We explore the effect of dimensionality on the nearest neighbor problem. We show that under a broad set of conditions (much broader than independent and identically distributed dimensions), as dimensionality increases, the distance to the nearest data point approaches the distance to the farthest data point. To provide a practical perspective, we present empirical results on both real and synthetic data sets that demonstrate that this effect can occur for as few as 10-15 dimensions. These results should not be interpreted to mean that high-dimensional indexing is never meaningful; we illustrate this point by identifying some high-dimensional workloads for which this effect does not occur. However, our results do emphasize that the methodology used almost universally in the database literature to evaluate high-dimensional indexing techniques is flawed, and should be modified. In particular, most such techniques proposed in the literature are not evaluated versus simple linear scan, and are evaluated over workloads for which nearest neighbor is not meaningful. Often, even the reported experiments, when analyzed carefully, show that linear scan would outperform the techniques being proposed on the workloads studied in high (10-15) dimensionality!.

When is nearest neighbor meaningful

The advances in location-acquisition and mobile computing techniques have generated massive spatial trajectory data, which represent the mobility of a diversity of moving objects, such as people, vehicles, and animals. Many techniques have been proposed for processing, managing, and mining trajectory data in the past decade, fostering a broad range of applications. In this article, we conduct a systematic survey on the major research into trajectory data mining, providing a panorama of the field as well as the scope of its research topics. Following a road map from the derivation of trajectory data, to trajectory data preprocessing, to trajectory data management, and to a variety of mining tasks (such as trajectory pattern mining, outlier detection, and trajectory classification), the survey explores the connections, correlations, and differences among these existing techniques. This survey also introduces the methods that transform trajectories into other data formats, such as graphs, matrices, and tensors, to which more data mining and machine learning techniques can be applied. Finally, some public trajectory datasets are presented. This survey can help shape the field of trajectory data mining, providing a quick understanding of this field to the community.

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Trajectory Data Mining: An Overview

This paper tackles a major privacy concern in current location-based services where users have to continuously report their locations to the database server in order to obtain the service. For example, a user asking about the nearest gas station has to report her exact location. With untrusted servers, reporting the location information may lead to several privacy threats. In this paper, we present Casper1; a new framework in which mobile and stationary users can entertain location-based services without revealing their location information. Casper consists of two main components, the location anonymizer and the privacy-aware query processor. The location anonymizer blurs the users' exact location information into cloaked spatial regions based on user-specified privacy requirements. The privacy-aware query processor is embedded inside the location-based database server in order to deal with the cloaked spatial areas rather than the exact location information. Experimental results show that Casper achieves high quality location-based services while providing anonymity for both data and queries.

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The new Casper: query processing for location services without compromising privacy

The increasing trend of embedding positioning capabilities (for example, GPS) in mobile devices facilitates the widespread use of location-based services. For such applications to succeed, privacy and confidentiality are essential. Existing privacy-enhancing techniques rely on encryption to safeguard communication channels, and on pseudonyms to protect user identities. Nevertheless, the query contents may disclose the physical location of the user. In this paper, we present a framework for preventing location-based identity inference of users who issue spatial queries to location-based services. We propose transformations based on the well-established K-anonymity concept to compute exact answers for range and nearest neighbor search, without revealing the query source. Our methods optimize the entire process of anonymizing the requests and processing the transformed spatial queries. Extensive experimental studies suggest that the proposed techniques are applicable to real-life scenarios with numerous mobile users.

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Preventing Location-Based Identity Inference in Anonymous Spatial Queries

Many applications require finding objects closest to a specified location that contains a set of keywords. For example, online yellow pages allow users to specify an address and a set of keywords. In return, the user obtains a list of businesses whose description contains these keywords, ordered by their distance from the specified address. The problems of nearest neighbor search on spatial data and keyword search on text data have been extensively studied separately. However, to the best of our knowledge there is no efficient method to answer spatial keyword queries, that is, queries that specify both a location and a set of keywords. In this work, we present an efficient method to answer top-k spatial keyword queries. To do so, we introduce an indexing structure called IR2-Tree (Information Retrieval R-Tree) which combines an R-Tree with superimposed text signatures. We present algorithms that construct and maintain an IR2-Tree, and use it to answer top-k spatial keyword queries. Our algorithms are experimentally compared to current methods and are shown to have superior performance and excellent scalability.

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Keyword Search on Spatial Databases

A continuous nearest neighbor query retrieves the nearest neighbor (NN) of every point on a line segment (e.g., "find all my nearest gas stations during my route from points to point e. The result contains a set of (point, interval) tuples, such that point is the NN of all points in the corresponding interval. Existing methods for continuous nearest neighbor search are based on the repetitive application of simple NN algorithms, which incurs significant overhead. In this paper we propose techniques that solve the problem by performing a single query for the whole input segment. As a result the cost, depending on the query and dataset characteristics, may drop by orders of magnitude. In addition, we propose analytical models for the expected size of the output, as well as, the cost of query processing, and extend out techniques to several variations of the problem.

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Continuous nearest neighbor search

Given two sets of points P and Q, a group nearest neighbor (GNN) query retrieves the point(s) of P with the smallest sum of distances to all points in Q. Consider, for instance, three users at locations q/sub 1/ q/sub 2/ and q/sub 3/ that want to find a meeting point (e.g., a restaurant); the corresponding query returns the data point p that minimizes the sum of Euclidean distances |pq/sub i/| for 1/spl les/i/spl les/3. Assuming that Q fits in memory and P is indexed by an R-tree, we propose several algorithms for finding the group nearest neighbors efficiently. As a second step, we extend our techniques for situations where Q cannot fit in memory, covering both indexed and nonindexed query points. An experimental evaluation identifies the best alternative based on the data and query properties.

/pdf/group-nearest-neighbor-queries-1j5zemaicy.pdf

Group nearest neighbor queries

Spatio-temporal databases store information about the positions of individual objects over time. In many applications however, such as traffic supervision or mobile communication systems, only summarized data, like the average number of cars in an area for a specific period, or phones serviced by a cell each day, is required. Although this information can be obtained from operational databases, its computation is expensive, rendering online processing inapplicable. A vital solution is the construction of a spatiotemporal data warehouse. In this paper, we describe a framework for supporting OLAP operations over spatiotemporal data. We argue that the spatial and temporal dimensions should be modeled as a combined dimension on the data cube and present data structures, which integrate spatiotemporal indexing with pre-aggregation. While the well-known materialization techniques require a-priori knowledge of the grouping hierarchy, we develop methods that utilize the proposed structures for efficient execution of ad-hoc group-bys. Our techniques can be used for both static and dynamic dimensions.

/pdf/indexing-and-retrieval-of-historical-aggregate-information-2zz515m919.pdf

Qiongmao Shen

Papers

Continuous nearest neighbor search

Group nearest neighbor queries

Indexing and Retrieval of Historical Aggregate Information about Moving Objects