Intelligent transport navigation system using LookAhead Continuous KNN

We suggest a simple modification to the Kd-tree search algorithm for nearest neighbor search resulting in an improved performance. The Kd-tree data structure seems to work well in finding nearest neighbors in low dimensions but its performance degrades even if the number of dimensions increases to more than two. Since the exact nearest neighbor search problem suffers from the curse of dimensionality we focus on approximate solutions; a c-approximate nearest neighbor is any neighbor within distance at most c times the distance to the nearest neighbor. We show that for a randomly constructed database of points if the query point is chosen close to one of the points in the data base, the traditional Kd-tree search algorithm has a very low probability of finding an approximate nearest neighbor; the probability of success drops exponentially in the number of dimensions d as e − Ω(d/c). However, a simple change to the search algorithm results in a much higher chance of success. Instead of searching for the query point in the Kd-tree we search for a random set of points in the neighborhood of the query point. It turns out that searching for e Ω(d/c) such points can find the c-approximate nearest neighbor with a much higher chance of success.KeywordsSuccess ProbabilityRandom PointNeighbor SearchComputational GeometryQuery PointThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This paper presents an algorithm, called the winner-update algorithm, for accelerating the nearest neighbor search. By constructing a hierarchical structure for each feature point in the l/sub p/ metric space, this algorithm can save a large amount of computation at the expense of moderate preprocessing and twice the memory storage. Given a query point, the cost for computing the distances from this point to all the sample points can be reduced by using a lower bound list of the distance established from Minkowski's inequality. Our experiments have shown that the proposed algorithm can save a large amount of computation, especially when the distance between the query point and its nearest neighbor is relatively small. With slight modification, the winner-update algorithm can also speed up the search for k nearest neighbors, neighbors within a specified distance threshold, and neighbors close to the nearest neighbor.

On multi-type reverse nearest neighbor search

Given a group $\mathcal {Q}$ of query points and a set $\mathcal {P}$ of points of interest (POIs), aggregate nearest neighbor (ANN) queries find a POI p from $\mathcal {P}$ that achieves the smallest aggregate distance. Specifically, the aggregate distance is defined over the set of distances between p and all query points in $\mathcal {Q}$ . Existing studies on ANN query mainly consider the spatial proximity, whereas the textual similarity has received considerable attention recently. In this work, we utilize user-specified query keywords to capture textual similarity. We study the aggregate keyword nearest neighbor (AKNN) queries, finding the POI that has the smallest aggregate distance and covers all query keywords. Nevertheless, existing methods on ANN query are either inapplicable or inefficient when applied to the AKNN query. To answer our query efficiently, we first develop a dual-granularity (DG) indexing schema. It preserves abstracts of the road network by a tree structure, and preserves detailed network information by an extended adjacency list. Then, we propose a minimal first search (MFS) algorithm. It traverses the tree and explores the node with the minimal aggregate distance iteratively. This method suffers from false hits arising from keyword tests. Thus, we propose the collaborative filtering technique, which performs keywords test by multiple keyword bitmaps collectively rather than by only one. Extensive experiments on both real and synthetic datasets demonstrate the superiority of our algorithms and optimizing strategies.

Nearest neighbor search, a classic way of identifying similar data, can be applied to various areas, including database, machine learning, natural language processing, software engineering, etc. Secure nearest neighbor search aims to find nearest neighbors to a given query point over encrypted data without accessing data in plaintext. It provides privacy protection to datasets when nearest neighbor queries need to be operated by an untrusted party (e.g., a public server). While different solutions have been proposed to support nearest neighbor queries on encrypted data, these existing solutions still encounter critical drawbacks either in efficiency or privacy. In light of the limitations in the current literature, we propose a novel approximate nearest neighbor search solution, referred to as Sparser, by leveraging a combination of space-filling curves, perturbation, and Order-Preserving Encryption. The advantages of Sparser are twofold, strengthening privacy and improving efficiency. Specifically, Sparser pre-processes plaintext data with space-filling curves and perturbation, such that data is sparse, which mitigates leakage abuse attacks and renders stronger privacy. In addition to privacy enhancement, Sparser can efficiently find approximate nearest neighbors over encrypted data with logarithmic time. Through extensive experiments over real-world datasets, we demonstrate that Sparser can achieve strong privacy protection under leakage abuse attacks and minimize search time.

Let [Formula: see text] be a set of stochastic sites, where each site is a tuple [Formula: see text] consisting of a point [Formula: see text] in [Formula: see text]-dimensional space and a probability [Formula: see text] of existence. Given a query point [Formula: see text], we define its most likely nearest neighbor (LNN) as the site with the largest probability of being [Formula: see text]’s nearest neighbor. The Most Likely Voronoi Diagram (LVD) of [Formula: see text] is a partition of the space into regions with the same LNN. We investigate the complexity of LVD in one dimension and show that it can have size [Formula: see text] in the worst-case. We then show that under non-adversarial conditions, the size of the [Formula: see text]-dimensional LVD is significantly smaller: (1) [Formula: see text] if the input has only [Formula: see text] distinct probability values, (2) [Formula: see text] on average, and (3) [Formula: see text] under smoothed analysis. We also describe a framework for LNN search using Pareto sets, which gives a linear-space data structure and sub-linear query time in 1D for average and smoothed analysis models as well as the worst-case with a bounded number of distinct probabilities. The Pareto-set framework is also applicable to multi-dimensional LNN search via reduction to a sequence of nearest neighbor and spherical range queries.

Complementary data are necessary to bind the positioning error growth of Pedestrian Dead Reckoning (PDR). In this paper, absolute position updates are made possible with the online detection of different types of points of interest (POIs) located on the map. The POIs are selected depending on specific motion patterns which are associated to absolute locations on the map. To create the POIs database, the correlation between pedestrian motion and different map locations is first studied and the outcome is a typology of POIs. A K-NN (K nearest neighbors) algorithm is used to train different motion modes, which are further exploited for the detection of POIs in order to update the PDR algorithm with position data. Experimental assessment of the POI-based PDR calibration is conducted in both outdoor and indoor spaces with a focus on the transition between both environments. 90% of the time, motion is correctly classified and the PDR position is corrected with an accuracy that depends on POIs features (width of corridor/door, staircase size…). Therefore, the approach is found to be promising for enhancing PDR positioning using only map data.

Theknearest neighbor classification (k‐NN) is a very simple and popular method for classification. However, it suffers from a major drawback, it assumes constant local class posterior probability. It is also highly dependent on and sensitive to the choice of the number of neighborsk. In addition, it severely lacks the desired probabilistic formulation. In this article, we propose a Bayesian adaptive nearest neighbor method (BANN) that can adaptively select the shape of the neighborhood and the number of neighborsk. The shape of the neighborhood is automatically selected according to the concentration of the data around each query point with the help of discriminants. The neighborhood size is not predetermined and is kept free using a prior distribution. Thus, we are able to make the model to select the appropriate neighborhood size. The model is fitted using Markov Chain Monte Carlo (MCMC), so we are not using exactly one neighborhood size but a mixture ofk. Our BANN model is highly flexible, determining any local pattern in the data‐generating process, and adapting it to give an improved prediction. We have applied our model on four simulated data sets with special structures and five real‐life benchmark data sets. Our proposed BANN method demonstrates substantial improvement overk‐NN and discriminant adaptive nearest neighbor (DANN) in all nine case studies. It also outperforms the probabilistic nearest neighbor (PNN) in most of the data analyses. Copyright © 2010 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 3: 92‐105, 2010

The growing need for location based services motivates the moving k nearest neighbor query (MkNN), which requires to find the k nearest neighbors of a moving query point continuously. In most existing solutions, data objects are abstracted as points. However, lots of real-world data objects, such as roads, rivers or pipelines, should be reasonably modeled as line segments or polyline segments. In this paper, we present LV*-Diagram to handle MkNN queries over line segment data objects. LV*-Diagram dynamically constructs a safe region. The query results remain unchanged if the query point is in the safe region, and hence, the computation cost of the server is greatly reduced. Experimental results show that our approach significantly outperforms the baseline method w.r.t. CPU load, I/O, and communication costs.

Reverse k-nearest neighbor (RkNN) queries are prevalent in location-based services to find those locations that have the query point as one of their k nearest neighbors. However, such query requires users to disclose the location of the query point to a service provider who might be untrustworthy. Previous attempts to preserve the privacy of RkNN queries are either based on weaker notions of privacy such as location cloaking or not efficient when k > 1. In this paper, we propose novel solutions based on the private information retrieval (PIR) mechanism to preserve the privacy of RkNN query points. Our solutions include server-side data indexing and client-side query processing methods to facilitate PIR which is an inherently expensive data retrieval mechanism. We experimentally evaluate our approach using real-world datasets and show that it preserves the location privacy of queries with reasonable computation and storage overhead.

Comparative Analysis of Nearest Neighbor Query Processing Techniques

Nearest neighbour searches in the image plane are among the most frequent problems in a variety of computer vision and image processing tasks. They can be used to replace missing values in image filtering, or to group close objects in image segmentation, or to access neighbouring points of interest in feature extraction. In particular, we address two nearest neighbour problems: The nearest neighbour problem is usually stated independently of the application as returning the point p ∈ S,S = {(x1,y1), . . . ,(xn,yn)} that minimises the Euclidean distance ||p− q||2 to a query point q = (x,y). The simple solution of a linear scan comprises a comparison of q to all elements of S, which is too time-consuming for most applications, especially those with real-time requirements. If the nearest neighbour p ∈ S must be found for every coordinate q ∈ I of an image I = {(0,0),(0,1),(0,2), . . . ,(W,H)} of width W and height H, we obtain the all nearest neighbours problem. This problem occurs frequently in modern saliency based approaches, where only robustly detectable image regions are processed (for example in SIFT). In this paper, we introduce an approximate solution to solve these problems that is based on using a space filling curve. The central idea of the proposed approach is to map the image plane to one dimension using the Hilbert curve (Fig. 1). The nearest-neighbour problem is then solved efficiently in one dimension and mapped back to the 2D-plane.

In this paper, we design the architecture of disk-based data structures for spatial network databases (SNDB). Based on this architecture, we propose new query processing algorithms for range search and k nearest neighbors (k-NN) search, depending on the density of point of interests (POIs) in the spatial network. For this, we effectively combine Euclidean restriction and the network expansion techniques according to the density of POIs. In addition, our two query processing algorithms can reduce the computation time of network distance between a pair of nodes and the number of disk I/Os required for accessing nodes by using maintaining the shortest network distances of all the nodes in the spatial network. It is shown that our range query processing algorithm achieves about up to one order of magnitude better performance than the existing range query processing algorithm, such as RER and RNE [1]. In addition, our k-NN query processing algorithm achieves about up to 170~400% performance improvements over the existing network expansion k-NN algorithm, called INE, while it shows about up to one order of magnitude better performance than the existing Euclidean restriction k-NN algorithm, called IER [1].

Due to the availability of media editing software, the authenticity and reliability of digital images are important. Region manipulation is a simple and effective method for digital image forgeries. Hence, the potential to identify the image manipulation is current research issue these days and copy–move forgery detection (CMFD) is a main domain in image authentication. In copy–move forgery, one region is simply copied and pasted over other region in the same image for manipulating the image. In this paper, we have proposed a method based on Harris corner and adaptive non-maximal Suppression (ANMS). Initially, the input image is taken, and then Harris corner detection algorithm is used to detect the interest points, and ANMS is adopted to control the number of Harris points in an image. This gives an appropriate number of interest points for different size of images and gives the assurance for finding the manipulated region in manageable time. For each extracted interest point, SIFT is used for calculating the descriptors. Now obtained descriptors are matched using the outlier rejection with nearest neighbour. Here RANSAC is used to find the best set of matches to identify the manipulated regions. Experimental results show the robustness against different transformation and post-processing operations.

Spatial sorting: An efficient strategy for approximate nearest neighbor searching