相关论文: Spontaneous clustering in theoretical and some emp…

The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary ergodic process. Stationary processes are perhaps the most general class of processes considered in…

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

The problem of clustering is considered, for the case when each data point is a sample generated by a stationary ergodic process. We propose a very natural asymptotic notion of consistency, and show that simple consistent algorithms exist,…

We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes are ergodic and the dissimilarity measure satisfies the…

Having reliable estimates of the occurrence rates of extreme events is highly important for insurance companies, government agencies and the general public. The rarity of an extreme event is typically expressed through its return period,…

The emergence of clustering and coarsening in crowded ensembles of self-propelled agents is studied using a lattice model in one-dimension. The persistent exclusion process, where particles move at directions that change randomly at a low…

We consider a stationary random field indexed by an increasing sequence of subsets of $\mathbb{Z}^d$ obeying a very broad geometrical assumption on how the sequence expands. Under certain mixing and local conditions, we show how the tail…

A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping…

We consider stochastic processes arising from dynamical systems by evaluating an observable function along the orbits of the system. The novelty is that we will consider observables achieving a global maximum value (possible infinite) at…

We study a two-species bidirectional exclusion process, and a single species variant, which is motivated by the motion of organelles and vesicles along microtubules. Specifically, we are interested in the clustering of the particles and…

We introduce a new unsupervised learning problem: clustering wide-sense stationary ergodic stochastic processes. A covariance-based dissimilarity measure together with asymptotically consistent algorithms is designed for clustering offline…

In colloidal suspensions, self-organization processes can be easily fueled by external fields. One particularly interesting class of phenomena occurs in monolayers of dipolar particles that are driven by rotating external fields. Here we…

Biologists have long observed periodic-like oxygen consumption oscillations in yeast populations under certain conditions and several unsatisfactory explanations for this phenomenon have been proposed. These "autonomous oscillations" have…

The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…

Clustering is one of the mayor collective phenomena observed in active matter. We study the overdamped motion of interacting active Brownian particles in two dimensions. An instability in the pair correlation function causes the onset of…

The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far from equilibrium. Far from equilibrium, nonergodicity reigns. Nonergodicity implies that the average outcome for…

An ensemble of inelastically colliding grains driven by a vibrating wall in 2D exhibits density clustering. Working in the limit of nearly elastic collisions and employing granular hydrodynamics, we predict, by a marginal stability…

Granular convergence is a property of a granular pack as it is repeatedly sheared in a cyclic, quasistatic fashion, as the packing configuration changes via discrete events. Under suitable conditions the set of microscopic configurations…

We consider a point process sequence induced by a stationary symmetric alpha-stable (0 < alpha < 2) discrete parameter random field. It is easy to prove, following the arguments in the one-dimensional case in Resnick and Samorodnitsky…

Clustering is a fundamental data mining tool that aims to divide data into groups of similar items. Generally, intuition about clustering reflects the ideal case -- exact data sets endowed with flawless dissimilarity between individual…