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We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…
A statistical description of heavy particles suspended in incompressible rough self-similar flows is developed. It is shown that, differently from smooth flows, particles do not form fractal clusters. They rather distribute inhomogeneously…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
We present an improved clustering based, unsupervised anomalous trajectory detection algorithm for crowded scenes. The proposed work is based on four major steps, namely, extraction of trajectories from crowded scene video, extraction of…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at…
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…
Process discovery algorithms automatically extract process models from event logs, but high variability often results in complex and hard-to-understand models. To mitigate this issue, trace clustering techniques group process executions…
Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering…
We present a computational study of sliding between gold clusters and a highly oriented pyrolytic graphite substrate, a material system that exhibits ultra-low friction due to structural lubricity. By means of molecular dynamics, it is…
We propose a simple model for periodic clustering of particles under forced oscillation. Effective viscosity is assumed to increase owing to neighboring particles by analogy with the Einstein viscosity law. The linear stability analysis and…
Clustering is one of the most fundamental and wide-spread techniques in exploratory data analysis. Yet, the basic approach to clustering has not really changed: a practitioner hand-picks a task-specific clustering loss to optimize and fit…
We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity…
Matter gets organized at several levels of structural rearrangements. At mesoscopic level one can distinguish between two types of rearrangements, conforming to different close-packing or densification conditions, appearing during different…
We present a new approach to clustering, based on the physical properties of an inhomogeneous ferromagnet. No assumption is made regarding the underlying distribution of the data. We assign a Potts spin to each data point and introduce an…
We present results from density functional theory and computer simulations that unambiguously predict the occurrence of first-order freezing transitions for a large class of ultrasoft model systems into cluster crystals. The clusters…
Ensemble clustering has been a popular research topic in data mining and machine learning. Despite its significant progress in recent years, there are still two challenging issues in the current ensemble clustering research. First, most of…
We construct a cross-entropy clustering (CEC) theory which finds the optimal number of clusters by automatically removing groups which carry no information. Moreover, our theory gives simple and efficient criterion to verify cluster…
The influence of clustering on the collision rate of inertial particles in a smooth random velocity field, mimicking the smaller scales of a turbulent flow, is analyzed. For small values of the the ratio between the relaxation time of the…