Many spatial access methods, such as the R-tree, have been designed to support spatial search operators (e.g., overlap, containment, and enclosure) over both points and regional objects in multi-dimensional spaces. Unfortunately, contemporary spatial access methods are limited by many problems that significantly degrade the query performance in high-dimensional spaces. This chapter reviews the ...

The governing equations of a transversely isotropic dissipative medium are solved analytically to obtain the surface wave solutions. The appropriate solutions satisfy the required boundary conditions at the stress-free surface to obtain the frequency equation of Rayleigh wave. The numerical values of the non-dimensional speed of Rayleigh wave speed are computed for different values of frequency...

We study the problem of finding an outlier-free subset of a set of points (or a probability distribution) in n-dimensional Euclidean space. As in [BFKV 99], a point x is defined to be a β-outlier if there exists some direction w in which its squared distance from the mean along w is greater than β times the average squared distance from the mean along w. Our main theorem is that for any ǫ > 0, ...

Global optimization methods including Particle Swarm Optimization are usually used to solve optimization problems when the number of parameters is small (hundreds). In the case of inverse problems the objective (or fitness) function used for sampling requires the solution of multiple forward solves. In inverse problems, both a large number of parameters, and very costly forward evaluations hamp...

In this project, we provide a review of efficient solutions to a few high-dimensional CG problems, with particular focus on the problem of nearest neighbour search. For the problems we examine, the general approach will be to either reduce the dimension (using the JL transform) or to preprocess the data and group together points that are close together (using locality sensitive hashing). Finall...

We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d=4, 5, and 6 to be phi(MRJ) approximately 0.46, 0.31, and 0.20, respectively. To a good approximation, t...

This paper summarizes analytical and experimental results for the nearest neighbor similarity search problem in high-dimensional vector spaces using some kind of space-or data-partitioning scheme. Under the assumptions of uniformity and independence of data, we are able to formally show and to demonstrate that conventional approaches to the nearest neighbor problem degenerate if the dimensional...

Preprocess: a set D of points in R d Query: given a new point q, report a point pD with the smallest distance to q q p Motivation

High dimensions have a devastating effect on the FCM algorithm and similar algorithms. One effect is that the prototypes run into the centre of gravity of the entire data set. The objective function must have a local minimum in the centre of gravity that causes FCM’s behaviour. In this paper, examine this problem. This paper answers the following questions: How many dimensions are necessary to ...