Related papers: Linked Cluster Expansions via Hypergraph Decomposi…
Hypergraphs are an invaluable tool to understand many hidden patterns in large data sets. Among many ways to represent hypergraph, one useful representation is that of weighted clique expansion. In this paper, we consider this…
Motivated by applications in community detection and dense subgraph discovery, we consider new clustering objectives in hypergraphs and bipartite graphs. These objectives are parameterized by one or more resolution parameters in order to…
Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively…
Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result…
Partitioning a graph into groups of vertices such that those within each group are more densely connected than vertices assigned to different groups, known as graph clustering, is often used to gain insight into the organisation of large…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. Real data distributed in a high-dimensional space can be disentangled into a union…
We present new results for LambdaCC and MotifCC, two recently introduced variants of the well-studied correlation clustering problem. Both variants are motivated by applications to network analysis and community detection, and have…
Previous hypergraph expansions are solely carried out on either vertex level or hyperedge level, thereby missing the symmetric nature of data co-occurrence, and resulting in information loss. To address the problem, this paper treats…
We present a generalization of the recently proposed variational cluster perturbation theory to extended Hubbard models at half filling with repulsive nearest neighbor interaction. The method takes into account short-range correlations…
We investigate an extended version of the quantum Ising model which includes beyond-nearest neighbour interactions and an additional site-dependent longitudinal magnetic field. Treating the interaction exactly and using perturbation theory…
We study hypergraph visualization via its topological simplification. We explore both vertex simplification and hyperedge simplification of hypergraphs using tools from topological data analysis. In particular, we transform a hypergraph to…
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
We revisit the classical approach to cluster expansions, based on tree graphs, and establish a new convergence condition that improves those by Kotecky-Preiss and Dobrushin, as we show in some examples. The two ingredients of our approach…
Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…
We propose a generic framework to describe classical Ising-like models defined on arbitrary graphs. The energy spectrum is shown to be the Hadamard transform of a suitably defined sparse "coding" vector associated with the graph. We expect…
We have studied the exact solution of the extended cluster compass ladder, which is equivalent to extended quantum compass model with cluster interaction between next-nearest-neighbor spins, by using the Jordan-Wigner transformation. We…
Graph model is emerging as a very effective tool for learning the complex structures and relationships hidden in data. Generally, the critical purpose of graph-oriented learning algorithms is to construct an informative graph for image…
We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically…