The framework is presented of Bayesian image restoration for multi-valued images by means of the multi-state classical spin systems. Hyperparameters in the probabilistic models are determined so as to maximize the marginal likelihood. A practical algorithm is described for multi-valued image restoration based on loopy belief propagations in probabilistic inference. Loopy belief propagations are...

In this paper we present the Multithreaded Advanced Fast Rational Approximation algorithm – MAFRA – for solving n-dimensional simultaneous Diophantine approximation problems. We show that in some particular applications the Lenstra-Lenstra-Lovász (L) algorithm can be substituted by the presented one in order to reduce their practical running time. MAFRA was implemented in the following architec...

In this paper the problem of image restoration (denoising and inpainting) is approached using sparse approximation of local image blocks. The local image blocks are extracted by sliding square windows over the image. An adaptive block size selection procedure for local sparse approximation is proposed, which affects the global recovery of underlying image. Ideally the adaptive local block selec...

We present KDI (Kernel Density Initialization), a density-based procedure for approximating centroids for the initialization step of iteration-based clustering algorithms. We show empirically that a rather low number of distance calculations in conjunction with a fast algorithm for nding the highest peaks are suucient for eeectively and eeciently nding a pre-speciied number of good centroids, w...

Aims. The so-called Limber equation is widely used in the literature to relate the projected angular clustering of galaxies to the spatial clustering of galaxies in an approximate way. This note gives estimates of where the regime of applicability of Limber's equation stops. Methods. This paper revisits Limber's equation, summarises its underlying assumptions, and compares its predictions to th...

In this paper, we study stationary variant of extended coupled-cluster response approach for properties. This has been studied at the singles and doubles approximation using cubic-truncated functional. This approximation has been studied earlier around equilibrium for small molecules. In this paper, efficacy of this approximation has been shown using perturbative arguments. Further we have calc...

We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we consider is that of approximating sample distributions by ones with sparse support. This provides a new viewpoint to clustering. We propose different relaxations o...

We give deterministic versions of randomized approximation algorithms for several ranking and clustering problems that were proposed by Ailon, Charikar and Newman[1]. We show that under a reasonable extension of the triangle inequality in clustering problems, we can resolve Ailon et al.’s open question whether there is an approximation algorithm for weighted correlation clustering with weights ...

We present a general approach for designing approximation algorithms for a fundamental class of geometric clustering problems in arbitrary dimensions. More specifically, our approach leads to simple randomized algorithms for the k-means, k-median and discrete k-means problems that yield (1 + ε) approximations with probability ≥ 1/2 and running times of O(2(k/ε)O(1)dn). These are the first algor...

Poisson approximation, random graphs, Stein's method Poisson approximations for the counts of a given subgraph in large random graphs were accomplished using Stein's method by Barbour and others. Compound Poisson approximation results, on the other hand, have not appeared, at least partly because of the lack of a suitable coupling. We address that problem by introducing the concept of cluster d...