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We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is…
We use two high resolution CDM simulations to show that (i) when clusters of galaxies form the infall pattern of matter is not random but shows clear features which are correlated in time; (ii) in addition, the infall patterns are…
Nonlinear field theories can be used to study both standard physics questions, or to study questions such as the emergence of order and complexity. These theories are generally derived from the symmetries of a given problem and the…
Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density,…
Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…
There are many cluster analysis methods that can produce quite different clusterings on the same dataset. Cluster validation is about the evaluation of the quality of a clustering; "relative cluster validation" is about using such criteria…
Clustering functional data is a challenging task due to intrinsic infinite-dimensionality and the need for stable, data-adaptive partitioning. In this work, we propose a clustering framework based on Random Projections, which simultaneously…
The evolution of tokens through deep transformer models can be modeled as an interacting particle system that has been shown to exhibit an asymptotic clustering behavior akin to the synchronization phenomenon in Kuramoto models. In this…
Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…
Clustered solutions in oscillator networks provide an important insight into how a system might diversify from a synchronous solution into spatiotemporal complex solutions. They can therefore form a link between fully synchronized and…
Cluster indices describe extremal behaviour of stationary time series. We consider runs estimators of cluster indices. Using a modern theory of multivariate, regularly varying time series, we obtain central limit theorems under conditions…
Dynamical mean-field approximations are performed to study the phase transition of a pair contact process with diffusion in different spatial dimensions. The level of approximation is extended up to 18-site clusters for the one-dimensional…
Hierarchical probabilistic models, such as mixture models, are used for cluster analysis. These models have two types of variables: observable and latent. In cluster analysis, the latent variable is estimated, and it is expected that…
In a stationary ergodic process, clustering is defined as the tendency of events to appear in series of increased frequency separated by longer breaks. Such behavior, contradicting the theoretical "unbiased behavior" with exponential…
The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are…
The cluster algorithm in the fully frustrated Ising model on the square lattice is essentially different from the ones used in other systems. Thus its better understanding is particularly important for finding new lines of development.…
We construct models describing the velocity field in the infall regions of clusters. The velocity field is the superposition of a systematic component and a "noise" component accounting for the effects of small scale substructure and…
Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby discover, relate, and structure types: of behaviour,…
We have designed a new multi-scale approach for Strongly Correlated Systems by combining the Dynamical Cluster Approximation (DCA) and the recently introduced dual-fermion formalism. This approach employs an exact mapping from a real…
We propose a Fourier-based approach for optimization of several clustering algorithms. Mathematically, clusters data can be described by a density function represented by the Dirac mixture distribution. The density function can be smoothed…