Related papers: Dempster-Shafer clustering using Potts spin mean f…
The Consensus Clustering problem has been introduced as an effective way to analyze the results of different microarray experiments. The problem consists of looking for a partition that best summarizes a set of input partitions (each…
Cluster Dynamical Mean Field Theories are analyzed in terms of their semiclassical limit and their causality properties, and a translation invariant formulation of the cellular dynamical mean field theory, PCDMFT, is presented. The…
The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal…
When one tries to simulate quantum spin systems by the Monte Carlo method, often the 'minus-sign problem' is encountered. In such a case, an application of probabilistic methods is not possible. In this paper the method has been proposed…
The geometrical critical behaviour of the two-dimensional Q-state Potts model is usually studied in terms of the Fortuin-Kasteleyn (FK) clusters, or their surrounding loops. In this paper we study a quite different geometrical object: the…
Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short…
We consider two models with disorder dominated critical points and study the distribution of clusters which are confined in strips and touch one or both boundaries. For the classical random bond Potts model in the large-q limit we study…
We present a technique, which we call "etching," which we use to study the harmonic measure of Fortuin-Kasteleyn clusters in the Q-state Potts model for Q=1-4. The harmonic measure is the probability distribution of random walkers diffusing…
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…
Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC…
Grouping objects into clusters based on similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message passing algorithms and spectral algorithms proposed for…
A recent developing trend in clustering is the advancement of algorithms that not only identify clusters within data, but also express and capture the uncertainty of cluster membership. Evidential clustering addresses this by using the…
In this work we extend the notion of what is meant by a meanfield. Meanfields are approximately maps - through some self consistency relation - of a complex, usually manybody, problem to a simpler more readily solvable problem. This mapping…
We prove sharpness of the phase transition for the random-cluster model with $q \geq 1$ on graphs of the form $\mathcal{S} := \mathcal{G} \times S$, where $\mathcal{G}$ is a planar lattice with mild symmetry assumptions, and $S$ a finite…
Deep clustering methods improve the performance of clustering tasks by jointly optimizing deep representation learning and clustering. While numerous deep clustering algorithms have been proposed, most of them rely on artificially…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
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…
The K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. However, it combines the K-means clustering and dimensionality reduction processes for…
Random quenched dilution of the triangular-lattice antiferromagnetic Ising model locally relieves frustration, leading to ordering phenomena. We have studied this system, under such dilution of one sublattice, using hard-spin mean-field…
A perturbation method is presented which can be applied to the description of a wide range of physical problems that deal with dynamics of dipolar coupled spins in solids. The method is based on expansion of the operator exponent in a…