Related papers: A Short Introduction to Numerical Linked-Cluster E…
This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows…
Given a complete graph $G = (V, E)$ where each edge is labeled $+$ or $-$, the Correlation Clustering problem asks to partition $V$ into clusters to minimize the number of $+$edges between different clusters plus the number of $-$edges…
A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system…
We show how to simulate the clustering of rich clusters of galaxies using a technique based on the Zel'dovich approximation. This method well reproduces the spatial distribution of clusters obtainable from full N-body simulations at a…
Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…
The clustering of bounded data presents unique challenges in statistical analysis due to the constraints imposed on the data values. This paper introduces a novel method for model-based clustering specifically designed for bounded data.…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
We develop an approach of calculating the many-body path integral based on the linked cluster expansion method. First, we derive a linked cluster expansion and we give the diagrammatic rules for calculating the free-energy and the pair…
Clustering is a commonplace problem in many areas of data science, with applications in biology and bioinformatics, understanding chemical structure, image segmentation, building recommender systems, and many more fields. While there are…
In this tutorial-style review we discuss basic concepts of coupled cluster theory and recent developments that increase its computational efficiency for calculations of molecules, solids and materials in general. We will touch upon the…
The latent block model (LBM) is a flexible probabilistic tool to describe interactions between node sets in bipartite networks, but it does not account for interactions of time varying intensity between nodes in unknown classes. In this…
This paper proposes an original approach to cluster multi-component data sets, including an estimation of the number of clusters. From the construction of a minimal spanning tree with Prim's algorithm, and the assumption that the vertices…
Simulating large quantum circuits on hardware with limited qubit counts is often attempted through methods like circuit knitting, which typically incur sample costs that grow exponentially with the number of connections cut. In this work,…
Neighbor Embedding (NE) aims to preserve pairwise similarities between data items and has been shown to yield an effective principle for data visualization. However, even the best existing NE methods such as Stochastic Neighbor Embedding…
Dynamical quantum-cluster approaches, such as different cluster extensions of the dynamical mean-field theory (cluster DMFT) or the variational cluster approximation (VCA), combined with efficient cluster solvers, such as the quantum…
In Constrained Correlation Clustering, the goal is to cluster a complete signed graph in a way that minimizes the number of negative edges inside clusters plus the number of positive edges between clusters, while respecting hard constraints…
The problem of clustering large complex networks plays a key role in several scientific fields ranging from Biology to Sociology and Computer Science. Many approaches to clustering complex networks are based on the idea of maximizing a…
We study the \LowerBoundedCenter (\lbc) problem, which is a clustering problem that can be viewed as a variant of the \kCenter problem. In the \lbc problem, we are given a set of points P in a metric space and a lower bound \lambda, and the…
By combining Hartree-Fock with a neural-network-supported quantum-cluster solver proposed recently in the context of solid-state lattice models, we formulate a scheme for selective neural-network configuration interaction (NNCI)…
In general, the clustering problem is NP-hard, and global optimality cannot be established for non-trivial instances. For high-dimensional data, distance-based methods for clustering or classification face an additional difficulty, the…