Related papers: Clustering piecewise stationary processes
Many clustering schemes are defined by optimizing an objective function defined on the partitions of the underlying set of a finite metric space. In this paper, we construct a framework for studying what happens when we instead impose…
A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
We study hierarchical clusterings of metric spaces that change over time. This is a natural geometric primitive for the analysis of dynamic data sets. Specifically, we introduce and study the problem of finding a temporally coherent…
We present a thermodynamic theory for a generic population of $M$ individuals distributed into $N$ groups (clusters). We construct the ensemble of all distributions with fixed $M$ and $N$, introduce a selection functional that embodies the…
Economic policy and research rely on the correct evaluation of the billions of high-frequency data points that we collect every day. Consistent clustering algorithms, like DBSCAN, allow us to make sense of the data in a useful way. However,…
Consider unsupervised clustering of objects drawn from a discrete set, through the use of human intelligence available in crowdsourcing platforms. This paper defines and studies the problem of universal clustering using responses of crowd…
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
The paper tackles the problem of clustering multiple networks, directed or not, that do not share the same set of vertices, into groups of networks with similar topology. A statistical model-based approach based on a finite mixture of…
Clustering is a fundamental problem in data analysis. In differentially private clustering, the goal is to identify $k$ cluster centers without disclosing information on individual data points. Despite significant research progress, the…
Time series clustering is a central machine learning task with applications in many fields. While the majority of the methods focus on real-valued time series, very few works consider series with discrete response. In this paper, the…
The aim of this paper is to shed light on the analysis of non-stationary time series by means of the method of diffusion entropy. For this purpose, we first study the case when infinitely many time series, as different realizations of the…
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…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…
One of the focal points of the modern literature on Bayesian nonparametrics has been the problem of clustering, or partitioning, where each data point is modeled as being associated with one and only one of some collection of groups called…
One basic requirement of many studies is the necessity of classifying data. Clustering is a proposed method for summarizing networks. Clustering methods can be divided into two categories named model-based approaches and algorithmic…
Projective clustering is a problem with both theoretical and practical importance and has received a great deal of attentions in recent years. Given a set of points $P$ in $\mathbb{R}^{d}$ space, projective clustering is to find a set…
In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the…
We present a new algorithm for clustering longitudinal data. Data of this type can be conceptualized as consisting of individuals and, for each such individual, observations of a time-dependent variable made at various times. Generically,…
Clustering methods must be tailored to the dataset it operates on, as there is no objective or universal definition of ``cluster,'' but nevertheless arbitrariness in the clustering method must be minimized. This paper develops a…