Related papers: Cluster update for tensor network states
We analyze the recently developed folding algorithm [Phys. Rev. Lett. 102, 240603 (2009)] to simulate the dynamics of infinite quantum spin chains, and relate its performance to the kind of entanglement produced under the evolution of…
We describe a method for reconstructing multi-scale entangled states from a small number of efficiently-implementable measurements and fast post-processing. The method only requires single particle measurements and the total number of…
The quantum computing scheme described in Phys. Rev. Lett. 98, 190504 (2007), when viewed as a cluster state computation, features a 3-D cluster state, novel adjustable strength error correction capable of correcting general errors through…
This paper investigates graph clustering in the planted cluster model in the presence of {\em small clusters}. Traditional results dictate that for an algorithm to provably correctly recover the clusters, {\em all} clusters must be…
The paper is concerned with methods for computing the best low multilinear rank approximation of large and sparse tensors. Krylov-type methods have been used for this problem; here block versions are introduced. For the computation of…
Based on the self-energy-functional approach proposed recently [M. Potthoff, Eur. Phys. J. B 32, 429 (2003)], we present an extension of the cluster-perturbation theory to systems with spontaneously broken symmetry. Our method applies to…
Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension. This introduces a certain degree of arbitrariness. To address this issue, we propose a new method, namely the…
Due to the explosive growth of large-scale data sets, tensors have been a vital tool to analyze and process high-dimensional data. Different from the matrix case, tensor decomposition has been defined in various formats, which can be…
Tensor-valued data benefits greatly from dimension reduction as the reduction in size is exponential in the number of modes. To achieve maximal reduction without loss in information, our objective in this work is to give an automated…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…
This paper studies inference in cluster randomized trials where treatment status is determined according to a "matched pairs" design. Here, by a cluster randomized experiment, we mean one in which treatment is assigned at the level of the…
Several fundamental tasks in data science rely on computing an extremal eigenspace of size $r \ll n$, where $n$ is the underlying problem dimension. For example, spectral clustering and PCA both require the computation of the leading…
Multi-view clustering attracts much attention recently, which aims to take advantage of multi-view information to improve the performance of clustering. However, most recent work mainly focus on self-representation based subspace…
The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…
While symmetry has been exploited to analyze synchronization patterns in complex networks, the identification of symmetries in large-size network remains as a challenge. We present in the present work a new method, namely the method of…
This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.
Given sparse multi-dimensional data (e.g., (user, movie, time; rating) for movie recommendations), how can we discover latent concepts/relations and predict missing values? Tucker factorization has been widely used to solve such problems…
The amount of available data about complex systems is increasing every year, measurements of larger and larger systems are collected and recorded. A natural representation of such data is given by networks, whose size is following the size…
Tensor Network States (TNS) offer an efficient representation for the ground state of quantum many body systems and play an important role in the simulations of them. Numerous TNS are proposed in the past few decades. However, due to the…
Temporal data, obtained in the setting where it is only possible to observe one time point per experiment, is widely used in different research fields, yet remains insufficiently addressed from the statistical point of view. Such data often…