Relational clustering with heterogeneous data objects has impact in various important applications, such as web mining, text mining and bioinformatics etc. In this paper, we build a star-structured general model for relational clustering. It is formulated as an orthogonal tri-nonnegative matrix factorization. The model performs matrix approximation among all different data types to look for hid...

This paper addresses the problem of efficient information theoretic, non-parametric data clustering. We develop a procedure for adapting the cluster memberships of the data patterns, in order to maximize the recent Cauchy-Schwarz (CS) probability density function (pdf) distance measure. Each pdf corresponds to a cluster. The CS distance is estimated analytically and non-parametrically by means ...

We consider two closely related fundamental clustering problems in this paper. In the min-sum k-clustering one is given a metric space and has to partition the points into k clusterswhile minimizing the sum of pairwise distances between the points within the clusters. In theBalanced k-Median problem the instance is the same and one has to obtain a clustering into kcluster C1, . ...

Extracting fuzzy rules from data allows relationships in the data to be modeled by "if-then" rules that are easy to understand, verify, and extend. This paper presents methods for extracting fuzzy rules for both function approximation and pattern classification. The rule extraction methods are based on estimating clusters in the data; each cluster obtained corresponds to a fuzzy rule that relat...

This paper introduces a novel ansatz-based technique for solution of the Hubbard model over two length scales. Short range correlations are treated exactly using a dynamical cluster approximation QMC simulation, while longer-length-scale physics requiring larger cluster sizes is incorporated through the introduction of the fluctuation exchange (FLEX) approximation. The properties of the resulti...

Approximation of a tensor network by approximating (e.g., factorizing) one or more its constituent tensors can be improved canceling the leading-order error due to constituents’ approximation. The utility such robust approximation is demonstrated for canonical polyadic (CP) (density-fitting) factorized two-particle Coulomb interaction tensor. resulting algebraic (grid-free) tensor, closely rela...

Following recent interest by the community, scaling of minimal singular value a Vandermonde matrix with nodes forming clusters on length scale Rayleigh distance complex unit circle is studied. Using approximation theoretic properties exponential sums, we show that decay only single in size largest cluster, and bound holds for arbitrary small separation distance. We also obtain generalization we...

We have examined the relative abilities of Hartree-Fock, density-functional theory (DFT), and coupled-cluster theory in describing second-order (pseudo) Jahn-Teller (SOJT) effects, perhaps the most commonly encountered form of symmetry breaking in polyatomic molecules. As test cases, we have considered two prototypical systems: the 2Sigmau+ states of D( infinity h) BNB and C3+ for which interac...

Correlation clustering is perhaps the most natural formulation of clustering. Given n objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same cluster and dissimilar objects are put in different clusters. Despite its theoretical appeal, the practical relevance of correlation clustering still remains l...

In molecular simulations, it is sometimes necessary to compute the electrostatic potential at M target sites due to a disjoint set of N charged source particles. Direct summation requires O(MN) operations, which is prohibitively expensive when M and N are large. Here, we consider two alternative tree-based methods that reduce the cost. The standard particle-cluster treecode partitions the N sou...