Regional co-location patterns represent subsets of object types that are located together in space (i.e. region). Discovering regional spatial co-location patterns is an important problem with many application domains. There are different methods in this field but they encounter a big problem: finding a unique optimum neighborhood radius or finding an optimum k value for nearest neighbor featur...

Sample weighting and variations in neighborhood or data-dependent distance metric definitions are three principal directions considered for improving k-NN classification technique. Recently, manifold-based distance metrics attracted considerable interest and computationally less demanding approximations are developed. However, a careful comparison of these alternative approaches is missing. In ...

In this paper, we develop a hierarchical classifier (an inverted tree-like structure) consisting of an organized set of "blocks" each of which is actually a module that performs a feature extraction and an associated classification. We build each of such blocks by coupling a Mirroring Neural Network (MNN) with a clustering (algorithm) wherein the functions of the MNN are automatic data reductio...

This paper studies a spatial queueing system on a circle, polled at random locations by a myopic server that can only observe customers in a bounded neighborhood. The server operates according to a greedy policy, always serving the nearest customer in its neighborhood, and leaving the system unchanged at polling instants where the neighborhood is empty. This system is modeled as a measure-value...

Locally Linear Embedding (LLE) algorithm is the first classic nonlinear manifold learning algorithm based on the local structure information about the data set, which aims at finding the low-dimension intrinsic structure lie in high dimensional data space for the purpose of dimensionality reduction. One deficiency appeared in this algorithm is that it requires users to give a free parameter k w...

Consider that the coordinates of N points are randomly generated along the edges of a d-dimensional hypercube (random point problem). The probability that an arbitrary point is the mth nearest neighbor to its own nth nearest neighbor (Cox probabilities) plays an important role in spatial statistics. Also, it has been useful in the description of physical processes in disordered media. Here we p...

Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, namely, the k-nearest neighbor graph, the k-relative neighborhood graph, the k-Gabriel graph and the k-Delaunay graph. For k = 0 (k = 1 in the case...

Nearest neighbor searching is an important geometric subproblem in vector quanti-zation. Existing studies have shown that the diiculty of solving this problem eeciently grows rapidly with dimension. Indeed, existing approaches on unstructured codebooks in dimension 16 are little better than brute-force search. We show that if one is willing to relax the requirement of nding the true nearest nei...

The k-local hyperplane distance nearest neighbors classification (HKNN) builds a non-linear decision surface with maximal local margin in the input space, with invariance inferred from the local neighborhood rather than the prior knowledge, so that it performs very well in many applications. However, it still cannot be comparable with human being in classification on the noisy, the sparse, and ...