Related papers: Cluster expansions in dilute systems: applications…
We study exact recovery conditions for convex relaxations of point cloud clustering problems, focusing on two of the most common optimization problems for unsupervised clustering: $k$-means and $k$-median clustering. Motivations for…
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…
We review the basics of the coupled-cluster expansion formalism for numerical solutions of the many-body problem, and we outline the principles of an approach directed towards an adequate inclusion of continuum effects in the associated…
Ashtiani et al. (NIPS 2016) introduced a semi-supervised framework for clustering (SSAC) where a learner is allowed to make same-cluster queries. More specifically, in their model, there is a query oracle that answers queries of the form…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
In this paper, we show that the popular K-means clustering problem can equivalently be reformulated as a conic program of polynomial size. The arising convex optimization problem is NP-hard, but amenable to a tractable semidefinite…
We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of…
The maximum-entropy method is applied to the problem of reconstructing the projected mass density of a galaxy cluster using its gravitational lensing effects on background galaxies. We demonstrate the method by reconstructing the mass…
One of the most employed yet simple algorithm for cluster analysis is the k-means algorithm. k-means has successfully witnessed its use in artificial intelligence, market segmentation, fraud detection, data mining, psychology, etc., only to…
Causal effects are often characterized with population summaries. These might provide an incomplete picture when there are heterogeneous treatment effects across subgroups. Since the subgroup structure is typically unknown, it is more…
We study graph clustering in the Stochastic Block Model (SBM) in the presence of both large clusters and small, unrecoverable clusters. Previous convex relaxation approaches achieving exact recovery do not allow any small clusters of size…
We use a previously introduced mapping between the continuum percolation model and the Potts fluid (a system of interacting s-states spins which are free to move in the continuum) to derive the low density expansion of the pair…
Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications…
Load shapes derived from smart meter data are frequently employed to analyze daily energy consumption patterns, particularly in the context of applications like Demand Response (DR). Nevertheless, one of the most important challenges to…
We provide a strategy to find in few elementary calculations the critical exponents of the overlaps for dilute spin glasses, in absence of external field. Such a strategy is based on the expansion of a suitably perturbed average of the…
Properly spin-adapted coupled-cluster theory for general open-shell configurations remains an active area of research in electronic structure theory. In this contribution we examine Lindgren's normal-ordered exponential ansatz to correlate…
Interacting particle systems in a finite-volume in equilibrium are often described by a grand-canonical ensemble induced by the corresponding Hamiltonian, i.e. a finite-volume Gibbs measure. However, in practice, directly measuring this…
The dynamical cluster approximation (DCA) is a systematic extension beyond the single site approximation in dynamical mean field theory (DMFT), to include spatially non-local correlations in quantum many-body simulations of strongly…
In 2011 Musiker, Schiffler and Williams obtained expansion formulae for cluster algebras from orientable surfaces. For singly and doubly notched arcs these formulae required the notion of $\gamma$-symmetric perfect matchings and…
We consider electricity capacity expansion models, which optimize investment and retirement decisions by minimizing both investment and operation costs. In order to provide credible support for planning and policy decisions, these models…