistical model in which volatility shifts at unobserved change-points. The model accommodates some classical stylized features of returns and its relation to GARCH is…