Related papers: Estimation of cluster functionals for regularly va…
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…
Network clustering reveals the organization of a network or corresponding complex system with elements represented as vertices and interactions as edges in a (directed, weighted) graph. Although the notion of clustering can be somewhat…
Clustering coefficient is one of the most important metrics to understand the complex structure of networks. This paper addresses the estimation of clustering coefficient in network streams. There have been substantial work in this area,…
In empirical work it is common to estimate parameters of models and report associated standard errors that account for "clustering" of units, where clusters are defined by factors such as geography. Clustering adjustments are typically…
Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In…
Unsupervised clustering of temporal data is both challenging and crucial in machine learning. In this paper, we show that neither traditional clustering methods, time series specific or even deep learning-based alternatives generalise well…
The paper is focused on the forecasting method for time series groups with the use of algorithms for cluster analysis. $K$-means algorithm is suggested to be a basic one for clustering. The coordinates of the centers of clusters have been…
The multivariate extremal index function relates the asymptotic distribution of the vector of pointwise maxima of a multivariate stationary sequence to that of the independent sequence from the same stationary distribution. It also measures…
In the extreme value analysis of time series, not only the tail behavior is of interest, but also the serial dependence plays a crucial role. Drees and Rootz\'en (2010) established limit theorems for a general class of empirical processes…
Motivated by theoretical advancements in dimensionality reduction techniques we use a recent model, called Block Markov Chains, to conduct a practical study of clustering in real-world sequential data. Clustering algorithms for Block Markov…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
This paper presents the first time series clustering benchmark utilizing all time series datasets currently available in the University of California Riverside (UCR) archive -- the state of the art repository of time series data.…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
Usual formulations of the clustering coefficient can be shown to be insufficient in the task of describing the local topology of very simple networks. Motivated by this, we review some alternatives in order to present an extension, the…
We investigate how large deviations events cluster in the framework of an infinite moving average process with light-tailed noise and long memory. The long memory makes clusters larger, and the asymptotic behaviour of the size of the…
We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…
The question whether a time series behaves as a random walk or as a station- ary process is an important and delicate problem, particularly arising in financial statistics, econometrics, and engineering. This paper studies the problem to…
Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common…
A key issue in cluster analysis is the choice of an appropriate clustering method and the determination of the best number of clusters. Different clusterings are optimal on the same data set according to different criteria, and the choice…
The community structure of complex networks reveals both their organization and hidden relationships among their constituents. Most community detection methods currently available are not deterministic, and their results typically depend on…