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Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…
A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found…
The discovery of community structure is a common challenge in the analysis of network data. Many methods have been proposed for finding community structure, but few have been proposed for determining whether the structure found is…
Unsupervised machine learning, and in particular data clustering, is a powerful approach for the analysis of datasets and identification of characteristic features occurring throughout a dataset. It is gaining popularity across scientific…
Using the APM cluster data we investigate whether the dynamical status of clusters is related to the large-scale structure of the Universe. We find that cluster substructure is strongly correlated with the tendency of clusters to be aligned…
Finding meaningful clusters in drive-by-download malware data is a particularly difficult task. Malware data tends to contain overlapping clusters with wide variations of cardinality. This happens because there can be considerable…
Consensus clustering, a fundamental task in machine learning and data analysis, aims to aggregate multiple input clusterings of a dataset, potentially based on different non-sensitive attributes, into a single clustering that best…
Network of nonlinear dynamical elements often show clustering of synchronization by chaotic instability. Relevance of the clustering to ecological, immune, neural, and cellular networks is discussed, with the emphasis of partially ordered…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
Consider a population consisting of clusters of sampling units, evolving temporally, spatially, or according to other dynamics. We wish to monitor the evolution of its means, medians, or other parameters. For administrative convenience and…
In the last years many studies examined the consistency of students' answers in a variety of contexts. Some of these papers tried to develop more detailed models of the consistency of students' reasoning, or to subdivide a sample of…
The avalanche quantity of the information developed by mankind has led to concept of automation of knowledge extraction - Data Mining ([1]). This direction is connected with a wide spectrum of problems - from recognition of the fuzzy set to…
Cluster algorithms are increasingly popular in biomedical research due to their compelling ability to identify discrete subgroups in data, and their increasing accessibility in mainstream software. While guidelines exist for algorithm…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
In this paper, we study the possibility of designing non-trivial random CSP models by exploiting the intrinsic connection between structures and typical-case hardness. We show that constraint consistency, a notion that has been developed to…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
Colloidal clusters consist of small numbers of colloidal particles bound by weak, short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well-described by a statistical mechanical model…
Cluster number is typically a parameter selected at the outset in clustering problems, and while impactful, the choice can often be difficult to justify. Inspired by bioinformatics, this study examines how the nature of clusters varies with…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…