Related papers: Correlations in random cluster model at $q=1$
A fractional fuzzy Potts measure is a probability distribution on spin configurations of a finite graph $G$ obtained in two steps: first a subgraph of $G$ is chosen according to a random cluster measure $\phi_{p,q}$, and then a spin…
Clustering is a central approach for unsupervised learning. After clustering is applied, the most fundamental analysis is to quantitatively compare clusterings. Such comparisons are crucial for the evaluation of clustering methods as well…
The well known bunkbed conjecture about percolation on finite graphs is now resolved; Gladkov, Pak and Zimin, building upon work of Hollom, have constructed a counterexample. We revisit this conjecture and study it in the broader context of…
Arboreal Gas is a type of (unrooted) random forest on a graph, where the probability is determined by a parameter $\beta>0$ per edge. This model is essentially equivalent to acyclic Bernoulli bond percolation with a parameter…
Correlation clustering provides a method for separating the vertices of a signed graph into the optimum number of clusters without specifying that number in advance. The main goal in this type of clustering is to minimize the number of…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
We investigate the pairwise negative correlation (p-NC) property for uniform probability measures on several families of spanning subgraphs of the complete graph $K_n$. Motivated by conjectured negative dependence properties of the…
We introduce a random recursive tree model with two communities, called balanced community modulated random recursive tree, or BCMRT in short. In this setting, pairs of nodes of different type appear sequentially. Each node of the pair…
In this paper, matching pairs of random graphs under the community structure model is considered. The problem emerges naturally in various applications such as privacy, image processing and DNA sequencing. A pair of randomly generated…
In the Correlation Clustering problem, we are given a complete weighted graph $G$ with its edges labeled as "similar" and "dissimilar" by a noisy binary classifier. For a clustering $\mathcal{C}$ of graph $G$, a similar edge is in…
We consider the problem of correlation clustering on graphs with constraints on both the cluster sizes and the positive and negative weights of edges. Our contributions are twofold: First, we introduce the problem of correlation clustering…
Clustering is an underspecified task: there are no universal criteria for what makes a good clustering. This is especially true for relational data, where similarity can be based on the features of individuals, the relationships between…
We consider the random cluster model with parameter $q<1$, for which the FKG inequalities are not valid. On the square lattice, stochastic comparison with Bernoulli percolation implies that the model is subcritical (respectively…
In the Correlation Clustering problem, we are given a weighted graph $G$ with its edges labeled as "similar" or "dissimilar" by a binary classifier. The goal is to produce a clustering that minimizes the weight of "disagreements": the sum…
The parameterized entanglement monotone, the $q$-concurrence, is also a reasonable parameterized entanglement measure. By exploring the properties of the $q$-concurrence with respect to the positive partial transposition and realignment of…
In this paper we propose a measure of clustering quality or accuracy that is appropriate in situations where it is desirable to evaluate a clustering algorithm by somehow comparing the clusters it produces with ``ground truth' consisting of…
We show that if a sample of galaxy clusters is complete above some mass threshold, then hierarchical clustering theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by…
The quantum fluctuations of fields can exhibit subtle correlations in space and time. As the interval between a pair of measurements varies, the correlation function can change sign, signaling a shift between correlation and…
In correlation clustering, we are given $n$ objects together with a binary similarity score between each pair of them. The goal is to partition the objects into clusters so to minimise the disagreements with the scores. In this work we…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…