Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating dis­ tribution that factorises into cluster poten­ tials. This includes undirected graphs, di­ rected acyclic graphs and junction trees. We derive generalised mean field equations to op­ timise the cluster potentials. We show t...

This paper analyses an adaptive nonconforming finite element method for eigenvalue clusters of self-adjoint operators and proves optimal convergence rates (with respect to the concept of nonlinear approximation classes) for the approximation of the invariant subspace spanned by the eigenfunctions of the eigenvalue cluster. Applications include eigenvalues of the Laplacian and of the Stokes system.

Due to the uncertainty in accessing web pages, analysis of web logs faces some challenges. Several rough k-means cluster algorithms have been proposed and successfully applied to web usage mining. However, they did not explain why rough approximations of these cluster algorithms were introduced. This paper analyzes the characteristics of the data in the boundary areas of clusters, and then a ro...

The cluster connecting problem inside a simple polygon is introduced in this paper. The problem is shown to be NP-complete. A logn-factor approximation algorithm is proposed.

We perform a detailed study of the phase transitions and mechanisms electron localization in extended Hubbard model using dynamical cluster approximation on $2\times 2$ cluster. explore interplay charge order Mott physics. find that nearest-neighbor Coulomb interaction $V$ causes "screening" effects close to transition, pushing boundary larger values $U$. also demonstrate different correlations...

In metric space theory connectedness can be described in terms of a mapping of sets onto the real axis. This function is essentially a labelling function which clustering methods approximate. With the use of metric space theory a proposition and a conjecture are given which are implemented to perform unsupervised clustering which lacks many of the limitations of other, model-based, methods.