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...

We present a fast approximate nearest neighbor algorithm for semantic segmentation. Our algorithm builds a graph over superpixels from an annotated set of training images. Edges in the graph represent approximate nearest neighbors in feature space. At test time we match superpixels from a novel image to the training images by adding the novel image to the graph. A move-making search algorithm a...

Partially due to the fact that the empirical data collected by devices with finite bandwidth often neither preserves the specified structure nor induces a certain desired rank, retrieving the nearest structured low rank approximation from a given data matrix becomes an imperative task in many applications. This paper investigates the case of approximating a given target matrix by a real-valued ...

the proliferation of multimedia data, there is an increasing need to support the indexing and searching of high-dimensional data. In this paper, we propose an efficient indexing method for high-dimensional multimedia databases using the filtering approach, known also as vector approximation approach which supports the nearest neighbor search efficiently. Our technique called RA +-Blocks (Region...