Related papers: Coupled-Cluster Theory Revisited. Part I: Discreti…
This article presents an in-depth educational overview of the latest mathematical developments in coupled cluster (CC) theory, beginning with Schneider's seminal work from 2009 that introduced the first local analysis of CC theory. We offer…
Clustering methods group a set of data points into a few coherent groups or clusters of similar data points. As an example, consider clustering pixels in an image (or video) if they belong to the same object. Different clustering methods…
Graph-based clustering methods have demonstrated the effectiveness in various applications. Generally, existing graph-based clustering methods first construct a graph to represent the input data and then partition it to generate the…
A general quantum many-body theory in configuration space is developed by extending the traditional coupled cluter method (CCM) to a variational formalism. Two independent sets of distribution functions are introduced to evaluate the…
An important form of prior information in clustering comes in form of cannot-link and must-link constraints. We present a generalization of the popular spectral clustering technique which integrates such constraints. Motivated by the…
Clustering trajectory data attracted considerable attention in the last few years. Most of prior work assumed that moving objects can move freely in an euclidean space and did not consider the eventual presence of an underlying road network…
This paper presents a co-clustering technique that, given a collection of images and their hierarchies, clusters nodes from these hierarchies to obtain a coherent multiresolution representation of the image collection. We formalize the…
A discrete version of the inverse scattering method proposed by Ablowitz and Ladik is generalized to study an integrable full-discretization (discrete time and discrete space) of the coupled nonlinear Schr\"{o}dinger equations. The…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing a representative example on the driven similarity renormalization group (DSRG). Starting from the least approximate method…
Coupled cluster theory produced arguably the most widely used high-accuracy computational quantum chemistry methods. Despite the approach's overall great computational success, its mathematical understanding is so far limited to results…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
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…
Clustering methods are applied regularly in the bibliometric literature to identify research areas or scientific fields. These methods are for instance used to group publications into clusters based on their relations in a citation network.…
Multiple clustering aims at discovering diverse ways of organizing data into clusters. Despite the progress made, it's still a challenge for users to analyze and understand the distinctive structure of each output clustering. To ease this…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
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…
We propose a novel method for multiple clustering that assumes a co-clustering structure (partitions in both rows and columns of the data matrix) in each view. The new method is applicable to high-dimensional data. It is based on a…