The references (e.g., Indyk and Motwani, 1999, Datar et al., 2004) contain extensive discussions of the complexity and applications of nearest neighbor algorithms and the motivations for introducing approximations. Complexity does not directly concern us in this paper, so we will not discuss it further; this paper is concerned with the utility and implications of the approximation scheme chosen...

Superconducting phase diagram of the extended Hubbard model supplemented with interaction and hopping terms exceeding nearest neighbour distance in range is analysed systematically at different band-filling and temperature values in a mean-field approximation. The obtained results clearly underline the importance of next-nearest neighbour terms in developing the main superconducting properties ...

I present first results from an in-progress calculation of BK in quenched approximation using overlap fermions. My particular implementation of the overlap uses a kernel with nearest and next-nearest neighbor interactions and HYP-blocked gauge connections. Matching to the continuum NDR regularization is done perturbatively. I present preliminary results at β = 5.9 and 6.1 (lattice spacings 0.12...

This paper describes a machine learning method, called Regression by Feature Projections (RFP), for predicting a real-valued target feature. In RFP training is based on simply storing the projections of the training instances on each feature separately. Prediction is computed through two approximation procedures. The first approximation process is to find the individual predictions of features ...

Many fundamental problems for approximate polynomials can be reformulated as structured linear approximation problems. Problems such as finding polynomials with a GCD which are nearest to given relatively prime polynomials, finding the nearest Ore polynomials with a non-trivial GCRD, finding the nearest polynomial which functionally decomposes, and finding the nearest multivariate polynomial wh...

Accurately representing synonymy using distributional similarity requires large volumes of data to reliably represent infrequent words. However, the naı̈ve nearest-neighbour approach to compare context vectors extracted from large corpora scales poorly. The Spatial Approximation Sample Hierarchy (SASH) is a data-structure for performing approximate nearest-neighbour queries, and has been previou...

Many pattern recognition tasks make use of the k nearest neighbour (k–NN) technique. In this paper we are interested on fast k– NN search algorithms that can work in any metric space i.e. they are not restricted to Euclidean–like distance functions. Only symmetric and triangle inequality properties are required for the distance. A large set of such fast k–NN search algorithms have been develope...

In this paper, we present an efficient algorithm for fast nearest-neighbour search in multidimensional space under a so called approximation-elimination framework. The algorithm is based on a new approximation procedure which selects codevectors for distance computation in the close proximity of the test vector and eliminates codevectors using the triangle inequality based elimination. The algo...

In this paper, we provide an overview of fast nearest-neighbor search algorithms based on an &approximation}elimination' framework under a class of elimination rules, namely, partial distance elimination, hypercube elimination and absolute-error-inequality elimination derived from approximations of Euclidean distance. Previous algorithms based on these elimination rules are reviewed in the cont...

We investigate the possibility of ferromagnetic ordering in non-degenerate Hubbard model on face-centered cubic lattice within functional renormalization group technique using temperature as a scale parameter. assume relations between nearest, next-nearest, and next-next-nearest hopping parameters providing higher order (giant) van Hove singularity density states. The instability formation with...