Related papers: Cluster mechanisms in the fully frustrated Ising m…
Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level…
We introduce and study the random "locked" constraint satisfaction problems. When increasing the density of constraints, they display a broad "clustered" phase in which the space of solutions is divided into many isolated points. While the…
With the membership function being strictly positive, the conventional fuzzy c-means clustering method sometimes causes imbalanced influence when clusters of vastly different sizes exist. That is, an outstandingly large cluster drags to its…
We analyze the collective spin noise in interacting spin systems. General expressions are derived for the short time behaviour of spin systems with general spin-spin interactions, and we suggest optimum experimental conditions for the…
Clustering ensemble has emerged as an important research topic in the field of machine learning. Although numerous methods have been proposed to improve clustering quality, most existing approaches overlook the need for interpretability in…
An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel…
Classical spin liquids are frustrated magnetic phases characterized by local constraints, flat bands in reciprocal space, and emergent gauge structures with distinctive signatures such as pinch points. These arise generally in \emph{cluster…
We demonstrate that a series of procedures for increasing the efficiency of transition matrix calculations can be realized by integrating the standard single-spin flip transition matrix method with global cluster flipping techniques. Our…
We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same…
Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the…
A cluster algorithm is presented for the simulation of the q-state Potts models in which the number of spins is conserved in each state. The algorithm constructs Fortuin-Kasteleyn cluster configurations from spin configurations, in a way…
Clustering is a widely used technique with a long and rich history in a variety of areas. However, most existing algorithms do not scale well to large datasets, or are missing theoretical guarantees of convergence. This paper introduces a…
The cluster state represents a highly entangled state which is one central object for measurement-based quantum computing. Here we study the robustness of the cluster state on the two-dimensional square lattice at zero temperature in the…
Many algorithms for processing probabilistic networks are dependent on the topological properties of the problem's structure. Such algorithms (e.g., clustering, conditioning) are effective only if the problem has a sparse graph captured by…
We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel those observables are used to construct…
Cluster matching by permuting cluster labels is important in many clustering contexts such as cluster validation and cluster ensemble techniques. The classic approach is to minimize the euclidean distance between two cluster solutions which…
The statistical mechanics method is developed for determination of generating function of like-sign spin clusters' size distribution in Ising model as modification of Ising-Potts model by K. K. Murata (1979). It is applied to the…
Clustering is one of the fundamental tasks in data analytics and machine learning. In many situations, different clusterings of the same data set become relevant. For example, different algorithms for the same clustering task may return…
We show that atoms in tilted optical superlattices provide a platform for exploring coupled spin chains of forms that are not present in other systems. In particular, using a period-2 superlattice in 1D, we show that coupled Ising spin…
This paper studies the design of cluster experiments to estimate the global treatment effect in the presence of network spillovers. We provide a framework to choose the clustering that minimizes the worst-case mean-squared error of the…