Methods of nearest neighbors are essential in wide range of applications where it is necessary to estimate probability density (e.g. Bayes’s classifier, problems of searching in large databases). This paper contemplates on features of distribution of nearest neighbors’ distances in high-dimensional spaces. It shows that for uniform distribution of points in n-dimensional Euclidean space the dis...

Interval arithmetic has been used to create guaranteed intersection tests in the ray tracing algorithms. Although those algorithms improve the reliability in the visualization of implicit surfaces, they do not provide an alternative to avoid point sampling inside the pixel. In this paper, we develop an interval adaptive antialiasing algorithm (IAA) by means of the study of the coherence of sets...

SVI is a promising new scheme for indexing high-dimensional points and vectors for use in vector retrieval and for nding the k-nearest neighbours. SVI performs an approximate search; that is, it trades oo the completeness of the search for speed. The indexing scheme is built around a rule that was found by applying data mining techniques to sets of random vectors. This approach could well lead ...

This paper discusses a new greedy algorithm for solving the sparse approximation problem over quasi-incoherent dictionaries. These dictionaries consist of waveforms that are uncorrelated “on average,” and they provide a natural generalization of incoherent dictionaries. The algorithm provides strong guarantees on the quality of the approximations it produces, unlike most other methods for spars...

Abstract We consider the level-crossing problem in a three-level system with non-linearly time-varying Hamiltonian (time-dependence t). We study the validity of the so-called independent crossing approximation in the Landau-Zener model by making comparison with results obtained numerically in density matrix approach. We also demonstrate the failure of the so-called ”nearest zero” approximation ...

Many applications require to determine the k-nearest neighbors for multiple query points simultaneously. This task is known as all-(k)-nearest-neighbor (AkNN) query. In this paper, we suggest a new method for efficient AkNN query processing which is based on spherical approximations for indexing and query set representation. In this setting, we propose trigonometric pruning which enables a sign...

This paper introduces the problem of fault tolerant topology control for one-to-all communications in symmetric wireless networks. We investigate two algorithms to address the problem, namely Minimum Weight Based Algorithm (MWBA) and Nearest Neighbor Augmentation Algorithm (NNAA), and prove that the former is a 4k approximation and the latter is a (k+4) approximation. Through simulations, we ev...

In this paper, we propose a novel lower-bound estimate for dynamic time warping (DTW) methods that use an inner product distance on multi-dimensional posterior probability vectors known as posteriorgrams. Compared to our previous work, the new lower-bound estimate uses piecewise aggregate approximation (PAA) to reduce the time required for calculating the lower-bound estimate. We describe the P...

We study the approximate nearest neighbour method for cost-sensitive classification on low-dimensional manifolds embedded within a high-dimensional feature space. We determine the minimax learning rates for distributions on a smooth manifold, in a cost-sensitive setting. This generalises a classic result of Audibert and Tsybakov. Building upon recent work of Chaudhuri and Dasgupta we prove that...