Related papers: Cluster point processes on manifolds

We construct a new random probability measure on the sphere and on the unit interval which in both cases has a Gibbs structure with the relative entropy functional as Hamiltonian. It satisfies a quasi-invariance formula with respect to the…

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary…

We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…

We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new…

We propose a simple, projection-based algorithm for clustering mixtures of discrete (Bernoulli) distributions. Unlike previous approaches that rely on coordinate-specific ``combinatorial projections,'' our algorithm is rotationally…

Let $X=(X_1,X_2,\ldots)$ be a sequence of random variables with values in a standard space $(S,\mathcal{B})$. Suppose \begin{gather*} X_1\sim\nu\quad\text{and}\quad P\bigl(X_{n+1}\in\cdot\mid…

We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process…

Let $X_t$ be the (reflecting) diffusion process generated by $L:=\Delta+\nabla V$ on a complete connected Riemannian manifold $M$ possibly with a boundary $\partial M$, where $V\in C^1(M)$ such that $\mu(d x):= e^{V(x)}d x$ is a probability…

We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating…

We are interested in phase transitions in certain percolation models on point processes and their dependence on clustering properties of the point processes. We show that point processes with smaller void probabilities and factorial moment…

We carry out analysis and geometry on a marked configuration space $\Omega^M_X$ over a Riemannian manifold $X$ with marks from a space $M$. We suppose that $M$ is a homogeneous space $M$ of a Lie group $G$. As a transformation group $\frak…

Mixtures of multivariate normal inverse Gaussian (MNIG) distributions can be used to cluster data that exhibit features such as skewness and heavy tails. However, for cluster analysis, using a traditional finite mixture model framework,…

After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…

We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that…

Semi-supervised clustering is the task of clustering data points into clusters where only a fraction of the points are labelled. The true number of clusters in the data is often unknown and most models require this parameter as an input.…

A compact metric space $(X, \rho)$ is given. Let $\mu$ be a Borel measure on $X$. By $r$-cluster we mean a measurable subset of $X$ with diameter at most $r$. A family of $k$ $2r$-clusters is called a $r$-cluster structure of order $k$ if…

Clustering multivariate data is a pervasive task in many applied problems, particularly in social studies and life science. Model-based approaches to clustering rely on mixture models, where each mixture component corresponds to the kernel…

We show that the chaos representation of some Compound Poisson Type processes displays an underlying intrinsic combinatorial structure, partly independent of the chosen process. From the computational viewpoint, we solve the arising…

The partition function of the finite $1+\epsilon$ state Potts model is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are…

We propose a bootstrap procedure for data that may exhibit clustering in two or more dimensions. We use insights from the theory of generalized U-statistics to analyze the large-sample properties of statistics that are sample averages from…