Given a query object q, reverse k -nearest neighbor (R k NN) search aims to locate those objects of the database that have q among their k -nearest neighbors. In this paper, we propose an approximation method for solving R k NN queries, where the pruning operations and termination tests are guided by a characterization of the intrinsic dimensionality of the data. The method can accommodate any index structure supporting incremental (forward) nearest-neighbor search for the generation and verification of candidates, while avoiding impractically-high preprocessing costs. We also provide experimental evidence that our method significantly outperforms its competitors in terms of the tradeoff between execution time and the quality of the approximation. Our approach thus addresses many of the scalability issues surrounding the use of previous methods in data mining.

This paper is concerned with the estimation of a local measure of intrinsic dimensionality (ID) recently proposed by Houle. The local model can be regarded as an extension of Karger and Ruhl's expansion dimension to a statistical setting in which the distribution of distances to a query point is modeled in terms of a continuous random variable. This form of intrinsic dimensionality can be particularly useful in search, classification, outlier detection, and other contexts in machine learning, databases, and data mining, as it has been shown to be equivalent to a measure of the discriminative power of similarity functions. Several estimators of local ID are proposed and analyzed based on extreme value theory, using maximum likelihood estimation (MLE), the method of moments (MoM), probability weighted moments (PWM), and regularly varying functions (RV). An experimental evaluation is also provided, using both real and artificial data.

This paper introduces a data structure for k-NN search, the Rank Cover Tree (RCT), whose pruning tests rely solely on the comparison of similarity values; other properties of the underlying space, such as the triangle inequality, are not employed. Objects are selected according to their ranks with respect to the query object, allowing much tighter control on the overall execution costs. A formal theoretical analysis shows that with very high probability, the RCT returns a correct query result in time that depends very competitively on a measure of the intrinsic dimensionality of the data set. The experimental results for the RCT show that non-metric pruning strategies for similarity search can be practical even when the representational dimension of the data is extremely high. They also show that the RCT is capable of meeting or exceeding the level of performance of state-of-the-art methods that make use of metric pruning or other selection tests involving numerical constraints on distance values.

In data mining applications such as subspace clustering or feature selection, changes to the underlying feature set can require the reconstruction of search indices to support fundamental data mining tasks. For such situations, multi-step search approaches have been proposed that can accommodate changes in the underlying similarity measure without the need to rebuild the index. In this paper, we present a heuristic multi-step search algorithm that utilizes a measure of intrinsic dimension, the generalized expansion dimension (GED), as the basis of its search termination condition. Compared to the current state-of-the-art method, experimental results show that our heuristic approach is able to obtain significant improvements in both the number of candidates and the running time, while losing very little in the accuracy of the query results.

In this paper we investigate the potential benefits from integrating Semantic Web technologies into the context of collaboration in virtual 3D environments. We provide a prototype e-commerce solution, the Seicos system, based on the SecondLife client and the OpenSimulator server. In the system, semantic information is retrieved and integrated from multiple heterogeneous sources and subsequently cached and accessed using Semantic Web methods. The semantic information gathered by our system can support the customer and is integrated into a knowledge base which is used for processing queries.