k-Nearest Neighbor Query Processing Algorithms for a Query Region in Road Networks

Recent development of wireless communication technologies and the popularity of smart phones are making location-based services (LBS) popular. However, requesting queries to LBS servers with users’ exact locations may threat the privacy of users. Therefore, there have been many researches on generating a cloaked query region for user privacy protection. Consequently, an effcient query processing algorithm for a query region is required. So, in this paper, we propose k-nearest neighbor query (k-NN) processing algorithms for a query region in road networks. To effciently retrieve k-NN points of interest (POIs), we make use of the Island index. We also propose a method that generates an adaptive Island index to improve the query processing performance and storage usage. Finally, we show by our performance analysis that our k-NN query processing algorithms outperform the existing k-Range Nearest Neighbor (kRNN) algorithm in terms of network expansion cost and query processing time.     

Composite Distance Transformation for Indexing and k-Nearest-Neighbor Searching in High-Dimensional Spaces

Due to the famous dimensionality curse problem, search in a high-dimensional space is considered as a ＂hard＂ problem. In this paper, a novel composite distance transformation method, which is called CDT, is proposed to support a fast κ-nearest-neighbor （κ-NN） search in high-dimensional spaces. In CDT, all （n） data points are first grouped into some clusters by a κ-Means clustering algorithm. Then a composite distance key of each data point is computed. Finally, these index keys of such n data points are inserted by a partition-based B^＋-tree. Thus, given a query point, its κ-NN search in high-dimensional spaces is transformed into the search in the single dimensional space with the aid of CDT index. Extensive performance studies are conducted to evaluate the effectiveness and efficiency of the proposed scheme. Our results show that this method outperforms the state-of-the-art high-dimensional search techniques, such as the X-Tree, VA-file, iDistance and NB-Tree.     

Instance optimal query processing in spatial networks

The performance optimization of query processing in spatial networks focuses on minimizing network data accesses and the cost of network distance calculations. This paper proposes algorithms for network k-NN queries, range queries, closest-pair queries and multi-source skyline queries based on a novel processing framework, namely, incremental lower bound constraint. By giving high processing priority to the query associated data points and utilizing the incremental nature of the lower bound, the performance of our algorithms is better optimized in contrast to the corresponding algorithms based on known framework incremental Euclidean restriction and incremental network expansion. More importantly, the proposed algorithms are proven to be instance optimal among classes of algorithms. Through experiments on real road network datasets, the superiority of the proposed algorithms is demonstrated.     

Efficiently support concurrent queries in multiuser CBIR systems

Various techniques have been developed for different query types in content-based image retrieval systems such as sampling queries, constrained sampling queries, multiple constrained sampling queries, k-NN queries, constrained k-NN queries, and multiple localized k-NN queries. In this paper, we propose a generalized query model suitable for expressing queries of different types, and investigate efficient processing techniques for this new framework. We exploit sequential access and data sharing by developing new storage and query processing techniques to leverage inter-query concurrency. Our experimental results, based on the Corel dataset, indicate that the proposed optimization can significantly reduce average response time in a multiuser environment, and achieve better retrieval precision and recall compared to two recent techniques.

Modified nearest neighbour classifier for hyperspectral data classification

A modified k-nearest neighbour (k-NN) classifier is proposed for supervised remote sensing classification of hyperspectral data. To compare its performance in terms of classification accuracy and computational cost, k-NN and a back-propagation neural network classifier were used. A classification accuracy of 91.2% was achieved by the proposed classifier with the data set used. Results from this study suggest that the accuracy achieved with this classifier is significantly better than the k-NN and comparable to a back-propagation neural network. Comparison in terms of computational cost also suggests the effectiveness of modified k-NN classifier for hyperspectral data classification. A fuzzy entropy-based filter approach was used for feature selection to compare the performance of modified and k-NN classifiers with a reduced data set. The results suggest a significant increase in classification accuracy by the modified k-NN classifier in comparison with k-NN classifier with selected features.     

On Bounded Leg Shortest Paths Problems

Let V be a set of points in a d-dimensional l _p -metric space. Let s,t∈V and let L be a real number. An L-bounded leg path from s to t is an ordered set of points which connects s to t such that the leg between any two consecutive points in the set has length of at most L. The minimal path among all these paths is the L-bounded leg shortest path from s to t. In the s–t Bounded Leg Shortest Path (stBLSP) problem we are given two points s and t and a real number L, and are required to compute an L-bounded leg shortest path from s to t. In the All-Pairs Bounded Leg Shortest Path (apBLSP) problem we are required to build a data structure that, given any two query points from V and a real number L, outputs the length of the L-bounded leg shortest path (a distance query) or the path itself (a path query). In this paper we obtain the following results:     

Shooting top-<Emphasis Type="Italic">k</Emphasis> stars in uncertain databases

Query processing in the uncertain database has played an important role in many real-world applications due to the wide existence of uncertain data. Although many previous techniques can correctly handle precise data, they are not directly applicable to the uncertain scenario. In this article, we investigate and propose a novel query, namely probabilistic top-k star (PTkS) query, which aims to retrieve k objects in an uncertain database that are “closest” to a static/dynamic query point, considering both distance and probability aspects. In order to efficiently answer PTkS queries with a static/moving query point, we propose effective pruning methods to reduce the PTkS search space, which can be seamlessly integrated into an efficient query procedure. Finally, extensive experiments have demonstrated the efficiency and effectiveness of our proposed PTkS approaches on both real and synthetic data sets, under various parameter settings.     

Forest attribute imputation using machine-learning methods and ASTER data: comparison of k-NN,SVR and random forest regression algorithms

In a small case study of mixed hardwood Hyrcanian forests of Iran, three non-parametric methods, namely k-nearest neighbour (k-NN), support vector machine regression (SVR) and tree regression based on random forest (RF), were used in plot-level estimation of volume/ha, basal area/ha and stems/ha using field inventory and Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data. Relevant pre-processing and processing steps were applied to the ASTER data for geometric and atmospheric correction and for enhancing quantitative forest parameters. After collecting terrestrial information on trees in the 101 samples, the volume, basal area and tree number per hectare were calculated in each plot. In the k-NN implementation using different distance measures and k, the cross-validation method was used to find the best distance measure and optimal k. In SVR, the best regularized parameters of four kernel types were obtained using leave-one-out cross-validation. RF was implemented using a bootstrap learning method with regularized parameters for decision tree model and stopping. The validity of performances was examined using unused test samples by absolute and relative root mean square error (RMSE) and bias metrics. In volume/ha estimation, the results showed that all the three algorithms had similar performances. However, SVR and RF produced better results than k-NN with relative RMSE values of 28.54, 25.86 and 26.86 (m³ ha^–1), respectively, using k-NN, SVR and RF algorithms, but RF could generate unbiased estimation. In basal area/ha and stems/ha estimation, the implementation results of RF showed that RF was slightly superior in relative RMSE (18.39, 20.64) to SVR (19.35, 22.09) and k-NN (20.20, 21.53), but k-NN could generate unbiased estimation compared with the other two algorithms used.     

k-Nearest neighbor query processing algorithm for cloaking regions towards user privacy protection in location-based services

Due to the advancement of wireless internet and mobile positioning technology, the application of location-based services (LBSs) has become popular for mobile users. Since users have to send their exact locations to obtain the service, it may lead to several privacy threats. To solve this problem, a cloaking method has been proposed to blur users’ exact locations into a cloaked spatial region with a required privacy threshold (k). With the cloaked region, an LBS server can carry out a k-nearest neighbor (k-NN) search algorithm. Some recent studies have proposed methods to search k-nearest POIs while protecting a user’s privacy. However, they have at least one major problem, such as inefficiency on query processing or low precision of retrieved result. To resolve these problems, in this paper, we propose a novel k-NN query processing algorithm for a cloaking region to satisfy both requirements of fast query processing time and high precision of the retrieved result. To achieve fast query processing time, we propose a new pruning technique based on a 2D-coodinate scheme. In addition, we make use of a Voronoi diagram for retrieving the nearest POIs efficiently. To satisfy the requirement of high precision of the retrieved result, we guarantee that our k-NN query processing algorithm always contains the exact set of k nearest neighbors. Our performance analysis shows that our algorithm achieves better performance in terms of query processing time and the number of candidate POIs compared with other algorithms.     

An empirical comparison of min–max-modular <Emphasis Type="Italic">k</Emphasis>-NN with different voting methods to large-scale text categorization

Text categorization refers to the task of assigning the pre-defined classes to text documents based on their content. k-NN algorithm is one of top performing classifiers on text data. However, there is little research work on the use of different voting methods over text data. Also, when a huge number of training data is available online, the response speed slows down, since a test document has to obtain the distance with each training data. On the other hand, min–max-modular k-NN (M³-k-NN) has been applied to large-scale text categorization. M³-k-NN achieves a good performance and has faster response speed in a parallel computing environment. In this paper, we investigate five different voting methods for k-NN and M³-k-NN. The experimental results and analysis show that the Gaussian voting method can achieve the best performance among all voting methods for both k-NN and M³-k-NN. In addition, M³-k-NN uses less k-value to achieve the better performance than k-NN, and thus is faster than k-NN in a parallel computing environment. The work of K. Wu and B. L. Lu was supported in part by the National Natural Science Foundation of China under the grants NSFC 60375022 and NSFC 60473040, and the Microsoft Laboratory for Intelligent Computing and Intelligent Systems of Shanghai Jiao Tong University.     

SMashQ: spatial mashup framework for k-NN queries in time-dependent road networks

The k-nearest-neighbor (k-NN) query is one of the most popular spatial query types for location-based services (LBS). In this paper, we focus on k-NN queries in time-dependent road networks, where the travel time between two locations may vary significantly at different time of the day. In practice, it is costly for a LBS provider to collect real-time traffic data from vehicles or roadside sensors to compute the best route from a user to a spatial object of interest in terms of the travel time. Thus, we design SMashQ, a server-side spatial mashup framework that enables a database server to efficiently evaluate k-NN queries using the route information and travel time accessed from an external Web mapping service, e.g., Microsoft Bing Maps. Due to the expensive cost and limitations of retrieving such external information, we propose three shared execution optimizations for SMashQ, namely, object grouping, direction sharing, and user grouping, to reduce the number of external Web mapping requests and provide highly accurate query answers. We evaluate SMashQ using Microsoft Bing Maps, a real road network, real data sets, and a synthetic data set. Experimental results show that SMashQ is efficient and capable of producing highly accurate query answers.     

A multiple-point spatially weighted k-NN classifier for remote sensing

A novel classification method based on multiple-point statistics (MPS) is proposed in this article. The method is a modified version of the spatially weighted k-nearest neighbour (k-NN) classifier, which accounts for spatial correlation through weights applied to neighbouring pixels. The MPS characterizes the spatial correlation between multiple points of land-cover classes by learning local patterns in a training image. This rich spatial information is then converted to multiple-point probabilities and incorporated into the k-NN classifier. Experiments were conducted in two study areas, in which the proposed method for classification was tested on a WorldView-2 sub-scene of the Sichuan mountainous area and an IKONOS image of the Beijing urban area. The multiple-point weighted k-NN method (MPk-NN) was compared to several alternatives; including the traditional k-NN and two previously published spatially weighted k-NN schemes; the inverse distance weighted k-NN, and the geostatistically weighted k-NN. The classifiers using the Bayesian and Support Vector Machine (SVM) methods, and these classifiers weighted with spatial context using the Markov random field (MRF) model, were also introduced to provide a benchmark comparison with the MPk-NN method. The proposed approach increased classification accuracy significantly relative to the alternatives, and it is, thus, recommended for the identification of land-cover types with complex and diverse spatial distributions.     

Regular path queries under approximate semantics

We give a general framework for approximate query processing in semistructured databases. We focus on regular path queries, which are the integral part of most of the query languages for semistructured databases. To enable approximations, we allow the regular path queries to be distorted. The distortions are expressed in the system by using weighted regular expressions, which correspond to weighted regular transducers. After defining the notion of weighted approximate answers we show how to compute them in order of their proximity to the query. In the new approximate setting, query containment has to be redefined in order to take into account the quantitative proximity information in the query answers. For this, we define the approximate containment, and its variants k-containment and reliable contain-ment. Then, we give an optimal algorithm for deciding the k-containment. Regarding the reliable approximate containment, we show that it is polynomial time equivalent to the notorious limitedness problem in distance automata.     

Practical protocol for Yao’s millionaires problem enables secure multi-party computation of metrics and efficient privacy-preserving k-NN for large data sets

Finding the nearest k objects to a query object is a fundamental operation for many data mining algorithms. With the recent interest in privacy, it is not surprising that there is strong interest in k-NN queries to enable clustering, classification and outlier-detection tasks. However, previous approaches to privacy-preserving k-NN have been costly and can only be realistically applied to small data sets. In this paper, we provide efficient solutions for k-NN queries for vertically partitioned data. We provide the first solution for the L _∞ (or Chessboard) metric as well as detailed privacy-preserving computation of all other Minkowski metrics. We enable privacy-preserving L _∞ by providing a practical approach to the Yao’s millionaires problem with more than two parties. This is based on a pragmatic and implementable solution to Yao’s millionaires problem with shares. We also provide privacy-preserving algorithms for combinations of local metrics into a global metric that handles the large dimensionality and diversity of attributes common in vertically partitioned data. To manage very large data sets, we provide a privacy-preserving SASH (a very successful data structure for associative queries in high dimensions). Besides providing a theoretical analysis, we illustrate the efficiency of our approach with an empirical evaluation.     

Algorithms for constrained <Emphasis Type="Italic">k</Emphasis>-nearest neighbor queries over moving object trajectories

An important query for spatio-temporal databases is to find nearest trajectories of moving objects. Existing work on this topic focuses on the closest trajectories in the whole data space. In this paper, we introduce and solve constrained k-nearest neighbor (CkNN) queries and historical continuous CkNN (HCCkNN) queries on R-tree-like structures storing historical information about moving object trajectories. Given a trajectory set D, a query object (point or trajectory) q, a temporal extent T, and a constrained region CR, (i) a CkNN query over trajectories retrieves from D within T, the k (≥ 1) trajectories that lie closest to q and intersect (or are enclosed by) CR; and (ii) an HCCkNN query on trajectories retrieves the constrained k nearest neighbors (CkNNs) of q at any time instance of T. We propose a suite of algorithms for processing CkNN queries and HCCkNN queries respectively, with different properties and advantages. In particular, we thoroughly investigate two types of CkNN queries, i.e., CkNN_P and CkNN_T, which are defined with respect to stationary query points and moving query trajectories, respectively; and two types of HCCkNN queries, namely, HCCkNN_P and HCCkNN_T, which are continuous counterparts of CkNN_P and CkNN_T, respectively. Our methods utilize an existing data-partitioning index for trajectory data (i.e., TB-tree) to achieve low I/O and CPU cost. Extensive experiments with both real and synthetic datasets demonstrate the performance of the proposed algorithms in terms of efficiency and scalability.     

k-NN classification of handwritten characters via accelerated GAT correlation

This paper addresses the problem of reinforcing the ability of the k-NN classification of handwritten characters via distortion-tolerant template matching techniques with a limited quantity of data. We compare three kinds of matching techniques: the conventional simple correlation, the tangent distance, and the global affine transformation (GAT) correlation. Although the k-NN classification method is straightforward and powerful, it consumes a lot of time. Therefore, to reduce the computational cost of matching in k-NN classification, we propose accelerating the GAT correlation method by reformulating its computational model and adopting efficient lookup tables. Recognition experiments performed on the IPTP CDROM1B handwritten numerical database show that the matching techniques of the simple correlation, the tangent distance, and the accelerated GAT correlation achieved recognition rates of 97.07%, 97.50%, and 98.70%, respectively. The computation time ratios of the tangent distance and the accelerated GAT correlation to the simple correlation are 26.3 and 36.5 to 1.0, respectively.     

Improving nearest neighbor classification with cam weighted distance

Nearest neighbor (NN) classification assumes locally constant class conditional probabilities, and suffers from bias in high dimensions with a small sample set. In this paper, we propose a novel cam weighted distance to ameliorate the curse of dimensionality. Different from the existing neighborhood-based methods which only analyze a small space emanating from the query sample, the proposed nearest neighbor classification using the cam weighted distance (CamNN) optimizes the distance measure based on the analysis of inter-prototype relationship. Our motivation comes from the observation that the prototypes are not isolated. Prototypes with different surroundings should have different effects in the classification. The proposed cam weighted distance is orientation and scale adaptive to take advantage of the relevant information of inter-prototype relationship, so that a better classification performance can be achieved. Experiments show that CamNN significantly outperforms one nearest neighbor classification (1-NN) and k-nearest neighbor classification (k-NN) in most benchmarks, while its computational complexity is comparable with that of 1-NN classification.     

Slicing the metric space to provide quick indexing of complex data in the main memory

Searching in a dataset for elements that are similar to a given query element is a core problem in applications that manage complex data, and has been aided by metric access methods (MAMs). A growing number of applications require indices that must be built faster and repeatedly, also providing faster response for similarity queries. The increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper, we propose the Onion-tree, a new and robust dynamic memory-based MAM that slices the metric space into disjoint subspaces to provide quick indexing of complex data. It introduces three major characteristics: (i) a partitioning method that controls the number of disjoint subspaces generated at each node; (ii) a replacement technique that can change the leaf node pivots in insertion operations; and (iii) range and k-NN extended query algorithms to support the new partitioning method, including a new visit order of the subspaces in k-NN queries. Performance tests with both real-world and synthetic datasets showed that the Onion-tree is very compact. Comparisons of the Onion-tree with the MM-tree and a memory-based version of the Slim-tree showed that the Onion-tree was always faster to build the index. The experiments also showed that the Onion-tree significantly improved range and k-NN query processing performance and was the most efficient MAM, followed by the MM-tree, which in turn outperformed the Slim-tree in almost all the tests.     

A direct boosting algorithm for the k-nearest neighbor classifier via local warping of the distance metric

Though the k-nearest neighbor (k-NN) pattern classifier is an effective learning algorithm, it can result in large model sizes. To compensate, a number of variant algorithms have been developed that condense the model size of the k-NN classifier at the expense of accuracy. To increase the accuracy of these condensed models, we present a direct boosting algorithm for the k-NN classifier that creates an ensemble of models with locally modified distance weighting. An empirical study conducted on 10 standard databases from the UCI repository shows that this new Boosted k-NN algorithm has increased generalization accuracy in the majority of the datasets and never performs worse than standard k-NN.