Cost Models and Efficient Algorithms on Existentially Uncertain Spatial Data

Uncertain data pervades many fields, including environmental monitoring, the monitoring of animal migrations, and urban warfare. Such uncertain data collected by field devices, such as Internet of Things (IoT) and Internet of Battlefield Things (IoBT) devices, may also be encrypted and outsourced to an untrustworthy third party for storage and data sharing such as a cloud server. However, the properties of uncertain data and the complication of operating over encrypted data make the searching schemes more ineffective. In this article, we design an efficient and safe K nearest neighbor (KNN) query scheme for uncertain data stored in semi-trusted cloud servers. We apply the modified homomorphic encryption, which requires two servers to interact and encrypt the uncertain data, and we use the authorized rank method to compute KNN. We protect the security of the data while simultaneously improving the query efficiency. Our detailed security analysis show that our scheme can realize the goal of concealing both the access and the search patterns. Comprehensive experiments are conducted to demonstrate the scheme's performance.

Nowadays, many applications return to the user a set of results that take the query as their nearest neighbor, which are commonly expressed through reverse nearest neighbor (RNN) queries. When considering moving objects, users would like to find objects that appear in the RNN result set for a period of time in some real-world applications such as collaboration recommendation and anti-tracking. In this work, we formally define the problem of interval reverse nearest neighbor (IRNN) queries over moving objects, which return the objects that maintain nearest neighboring relations to the moving query objects for the longest time in the given interval. Location uncertainty of moving data objects and moving query objects is inherent in various domains, and we investigate objects that exhibit Markov correlations, that is, each object's location is only correlated with its own location at previous timestamp while being independent of other objects. There exists the efficiency challenge for answering IRNN queries on uncertain moving objects with Markov correlations since we have to retrieve not only all the possible locations of each object at current time but also its historically possible locations. To speed up the query processing, we present a general framework for answering IRNN queries on uncertain moving objects with Markov correlations in two phases. In the first phase, we apply space pruning and probability pruning techniques, which reduce the search space significantly. In the second phase, we verify whether each unpruned object is an IRNN of the query object. During this phase, we propose an approach termed Probability Decomposition Verification (PDV) algorithm which avoid computing the probability of any object being an RNN of the query object exactly and thus improve the efficiency of verification. The performance of the proposed algorithm is demonstrated by extensive experiments on synthetic and real datasets, and the experimental results show that our algorithm is more efficient than the Monte-Carlo based approximate algorithm.

Reverse nearest neighbor (RNN) queries in spatial and spatio-temporal databases have received significant attention in the database research community over the last decade. A reverse nearest neighbor (RNN) query finds the objects having a given query object as its nearest neighbor. RNN queries find applications in data mining, marketing analysis, and decision making. Most previous research on RNN queries over trajectory databases assume that the data are certain. In realistic scenarios, however, trajectories are inherently uncertain due to measurement errors or time-discretized sampling. In this paper, we study RNN queries in databases of uncertain trajectories. We propose two types of RNN queries based on a well established model for uncertain spatial temporal data based on stochastic processes, namely the Markov model. To the best of our knowledge our work is the first to consider RNN queries on uncertain trajectory databases in accordance with the possible worlds semantics. We include an extensive experimental evaluation on both real and synthetic data sets to verify our theoretical results.KeywordsQuery EvaluationCandidate ObjectQuery ObjectNeighbor QueryWorld SemanticThese 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.

A range nearest-neighbor (RNN) query retrieves the nearest neighbor (NN) for every point in a range. It is a natural generalization of point and continuous nearest-neighbor queries and has many applications. In this paper, we consider the ranges as (hyper)rectangles and propose efficient in-memory processing and secondary memory pruning techniques for RNN queries in both 2D and high-dimensional spaces. These techniques are generalized for kRNN queries, which return the k nearest neighbors for every point in the range. In addition, we devise an auxiliary solution-based index EXO-tree to speed up any type of NN query. EXO-tree is orthogonal to any existing NN processing algorithm and, thus, can be transparently integrated. An extensive empirical study was conducted to evaluate the CPU and I/O performance of these techniques, and the study showed that they are efficient and robust under various data sets, query ranges, numbers of nearest neighbors, dimensions, and cache sizes.

The great advances in deep learning enable human beings to extract the semantic information in ubiquitous unstructured data into high-dimensional vectors, leading to an urgent priority of managing vector data. Nearest neighbor (NN) query is a pivotal question in vector data management. Unfortunately, the NN query has been proved to be intrinsically hard. Researchers, thus, turn to approximate nearest neighbor (ANN) query which targets better efficiency by slightly compromising accuracy. Despite this, existing ANN methods still incur high time and space costs, which are mainly due to the high dimensionality. Specifically, in most in-memory ANN algorithms, the time cost is dominated by the time for comparing the distances among vectors. Each distance comparison operation (DCO) involves hundreds of arithmetic operations as each vector has hundreds of dimensions. Similarly, the space cost is dominated by the space for storing the vectors. Towards the goal of reducing the time and space costs, we present three methods in this thesis. First, we observe that, for a DCO, if an approximate distance can confirm that a vector is not a NN, then it can be discarded without computing exact distances. Based on this observation, we propose a method named ADSampling. For a DCO, it iteratively and incrementally samples a few dimensions and computes an approximate distance. When this distance is accurate enough to decide the result of the DCO, it terminates sampling. Second, to further improve the efficiency of DCOs, we design an efficient distance estimator. We propose a new quantization method named RaBitQ, which maps $D$-dimensional vectors into $D$-bit strings. RaBitQ provides an unbiased and asymptotically optimal estimator with good empirical accuracy. In addition, we introduce efficient implementations of RaBitQ based on bitwise operations or SIMD-based operations. Third, by extending the RaBitQ method, we develop an algorithm which compresses a floating-point vector into a $B$-bit unsigned integer vector. We prove that our algorithm is asymptotically optimal in terms of the space-accuracy trade-off.

Case Based Reasoning (CBR) is a method that aims to resolve a new case by adapting the solutions contained in previous cases that are similar to the new case. The system built in this study is the CBR system to make recommendations on the topic of student thesis concentration. This study used data from undergraduate students of Informatics Engineering IST AKPRIND Yogyakarta with a total of 115 data consisting of 80 training data and 35 test data. This study aims to design and build a Case Based Reasoning system using the Nearest Neighbor and Manhattan Distance Similarity Methods, and to compare the results of the accuracy value using the Nearest Neighbor Similarity and Manhattan Distance Similarity methods. The recommendation process is carried out by calculating the value of closeness or similarity between new cases and old cases stored on a case basis using the Nearest Neighbor Method and Manhattan Distance. The features used in this study consisted of GPA and course grades. The case taken is the case with the highest similarity value. If a case doesnt get a topic recommendation or is less than the trashold value of 0.8, a case revision will be carried out by an expert. Successfully revised cases are stored in the system to be made new knowledge. The test results using the Nearest Neighbor Method get an accuracy value of 97.14% and Manhattan Distance Method 94.29%.

Nearest neighbor (NN) searches represent an important class of queries in geographic information systems (GIS). Most nearest neighbor algorithms rely on static distance information to compute NN queries (e.g., Euclidean distance or spatial network distance). However, the final goal of a user when performing an NN search is often to travel to one of the points of the search result. In this case, finding the nearest neighbors in terms of travel time is more important than the actual distance. In the existing NN algorithms dynamic real-time events (e.g., traffic congestions, detours, etc.) are usually not considered and hence the pre-computed nearest neighbor objects may not accurately reflect the shortest travel time. In this paper we propose a novel travel time network that integrates both spatial networks and real-time traffic event information. Based on this foundation of the travel time network, we develop a local-based greedy nearest neighbor algorithm and a global-based adaptive nearest neighbor algorithm that both utilize real-time traffic information to provide adaptive nearest neighbor search results. We have performed a theoretical analysis and simulations to verify our methods. The results indicate that our algorithms remarkably reduce the travel time compared with previous nearest neighbor solutions.

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.

In this paper, we study the Obstructed Nearest Neighbor (ONN) problem: given a set of points and a set of polygonal obstacles in two dimensions, find the k nearest neighbors to a query point according to the length of the shortest obstacle-avoiding path between two points. ONN query is useful both as a stand-alone tool in geographical information systems and as a primitive for spatial data analysis such as clustering and classification in the presence of obstacles. We propose an efficient ONN algorithm that processes only the data points and obstacles relevant to the query in an incremental way and thus filters out a large number of points and obstacles. Experiments on spatial data sets show the algorithm scales well with respect to the input data size and the number of nearest neighbors requested.

In recent years,location-based services(LBS) are getting more and more attention.The nearest neighbor query is the most common query type in the LBS area.The uncertainty of data exists commonly due to the inaccuracy of measurement instructions and the data attributes itself.This uncertainty will affect the results of nearest neighbor queries.The existence of obstacles in planes also put challenges to spatial data queries.This paper studies the continuous nearest neighbor query by the existence of obstacles and the uncertainty of data.It also gives a pruning strategy that greatly reducs the number of objects which need to be calculated.Furthermore,this paper proposes the safe region concept with regard to uncertain data in obstructed spaces,an algorithm to generate the safe regions,and an indexing method for saving safe regions.Experimental results show that the proposed method has good efficiency and scalability.

A reverse k-nearest neighbors (RkNN) query returns all the objects that take the query object q as their k nearest neighbors. However, data are often uncertain in numerous applications. In this paper, we focus on the problem of processing RkNN on uncertain data. A probabilistic RkNN (PRkNN) query retrieves all the objects that have higher probabilities than a user-specified threshold to be the RkNN of q. The previous work for answering PRNN query are mainly based on the distance relationship between uncertain objects, and are inapplicable for PRkNN when k > 1. In this paper, we design a novel algorithm for PRkNN query to support arbitrary values of k on the basis of two pruning strategies, namely spatial pruning and probabilistic pruning. The spatial pruning rule is defined on both the distances and the angle ranges between uncertain objects. And an efficient upper bound of probability is estimated by the probabilistic pruning algorithm. Extensive experiments are conducted to study the performance of the proposed approach. The results show that our proposed algorithm has a better performance and scalability than the existing solution regarding the growth of k.KeywordsQuery ProcessingAngle RangeQuery TimeUncertain DataQuery ObjectThese 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.

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.

Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases, location-based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest-neighbor queries in a probabilistic framework in which the location of each input point is specified as a probability distribution function. We present efficient algorithms for - computing all points that are nearest neighbors of a query point with nonzero probability; and - estimating the probability of a point being the nearest neighbor of a query point, either exactly or within a specified additive error.

Currently, Nearest-Neighbor approaches (NN) have been widely applied to real world image data mining. These approaches have the following three disadvantages: (i) the performance is inferior on small datasets; (ii) the performance of approximated nearest neighbor search will degrade for data with high dimensions; (iii) they are heavily dependent on the chosen feature and distance measure. To overcome these intrinsic weaknesses, we propose a novel Nearest-Neighbor method, which improves the original NN approaches from three aspects. Firstly, we propose a novel neighborhood similarity measure, where the similarity between test images and labeled images in the database is calculated jointly by the original image-to-image similarity and the average similarity of their neighboring unlabeled data. Secondly, we adopt the kernelized locality sensitive hashing to effectively conduct the nearest neighbor search for high dimensional data. Finally, to enhance the robustness of the method on different genres of images, we propose to fuse the discrimination power of different features by considering all the retrieved nearest neighbors via hashing systems using different features/kernels. Experimental result shows the advantage over traditional Nearest-Neighbor methods using the labeled data only. Even when the ratio of labeled data is very small, our method could also achieve remarkable results, thanks to the help of unlabeled data and multiple features.

In this paper, we propose an &cient solution to the problem of nearest neighbor query processing in decluste red spatial data. Recently a branch-and-bound nearest neighbor finding (BB-NNF) algorithm has been designed to process nearest neighbor queries in R-trees. However, this algorithm is strictly serial (branch-and-bound oriented) and its performance degrades if applied to a parallel environment, since it does not exploit any kind of parallelization. We develop an eEicient query processing strategy tir parallel nearest neighbor finding (P-NNF), assuming a shared nothing multi-processor architecture, where the processors i communicate via a network. In our method, the relevant : sites are activated simultaneously. In order to achieve this goal, statistical information is used. The dTiciency mcasurc is the response time of a given query. E2cperimental results, based on real-life and synthetic datasets, show that the proposed method outperforms the branch-andbound method by factors. We focus on Zd space but generalizations to higher dimensions are straightforward.