This paper introduces a scalable approach for probabilistic top-k similarity ranking on uncertain vector data. Each uncertain object is represented by a set of vector instances that are assumed to be mutually-exclusive. The objective is to rank the uncertain data according to their distance to a reference object. We propose a framework that incrementally computes for each object instance and ranking position, the probability of the object falling at that ranking position. The resulting rank probability distribution can serve as input for several state-of-the-art probabilistic ranking models. Existing approaches compute this probability distribution by applying a dynamic programming approach of quadratic complexity. In this paper we theoretically as well as experimentally show that our framework reduces this to a linear-time complexity while having the same memory requirements, facilitated by incremental accessing of the uncertain vector instances in increasing order of their distance to the reference object. Furthermore, we show how the output of our method can be used to apply probabilistic top-k ranking for the objects, according to different state-of-the-art definitions. We conduct an experimental evaluation on synthetic and real data, which demonstrates the efficiency of our approach.
@cite_4: Probabilistic data have recently become popular in applications such as scientific and geospatial databases. For images and other spatial datasets, probabilistic values can capture the uncertainty in extent and class of the objects in the images. Relating one such dataset to another by spatial joins is an important operation for data management systems. We consider probabilistic spatial join (PSJ) queries, which rank the results according to a score that incorporates both the uncertainties associated with the objects and the distances between them. We present algorithms for two kinds of PSJ queries: Threshold PSJ queries, which return all pairs that score above a given threshold, and top-k PSJ queries, which return the k top-scoring pairs. For threshold PSJ queries, we propose a plane sweep algorithm that, because it exploits the special structure of the problem, runs in 0(n (log n + k)) time, where n is the number of points and k is the number of results. We extend the algorithms to 2-D data and to top-k PSJ queries. To further speed up top-k PSJ queries, we develop a scheduling technique that estimates the scores at the level of blocks, then hands the blocks to the plane sweep algorithm. By finding high-scoring pairs early, the scheduling allows a large portion of the datasets to be pruned. Experiments demonstrate speed-ups of two orders of magnitude.
@cite_22: Top-k processing in uncertain databases is semantically and computationally different from traditional top-k processing. The interplay between score and uncertainty makes traditional techniques inapplicable. We introduce new probabilistic formulations for top-k queries. Our formulations are based on "marriage" of traditional top-k semantics and possible worlds semantics. In the light of these formulations, we construct a framework that encapsulates a state space model and efficient query processing techniques to tackle the challenges of uncertain data settings. We prove that our techniques are optimal in terms of the number of accessed tuples and materialized search states. Our experiments show the efficiency of our techniques under different data distributions with orders of magnitude improvement over naive materialization of possible worlds.
@cite_10: This work introduces novel polynomial algorithms for processing top-k queries in uncertain databases under the generally adopted model of x-relations. An x-relation consists of a number of x-tuples, and each x-tuple randomly instantiates into one tuple from one or more alternatives. Our results significantly improve the best known algorithms for top-k query processing in uncertain databases, in terms of both runtime and memory usage. In the single-alternative case, the new algorithms are 2 to 3 orders of magnitude faster than the previous algorithms. In the multialternative case, we introduce the first-known polynomial algorithms, while the current best algorithms have exponential complexity in both time and space. Our algorithms run in near linear or low polynomial time and cover both types of top-k queries in uncertain databases. We provide both the theoretical analysis and an extensive experimental evaluation to demonstrate the superiority of the new approaches over existing solutions.
@cite_9: Many applications employ sensors for monitoring entities such as temperature and wind speed. A centralized database tracks these entities to enable query processing. Due to continuous changes in these values and limited resources (e.g., network bandwidth and battery power), it is often infeasible to store the exact values at all times. A similar situation exists for moving object environments that track the constantly changing locations of objects. In this environment, it is possible for database queries to produce incorrect or invalid results based upon old data. However, if the degree of error (or uncertainty) between the actual value and the database value is controlled, one can place more confidence in the answers to queries. More generally, query answers can be augmented with probabilistic estimates of the validity of the answers. In this paper we study probabilistic query evaluation based upon uncertain data. A classification of queries is made based upon the nature of the result set. For each class, we develop algorithms for computing probabilistic answers. We address the important issue of measuring the quality of the answers to these queries, and provide algorithms for efficiently pulling data from relevant sensors or moving objects in order to improve the quality of the executing queries. Extensive experiments are performed to examine the effectiveness of several data update policies.
@cite_21: An important database primitive for commonly used feature databases is the similarity join. It combines two datasets based on some similarity predicate into one set such that the new set contains pairs of objects of the two original sets. In many different application areas, e.g. sensor databases, location based services or face recognition systems, distances between objects have to be computed based on vague and uncertain data. In this paper, we propose to express the similarity between two uncertain objects by probability density functions which assign a probability value to each possible distance value. By integrating these probabilistic distance functions directly into the join algorithms the full information provided by these functions is exploited. The resulting probabilistic similarity join assigns to each object pair a probability value indicating the likelihood that the object pair belongs to the result set. As the computation of these probability values is very expensive, we introduce an efficient join processing strategy exemplarily for the distance-range join. In a detailed experimental evaluation, we demonstrate the benefits of our probabilistic similarity join. The experiments show that we can achieve high quality join results with rather low computational cost.
@cite_19: 
@cite_13: 
We can categorize existing probabilistic querying approaches according to the uncertainty model they use. While probabilistic similarity queries over uncertain vector data are dedicated to the attribute value uncertainty model @cite_9 @cite_21 , probabilistic top- @math query approaches are usually associated with tuple uncertainty data in probabilistic databases @cite_22 @cite_19 @cite_13 @cite_10 . There exists a third probabilistic query category concerning spatially extended uncertain data as proposed in @cite_4 . But there is only little work in this direction.