in this work, one and two-dimensional lattices are studied theoretically by a statistical mechanical approach. the nearest and next-nearest neighbor interactions are both taken into account, and the approximate thermodynamic properties of the lattices are calculated. the results of our calculations show that: (1) even though the next-nearest neighbor interaction may have an insignificant effect...

In many applications, it is important to quickly find, from a database of patterns, the nearest neighbors of highdimensional query points that come into the system in a streaming form. Treating each query point as a separate one is inefficient. Consecutive query points are often neighbors in the high-dimensional space, and intermediate results in the processing of one query should help the proc...

We consider n independent points with a common but arbitrary density fin R a. Two points (X~, Xj) are joined by an edge when a certain set S(X~, Xj) does not contain any other data points. The expected number E(N) of edges in the graph depends upon n, f and the definition of S. Examples include rectangles, spheres and loons; these lead to the graph of all dominance pairs, the Gabriel graph and ...

We introduce a nonparametric model for sensitivity estimation which relies on generating points similar to the prediction point using its k nearest neighbors. Unlike most previous work, the sampled points differ simultaneously in multiple dimensions from the prediction point in a manner dependent on the local density. Our approach is based on an intuitive idea of locality which uses the Voronoi...

In this paper we learn a dissimilarity measure for categorical data, for effective classification of the data points. Each categorical feature (with values taken from a finite set of symbols) is mapped onto a continuous feature whose values are real numbers. Guided by the classification error based on a nearest neighbor based technique, we repeatedly update the assignment of categorical symbols...

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the Euclidean cluster diameter is large. Therefore, it is preferred to assign smaller costs to the paths that stay close to the input points. In this paper, we c...

Given a set S of n points in IR D , D 2. Each point p 2 S is assigned a color c(p) chosen from a xed color set. The All-Nearest-Foreign-Neighbors Problem (ANFNP) is to nd for each point p 2 S its nearest foreign neighbors, i.e. the set of all points in Snfpg that are closest to p among the points in S with a color diierent from c(p). We introduce the Well Separated Color Decomposition (WSCD) wh...

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...

Randomly generated points in IR are connected to their nearest neighbours (Euclidean distance). The resulting connected clusters of points are studied. This paper examines questions related to the collection of clusters formed and to the internal structure of a cluster. In particular, the one-dimensional structure is examined in detail.