Related papers: Extremal clustering and cluster counting for spati…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with…
This paper introduces a new clustering technique, called {\em dimensional clustering}, which clusters each data point by its latent {\em pointwise dimension}, which is a measure of the dimensionality of the data set local to that point.…
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,…
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…
The present report extends the method of fixed point clustering (Phys.Rev. E 61,5, R4691-4693, 2000) by introducing an indirect criterion for the number of clusters. The derived probability function allows an objective distinction of…
Within the field of process mining, several different trace clustering approaches exist for partitioning traces or process instances into similar groups. Typically, this partitioning is based on certain patterns or similarity between the…
Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different…
Maxima of the linear density field form a point process that can be used to understand the spatial distribution of virialized halos that collapsed from initially overdense regions. However, owing to the peak constraint, clustering…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
Some key issues in robust clustering are discussed with focus on Gaussian mixture model based clustering, namely the formal definition of outliers, ambiguity between groups of outliers and clusters, the interaction between robust clustering…
The birth/death process with mutation describes the evolution of a population, and displays rich dynamics including clustering and fluctuations. We discuss an analytical `field-theoretical' approach to the birth/death process, using a…
A family of self-similar and translation-invariant random sup-measures with long-range dependence are investigated. They are shown to arise as the limit of the empirical random sup-measure of a stationary heavy-tailed process, inspired by…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
Asymptotic behavior of the point process of high and medium values of a Gaussian stationary process with discrete time is considered. An approximation by a Poisson cluster point process is given for the point process.
We introduce a fast and explainable clustering method called CLASSIX. It consists of two phases, namely a greedy aggregation phase of the sorted data into groups of nearby data points, followed by the merging of groups into clusters. The…
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
One key use of k-means clustering is to identify cluster prototypes which can serve as representative points for a dataset. However, a drawback of using k-means cluster centers as representative points is that such points distort the…