Emerging location-based systems and data analysis frameworks requires efficient management of spatial data for approximate and exact search. Exact similarity search can be done using space partitioning data structures, such as Kd-tree, R*-tree, and Ball-tree. In this paper, we focus on Ball-tree, an efficient search tree that is specific for spatial queries which use euclidean distance. Each node of a Ball-tree defines a ball, i.e. a hypersphere that contains a subset of the points to be searched. In this paper, we propose Ball*-tree, an improved Ball-tree that is more efficient for spatial queries. Ball*-tree enjoys a modified space partitioning algorithm that considers the distribution of the data points in order to find an efficient splitting hyperplane. Also, we propose a new algorithm for KNN queries with restricted range using Ball*-tree, which performs better than both KNN and range search for such queries. Results show that Ball*-tree performs 39 -57 faster than the original Ball-tree algorithm.
Abstract The Approximating and Eliminating Search Algorithm (AESA) can currently be considered as one of the most efficient procedures for finding Nearest Neighbours in Metric Spaces where distances computation is expensive. One of the major bottlenecks of the AESA, however, is its quadratic preprocessing time and memory space requirements which, in practice, can severely limit the applicability of the algorithm for large sets of data. In this paper a new version of the AESA is introduced which only requires linear preprocessing time and memory. The performance of the new version, referred to as ‘Linear AESA’ (LAESA), is studied through a number of simulation experiments in abstract metric spaces. The results show that LAESA achieves a search performance similar to that of the AESA, while definitely overcoming the quadratic costs bottleneck. Nearest neighbour search (NNS) is an old problem that is of practical importance in a number of fields. It involves finding, for a given point q, called the query, one or more points from a given set of points that are nearest to the query q. Since the initial inception of the problem a great number of algorithms and techniques have been proposed for its solution. However, it remains the case that many of the proposed algorithms have not been compared against each other on a wide variety of datasets. This research attempts to fill this gap to some extent by presenting a detailed empirical comparison of three prominent data structures for exact NNS: KD-Trees, Metric Trees, and Cover Trees. Our results suggest that there is generally little gain in using Metric Trees or Cover Trees instead of KD-Trees for the standard NNS problem. The nearest neighbor (NN) technique is very simple, highly efficient and effective in the field of pattern recognition, text categorization, object recognition etc. Its simplicity is its main advantage, but the disadvantages can't be ignored even. The memory requirement and computation complexity also matter. Many techniques are developed to overcome these limitations. NN techniques are broadly classified into structure less and structure based techniques. In this paper, we present the survey of such techniques. Weighted kNN, Model based kNN, Condensed NN, Reduced NN, Generalized NN are structure less techniques whereas k-d tree, ball tree, Principal Axis Tree, Nearest Feature Line, Tunable NN, Orthogonal Search Tree are structure based algorithms developed on the basis of kNN. The structure less method overcome memory limitation and structure based techniques reduce the computational complexity.  Balltrees are simple geometric data structures with a wide range of practical applica­ tions to geometric ·learning tasks. In this report we compare 5 different algorithms for . constructing ball trees from data. We study the trade-off between construction time and the quality of the constructed tree. Two of the algorithms are on-line, two construct the structures from the data set in a top down fashion, and one uses a bottom up approach. We empirically study the algorithms on random data drawn from eight different probability distributions representing smooth, clustered, and curve distributed data in different ambient space dimen­ sions. We find that the bottom up approach usually produces the best trees but has the longest construction time. The other approaches have uses in specific circumstances. 1. IntemauonaI.Computer Science Institute, Berkeley, CA. Now a day’s many algorithms are invented being inventing to find the solution for Euclidean Minimum Spanning Tree (EMST) problem, as its applicability is increasing in much wide range of fields containing spatial spatio – temporal data viz. astronomy which consists of millions of spatial data. To solve this problem, we are presenting a technique by adopting the dual tree algorithm for finding efficient EMST and experimented on a variety of real time and synthetic datasets. This paper presents the observed experimental observations and the efficiency of the dual tree framework,in the context of kd-tree and ball-tree on spatial datasets of different dimensions.