Related papers: Cluster expansions in dilute systems: applications…
Finding the ground state of Ising spin glasses is notoriously difficult due to disorder and frustration. Often, this challenge is framed as a combinatorial optimization problem, for which a common strategy employs simulated annealing, a…
We study the thermodynamics of cubic Ti1-xAlxN using a unified cluster expansion approach for the alloy problem. The purely configurational part of the alloy Hamiltonian is expanded in terms of concentration and volume dependent effective…
We introduce a numerical linked cluster expansion for square-lattice models whose building block is an L-shape cluster. For the spin-1/2 models studied in this work, we find that this expansion exhibits a similar or better convergence of…
We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity…
We introduce a generic scheme to perform non-perturbative linked cluster expansions in long-range ordered quantum phases. Clusters are considered to be surrounded by an ordered reference state leading to effective edge-fields in the exact…
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…
In this work, we extend the dual triply irreducible local expansion (D-TRILEX) approach for correlated electronic systems by introducing a cluster reference system for the diagrammatic expansion. This framework allows us to consistently…
A self-energy-functional approach is applied to construct cluster approximations for correlated lattice models. It turns out that the cluster-perturbation theory (Senechal et al, PRL 84, 522 (2000)) and the cellular dynamical mean-field…
The method of sub-iteration, which was previously applied to the higher-order coupled cluster amplitude equations, is extended to the case of the coupled cluster $\Lambda$ equations. The sub-iteration procedure for the $\Lambda$ equations…
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data…
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into…
One of the fundamental problems in network analysis is detecting community structure in multi-layer networks, of which each layer represents one type of edge information among the nodes. We propose integrative spectral clustering approaches…
We present approximation algorithms for some variants of center-based clustering and related problems in the fully dynamic setting, where the pointset evolves through an arbitrary sequence of insertions and deletions. Specifically, we…
In this paper we develop a general theory which provides a unified treatment of two apparently different problems. The weak Gibbs property of measures arising from the application of Renormalization Group maps and the mixing properties of…
For theoretical description of pseudospin systems with essential short-range and long-range interactions we use the method based on calculations of the free energy functional with taking into account the short-range interactions within the…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
Spectral clustering has become one of the most widely used clustering techniques when the structure of the individual clusters is non-convex or highly anisotropic. Yet, despite its immense popularity, there exists fairly little theory about…
Using computer simulations, we validate a simple free energy model that can be analytically solved to predict the equilibrium size of self-limiting clusters of particles in the fluid state governed by a combination of short-range attractive…
Clustering is a fundamental task in unsupervised learning. Previous research has focused on learning-augmented $k$-means in Euclidean metrics, limiting its applicability to complex data representations. In this paper, we generalize…
For $\Delta \ge 5$ and $q$ large as a function of $\Delta$, we give a detailed picture of the phase transition of the random cluster model on random $\Delta$-regular graphs. In particular, we determine the limiting distribution of the…