Related papers: Cluster expansion methods from physical concepts
Compressed sensing has become a widely accepted paradigm to construct high dimensional cluster expansion models used for statistical mechanical studies of atomic configuration in complex multicomponent crystalline materials. However, strict…
Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description - few…
Long-standing challenges in cluster expansion (CE) construction include choosing how to truncate the expansion and which crystal structures to use for training. Compressive sensing (CS), which is emerging as a powerful tool for model…
In order to efficiently explore the chemical space of all possible small molecules, a common approach is to compress the dimension of the system to facilitate downstream machine learning tasks. Towards this end, we present a data driven…
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…
We study cluster algebras with principal coefficient systems that are associated to unpunctured surfaces. We give a direct formula for the Laurent polynomial expansion of cluster variables in these cluster algebras in terms of perfect…
A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…
While clusters of galaxies are considered one of the most important cosmological probes, the standard spherical modelling of the dark matter and the intracluster medium is only a rough approximation. Indeed, it is well established both…
A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the…
With the inflation of the data, clustering analysis, as a branch of unsupervised learning, lacks unified understanding and application of its mathematical law. Based on the view of fixed point, this paper restates the model-based clustering…
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…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
Materials exhibiting a substitutional disorder such as multicomponent alloys and mixed metal oxides/oxyfluorides are of great importance in many scientific and technological sectors. Disordered materials constitute an overwhelmingly large…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
Multi-view clustering has become a significant area of research, with numerous methods proposed over the past decades to enhance clustering accuracy. However, in many real-world applications, it is crucial to demonstrate a clear…
A method of cluster diagonalization in a systematically expanded Hilbert space is described. We discuss some applications of this procedure to models of high-T_c superconductors, like the t - J and one and three bands Hubbard models in two…
Correlations in interacting many-particle systems can lead to the formation of clusters, in particular bound states and resonances. Systematic quantum statistical approaches allow to combine the nuclear statistical equilibrium description…
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the…
The atomic cluster expansion (Drautz, Phys. Rev. B 99, 014104 (2019)) is extended in two ways, the modelling of vectorial and tensorial atomic properties and the inclusion of atomic degrees of freedom in addition to the positions of the…
Biclustering is used for simultaneous clustering of the observations and variables when there is no group structure known \textit{a priori}. It is being increasingly used in bioinformatics, text analytics, etc. Previously, biclustering has…