Probabilistic skylines on uncertain data: model and bounding-pruning-refining methods

Uncertain data are inherent in some important applications. Although a considerable amount of research has been dedicated to modeling uncertain data and answering some types of queries on uncertain data, how to conduct advanced analysis on uncertain data remains an open problem at large. In this paper, we tackle the problem of skyline analysis on uncertain data. We propose a novel probabilistic skyline model where an uncertain object may take a probability to be in the skyline, and a p-skyline contains all objects whose skyline probabilities are at least p (0 < p ≤ 1). Computing probabilistic skylines on large uncertain data sets is challenging. We develop a bounding-pruning-refining framework and three algorithms systematically. The bottom-up algorithm computes the skyline probabilities of some selected instances of uncertain objects, and uses those instances to prune other instances and uncertain objects effectively. The top-down algorithm recursively partitions the instances of uncertain objects into subsets, and prunes subsets and objects aggressively. Combining the advantages of the bottom-up algorithm and the top-down algorithm, we develop a hybrid algorithm to further improve the performance. Our experimental results on both the real NBA player data set and the benchmark synthetic data sets show that probabilistic skylines are interesting and useful, and our algorithms are efficient on large data sets.     

Distributed top-k query processing by exploiting skyline summaries

Recently, a trend has been observed towards supporting rank-aware query operators, such as top-k, that enable users to retrieve only a limited set of the most interesting data objects. As data nowadays is commonly stored distributed over multiple servers, a challenging problem is to support rank-aware queries in distributed environments. In this paper, we propose a novel approach, called DiTo, for efficient top-k processing over multiple servers, where each server stores autonomously a fraction of the data. Towards this goal, we exploit the inherent relationship of top-k and skyline objects, and we employ the skyline objects of servers as a data summarization mechanism for efficiently identifying the servers that store top-k results. Relying on a thresholding scheme, DiTo retrieves the top-k result set progressively, while the number of queried servers and transferred data is minimized. Furthermore, we extend DiTo to support data summarizations of bounded size, thus restricting the cost of summary distribution and maintenance. To this end, we study the challenging problem of finding an abstraction of the skyline set of fixed size that influences the performance of DiTo only slightly. Our experimental evaluation shows that DiTo performs efficiently and provides a viable solution when a high degree of distribution is required.     

Top-k outlier detection from uncertain data

Uncertain data are common due to the increasing usage of sensors, radio frequency identification(RFID), GPS and similar devices for data collection. The causes of uncertainty include limitations of measurements, inclusion of noise, inconsistent supply voltage and delay or loss of data in transfer. In order to manage, query or mine such data, data uncertainty needs to be considered. Hence,this paper studies the problem of top-k distance-based outlier detection from uncertain data objects. In this work, an uncertain object is modelled by a probability density function of a Gaussian distribution. The naive approach of distance-based outlier detection makes use of nested loop. This approach is very costly due to the expensive distance function between two uncertain objects. Therefore,a populated-cells list(PC-list) approach of outlier detection is proposed. Using the PC-list, the proposed top-k outlier detection algorithm needs to consider only a fraction of dataset objects and hence quickly identifies candidate objects for top-k outliers. Two approximate top-k outlier detection algorithms are presented to further increase the efficiency of the top-k outlier detection algorithm.An extensive empirical study on synthetic and real datasets is also presented to prove the accuracy, efficiency and scalability of the proposed algorithms.     

Threshold-based probabilistic top-k dominating queries

Recently, due to intrinsic characteristics in many underlying data sets, a number of probabilistic queries on uncertain data have been investigated. Top-k dominating queries are very important in many applications including decision making in a multidimensional space. In this paper, we study the problem of efficiently computing top-k dominating queries on uncertain data. We first formally define the problem. Then, we develop an efficient, threshold-based algorithm to compute the exact solution. To overcome some inherent computational deficiency in an exact computation, we develop an efficient randomized algorithm with an accuracy guarantee. Our extensive experiments demonstrate that both algorithms are quite efficient, while the randomized algorithm is quite scalable against data set sizes, object areas, k values, etc. The randomized algorithm is also highly accurate in practice.     

Ranking queries on uncertain data

Uncertain data is inherent in a few important applications. It is far from trivial to extend ranking queries (also known as top-k queries), a popular type of queries on certain data, to uncertain data. In this paper, we cast ranking queries on uncertain data using three parameters: rank threshold k, probability threshold p, and answer set size threshold l. Systematically, we identify four types of ranking queries on uncertain data. First, a probability threshold top-k query computes the uncertain records taking a probability of at least p to be in the top-k list. Second, a top-(k, l) query returns the top-l uncertain records whose probabilities of being ranked among top-k are the largest. Third, the p-rank of an uncertain record is the smallest number k such that the record takes a probability of at least p to be ranked in the top-k list. A rank threshold top-k query retrieves the records whose p-ranks are at most k. Last, a top-(p, l) query returns the top-l uncertain records with the smallest p-ranks. To answer such ranking queries, we present an efficient exact algorithm, a fast sampling algorithm, and a Poisson approximation-based algorithm. To answer top-(k, l) queries and top-(p, l) queries, we propose PRist+, a compact index. An efficient index construction algorithm and efficacious query answering methods are developed for PRist+. An empirical study using real and synthetic data sets verifies the effectiveness of the probabilistic ranking queries and the efficiency of our methods.     

Approximate Continuous Top-<Emphasis Type="Italic">k</Emphasis> Query over Sliding Window

Continuous top-k query over sliding window is a fundamental problem in database, which retrieves k objects with the highest scores when the window slides. Existing studies mainly adopt exact algorithms to tackle this type of queries, whose key idea is to maintain a subset of objects in the window, and try to retrieve answers from it. However, all the existing algorithms are sensitive to query parameters and data distribution. In addition, they suffer from expensive overhead for incremental maintenance, and thus cannot satisfy real-time requirement. In this paper, we define a novel query named (ε, δ)-approximate continuous top-k query, which returns approximate answers for top-k query. In order to efficiently support this query, we propose an efficient framework, named PABF (Probabilistic Approximate Based Framework), to support approximate top-k query over sliding window. We firstly maintain a self-adaptive pruning value, which could filter out newly arrived objects who have a probability less than 1 ? δ of being a query result. For those objects that are not filtered, we combine them together, if the score difference among them is less than a threshold. To efficiently maintain these combined results, the framework PABF also proposes a multi-phase merging algorithm. Theoretical analysis indicates that even in the worst case, we require only logarithmic complexity for maintaining each candidate.     

A top-k spatial join querying processing algorithm based on spark

Aiming at the problem of top-k spatial join query processing in cloud computing systems, a Spark-based top-k spatial join (STKSJ) query processing algorithm is proposed. In this algorithm, the whole data space is divided into grid cells of the same size by a grid partitioning method, and each spatial object in one data set is projected into a grid cell. The Minimum Bounding Rectangle (MBR) of all spatial objects in each grid cell is computed. The spatial objects overlapping with these MBRs in another spatial data set are replicated to the corresponding grid cells, thereby filtering out spatial objects for which there are no join results, thus reducing the cost of subsequent spatial join processing. An improved plane sweeping algorithm is also proposed that speeds up the scanning mode and applies threshold filtering, thus greatly reducing the communication and computation costs of intermediate join results in subsequent top-k aggregation operations. Experimental results on synthetic and real data sets show that the proposed algorithm has clear advantages, and better performance than existing top-k spatial join query processing algorithms.     

Top-k/w publish/subscribe: A publish/subscribe model for continuous top-k processing over data streams

Continuous processing of top-k queries over data streams is a promising technique for alleviating the information overload problem as it distinguishes relevant from irrelevant data stream objects with respect to a given scoring function over time. Thus it enables filtering of irrelevant data objects and delivery of top-k objects relevant to user interests in real-time. We propose a solution for distributed continuous top-k processing based on the publish/subscribe communication paradigm—top-k publish/subscribe over sliding windows (top-k/w publish/subscribe). It identifies k best-ranked objects with respect to a given scoring function over a sliding window of size w, and extends the publish/subscribe communication paradigm by continuous top-k processing algorithms coming from the field of data stream processing.In this paper, we introduce, analyze and evaluate the essential building blocks of distributed top-k/w publish/subscribe systems: first, we present a formal top-k/w publish/subscribe model and compare it to the prevailing Boolean publish/subscribe model. Next, we outline the top-k/w processing tasks performed by publish/subscribe nodes and investigate the properties of supported scoring functions. Furthermore, we explore potential routing strategies for distributed top-k/w publish/subscribe systems. Finally, we experimentally evaluate model properties and provide a comparative study investigating traffic requirements of potential routing strategies.     

Continuous monitoring of skylines over uncertain data streams

Uncertain data are inevitable in many applications due to various factors such as the limitations of measuring equipment and delays in data updates. Although modeling and querying uncertain data have recently attracted considerable attention from the database community, there are still many critical issues to be resolved with respect to conducting advanced analysis on uncertain data. In this paper, we study the execution of the probabilistic skyline query over uncertain data streams. We propose a novel sliding window skyline model where an uncertain tuple may take the probability to be in the skyline at a certain timestamp t. Formally, a Wp-Skyline(p, t) contains all the tuples whose probabilities of becoming skylines are at least p at timestamp t. However, in the stream environment, computing a probabilistic skyline on a large number of uncertain tuples within the sliding window is a daunting task in practice. In order to efficiently calculate Wp-Skyline, we propose an efficient and effective approach, namely the candidate list approach, which maintains lists of candidates that might become skylines in future sliding windows. We also propose algorithms that continuously monitor the newly incoming and expired data to maintain the skyline candidate set incrementally. To further reduce the computation cost of deciding whether or not a candidate tuple belongs to the skyline, we propose an enhanced refinement strategy that is based on a multi-dimensional indexing structure combined with a grouping-and-conquer strategy. To validate the effectiveness of our proposed approach, we conduct extensive experiments on both real and synthetic data sets and make comparisons with basic techniques.     

Top-<Emphasis Type="Italic">k</Emphasis> probabilistic prevalent co-location mining in spatially uncertain data sets

A co-location pattern is a set of spatial features whose instances frequently appear in a spatial neighborhood. This paper efficiently mines the top-k probabilistic prevalent co-locations over spatially uncertain data sets and makes the following contributions: 1) the concept of the top-k probabilistic prevalent co-locations based on a possible world model is defined; 2) a framework for discovering the top-k probabilistic prevalent co-locations is set up; 3) a matrix method is proposed to improve the computation of the prevalence probability of a top-k candidate, and two pruning rules of the matrix block are given to accelerate the search for exact solutions; 4) a polynomial matrix is developed to further speed up the top-k candidate refinement process; 5) an approximate algorithm with compensation factor is introduced so that relatively large quantity of data can be processed quickly. The efficiency of our proposed algorithms as well as the accuracy of the approximation algorithms is evaluated with an extensive set of experiments using both synthetic and real uncertain data sets.     

Continuous distance-based skyline queries in road networks

In recent years, the research community has introduced various methods for processing skyline queries in road networks. A skyline query retrieves the skyline points that are not dominated by others in terms of static and dynamic attributes (i.e., the road distance). This paper addresses the issue of efficiently processing continuous skyline queries in road networks. Two novel and important distance-based skyline queries are presented, namely, the continuous  _dε-skyline$d_{\epsilon }\mathrm{-}\mathit{skyline}$query   (_Cdε-SQ${\mathit{Cd}}_{\epsilon }\mathrm{-}\mathit{SQ}$) and the continuous k nearest neighbor-skyline query (Cknn-SQ  ). A grid index is first designed to effectively manage the information of data objects and then two algorithms are proposed, the _Cdε-SQ${\mathit{Cd}}_{\epsilon }\mathrm{-}\mathit{SQ}$algorithm   and the _Cdε-SQ⁺${\mathit{Cd}}_{\epsilon }\mathrm{-}{\mathit{SQ}}^{+}$algorithm  , which are combined with the grid index to answer the _Cdε-SQ${\mathit{Cd}}_{\epsilon }\mathrm{-}\mathit{SQ}$. Similarly, the Cknn-SQ algorithm and the Cknn-SQ⁺algorithm are developed to efficiently process the Cknn-SQ. Extensive experiments using real road network datasets demonstrate the effectiveness and the efficiency of the proposed algorithms.     

基于事件的位置不确定移动对象连续概率Skyline查询

Skyline查询是基于位置服务(Location based service, LBS)的一项重要操作,其目的是发现数据集中不被其他点支配的点的集合.移动对象在运动过 程中,其位置信息具有不确定性,导致各数据点间的支配关系不稳定,从而影响Skyline操作.本文针对以位置不确定移动对象为查 询点的Skyline查询进行研究,首先,定义了查询点移动时各对象间支配概率,提出了支配概率和Skyline概率的微元计算方法.在此基 础上,提出一种面向不确定移动对象进行连续概率Skyline查询的有效算法U_CPSC.该算法首先快速计算初始时刻的p-Skyline集合; 然后,定义了两类可能引起p-Skyline变动的事件,通过对这些事件的跟踪计算快速更新p-Skyline集合,无需在移动对象的每一运动 时刻去遍历整个数据集,实现了对p-Skyline的连续更新操作,大大减少了算法的查找和计算开销,提高了运算效率;最后,提出一 种静态算法U_SPSC,与U_CPSC进行了对比试验,实验结果证明了算法的有效性.     

An efficient approach to finding potential products continuously

Skyline points and queries are important in the context of processing datasets with multiple dimensions. As skyline points can be viewed as representing marketable products that are useful for clients and business owners, one may also consider non-skyline points that are highly competitive with the current skyline points. We address the problem of continuously finding such potential products from a dynamic d-dimensional dataset, and formally define a potential product and its upgrade promotion cost. In this paper, we propose the CP-Sky algorithm, an efficient approach for continuously evaluating potential products by utilizing a second-order skyline set, which consists of candidate points that are closest to regular skyline points (also termed the first-order skyline set), to facilitate efficient computations and updates for potential products. With the knowledge of the second-order skyline set, CP-Sky enables the system to (1) efficiently find substitute skyline points from the second-order skyline set only if a first-order skyline point is removed, and (2) continuously retrieve the top-k potential products. Within this context, the Approximate Exclusive Dominance Region algorithm (AEDR) is proposed to reduce the computational complexity of determining a candidate set for second-order skyline updates over a dynamic data set without affecting the result accuracy. Additionally, we extend the CP-Sky algorithm to support the computations of top-k potential products. Finally, we present experimental results on data sets with various distributions to demonstrate the performance and utility of our approach.     

基于高斯模型的不确定数据流Skyline查询方法

由于数据的动态性及不确定性等特征,使得不确定数据流上Skyline查询研究面临挑战.不确定对象一般采用多元概率密度函数(PDF)表示,现有的不确定数据流Skyline查询方法均采用离散型随机变量建模.然而不确定数据流中的对象可能是连续变化的,离散模型对连续性随机变量难以适用.针对连续PDF建模的不确定数据流Skyline查询进行了研究,提出了基于高斯模型的不确定数据流Skyline查询方法(SGMU),该方法包含2个过程:1)动态高斯建模算法(DGM):对滑动窗口采样并建立高斯模型,将原始的数据流转化为不确定对象PDF的参数流;2)提出了基于高斯树的查询算法(GTS)以建立空间索引结构和执行Skyline查询.实验结果表明,SGMU算法不仅能够对连续型不确定对象进行有效建模以辅助Skyline查询,而且能够有效地减少查询对象个数,提高Skyline查询效率.     

Efficient continuous skyline computation

In a number of emerging streaming applications, the data values that are produced have an associated time interval for which they are valid. A useful computation over such streaming data is to produce a continuous and valid skyline summary. Previous work on skyline algorithms have only focused on evaluating skylines over static data sets, and there are no known algorithms for skyline computation in the continuous setting. In this paper, we introduce the continuous time-interval skyline operator, which continuously computes the current skyline over a data stream. We present a new algorithm called LookOut for evaluating such queries efficiently, and empirically demonstrate the scalability of this algorithm. In addition, we also examine the effect of the underlying spatial index structure when evaluating skylines. Whereas previous work on skyline computations have only considered using the R^∗-tree index structure, we show that for skyline computations using an underlying quadtree has significant performance benefits over an R^∗-tree index.     

Mining collective knowledge: inferring functional labels from online review for business

Uncertain graph has been widely used to represent graph data with inherent uncertainty in structures. Reliability search is a fundamental problem in uncertain graph analytics. This paper investigates on a new problem with broad real-world applications, the top-k reliability search problem on uncertain graphs, that is, finding the k vertices v with the highest reliabilities of connections from a source vertex s to v. Note that the existing algorithm for the threshold-based reliability search problem is inefficient for the top-k reliability search problem. We propose a new algorithm to efficiently solve the top-k reliability search problem. The algorithm adopts two important techniques, namely the BFS sharing technique and the offline sampling technique. The BFS sharing technique exploits overlaps among different sampled possible worlds of the input uncertain graph and performs a single BFS on all possible worlds simultaneously. The offline sampling technique samples possible worlds offline and stores them using a compact structure. The algorithm also takes advantages of bit vectors and bitwise operations to improve efficiency. In addition, we generalize the top-k reliability search problem from single-source case to the multi-source case and show that the multi-source case of the problem can be equivalently converted to the single-source case of the problem. Moreover, we define two types of the reverse top-k reliability search problems with different semantics on uncertain graphs. We propose appropriate solutions for both of them. Extensive experiments carried out on both real and synthetic datasets verify that the optimized algorithm outperforms the baselines by 1–2 orders of magnitude in execution time while achieving comparable accuracy. Meanwhile, the optimized algorithm exhibits linear scalability with respect to the size of the input uncertain graph.     

Uncertain top-<Emphasis Type="Italic">k</Emphasis> query processing in distributed environments

The top-k query on uncertain data set has been a very hot topic these years, and there have been many studies on uncertain top-k queries. Unfortunately, most of the existing algorithms only consider centralized processing environments, and they are not suitable for the large-scale data. In this paper, it is the first attempt to process probabilistic threshold top-k queries (an important uncertain top-k query, PT-k for short) in a distributed environment. We propose 3 efficient algorithms. The serial distributed approach adopts a new method, which only requires a few amount of calculations, to serially process PT-k queries in distributed environments. The global sorting first algorithm for PT-k query processing (GSP) is designed for improving the computation speed. In GSP, a distributed sorting operation is performed, and then we compute the candidates for PT-k queries in parallel. The query results can be computed by using a novel incremental method which can reduce the number of calculations. The local filtering first algorithm for PT-k query processing is designed for reducing the network overhead. Specifically, several filtering strategies are proposed to filter out redundant data locally, and then the incremental method in GSP is used to process the PT-k queries. Finally, the effectiveness of our proposed algorithms is verified through a series of experiments.     

Multi-dimensional top-k dominating queries

The top-k dominating query returns k data objects which dominate the highest number of objects in a dataset. This query is an important tool for decision support since it provides data analysts an intuitive way for finding significant objects. In addition, it combines the advantages of top-k and skyline queries without sharing their disadvantages: (i) the output size can be controlled, (ii) no ranking functions need to be specified by users, and (iii) the result is independent of the scales at different dimensions. Despite their importance, top-k dominating queries have not received adequate attention from the research community. This paper is an extensive study on the evaluation of top-k dominating queries. First, we propose a set of algorithms that apply on indexed multi-dimensional data. Second, we investigate query evaluation on data that are not indexed. Finally, we study a relaxed variant of the query which considers dominance in dimensional subspaces. Experiments using synthetic and real datasets demonstrate that our algorithms significantly outperform a previous skyline-based approach. We also illustrate the applicability of this multi-dimensional analysis query by studying the meaningfulness of its results on real data.     

Top-$\boldsymbol{k}$ query processing over uncertain data in distributed environments

Although top-k queries over uncertain data in centralized databases have been studied widely in recent years, it is still a challenging issue in distributed environments. In distributed environments, such as Peer-to-Peer (P2P) systems and sensor networks, there exists an inherent uncertainty on the data objects due to imprecise measurements and network delays. Therefore, it is necessary to study the problem of how to efficiently retrieve top-k uncertain data objects over distributed environments with minimum network overhead. In this paper, we propose a novel approach of processing uncertain top-k queries in large-scale P2P networks, where datasets are horizontally partitioned over peers. In our approach, each peer constructs an Uncertain Quad-Tree (UQ-Tree) index for its local uncertain data, while the P2P network constructs a global index by summarizing the local indexes. Based on the global index, we propose a spatial-pruning algorithm to reduce communication costs and a distributed-pruning algorithm to reduce computation costs. Extensive experiments are conducted to verify the effectiveness and efficiency of the proposed methods in terms of communication costs and response time.     

高速流环境下近似连续k代表轮廓查询算法

k代表轮廓查询是从传统轮廓查询中衍生出来的一类查询.给定多维数据集合D,轮廓查询从D中找到所有不被其他对象支配的对象,将其返回给用户,便于用户结合自身偏好选择高质量对象.然而,轮廓对象规模通常较大,用户需要从大量数据中进行选择,导致选择速度和质量无法得到保证.与传统轮廓查询相比,k代表轮廓查询从所有轮廓对象中选择“代表性”最强的k个对象返回给用户,有效地解决了传统轮廓查询存在的这一问题.给定滑动窗口W和连续查询q,q监听窗口中的数据.当窗口滑动时,查询q返回窗口中,组合支配面积最大的k个对象.现有算法的核心思想是:实时监测当前窗口中的轮廓对象集合,当轮廓对象集合更新时,算法更新k代表轮廓.然而,实时监测窗口中,轮廓集合的计算代价通常较大.此外,当轮廓集合规模较大时,从中选择k代表轮廓的计算代价是同样巨大的,导致已有算法无法在高速流环境下使用.针对上述问题,提出了ρ-近似k代表轮廓查询.为了支持该查询,提出了查询处理框架PAKRS(predict-basedapproximatekrepresentativeskyline).首先,PAKRS利用高速流的特性对当前窗口进行划分,根据划分结...