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.
In @cite_0 , objects which have the highest probability of being located inside a given query range are reported. In contrast, the approaches for managing uncertain vector objects proposed in @cite_9 @cite_27 @cite_7 support arbitrarily shaped probability distribution functions for uncertain object attributes. Similar to @cite_0 , the approaches in @cite_27 @cite_7 focus on probability computations based on query predicates according to a given query range and, thus, are not applicable for our problem. Although @cite_17 studies probabilistic ranking of objects according to their distance from a reference query point, the solutions are limited to existentially uncertain spatial data with a single alternative.
@cite_7 @cite_9 @cite_0 @cite_27 @cite_17
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In applications like location-based services, sensor monitoring and biological databases, the values of the database items are inherently uncertain in nature. An important query for uncertain objects is the probabilistic nearest-neighbor query (PNN), which computes the probability of each object for being the nearest neighbor of a query point. Evaluating this query is computationally expensive, since it needs to consider the relationship among uncertain objects, and requires the use of numerical integration or Monte-Carlo methods. Sometimes, a query user may not be concerned about the exact probability values. For example, he may only need answers that have sufficiently high confidence. We thus propose the constrained nearest-neighbor query (C-PNN), which returns the IDs of objects whose probabilities are higher than some threshold, with a given error bound in the answers. The C-PNN can be answered efficiently with probabilistic verifiers. These are methods that derive the lower and upper bounds of answer probabilities, so that an object can be quickly decided on whether it should be included in the answer. We have developed three probabilistic verifiers, which can be used on uncertain data with arbitrary probability density functions. Extensive experiments were performed to examine the effectiveness of these approaches. In emerging applications such as location-based services, sensor monitoring and biological management systems, the values of the database items are naturally imprecise. For these uncertain databases, an important query is the Probabilistic k-Nearest-Neighbor Query (k-PNN), which computes the probabilities of sets of k objects for being the closest to a given query point. The evaluation of this query can be both computationally- and I O-expensive, since there is an exponentially large number of k object-sets, and numerical integration is required. Often a user may not be concerned about the exact probability values. For example, he may only need answers that have sufficiently high confidence. We thus propose the Probabilistic Threshold k-Nearest-Neighbor Query (T-k-PNN), which returns sets of k objects that satisfy the query with probabilities higher than some threshold T. Three steps are proposed to handle this query efficiently. In the first stage, objects that cannot constitute an answer are filtered with the aid of a spatial index. The second step, called probabilistic candidate selection, significantly prunes a number of candidate sets to be examined. The remaining sets are sent for verification, which derives the lower and upper bounds of answer probabilities, so that a candidate set can be quickly decided on whether it should be included in the answer. We also examine spatially-efficient data structures that support these methods. Our solution can be applied to uncertain data with arbitrary probability density functions. We have also performed extensive experiments to examine the effectiveness of our methods. In an uncertain database, every object o is associated with a probability density function, which describes the likelihood that o appears at each position in a multidimensional workspace. This article studies two types of range retrieval fundamental to many analytical tasks. Specifically, a nonfuzzy query returns all the objects that appear in a search region rq with at least a certain probability tq. On the other hand, given an uncertain object q, fuzzy search retrieves the set of objects that are within distance eq from q with no less than probability tq. The core of our methodology is a novel concept of “probabilistically constrained rectangle”, which permits effective pruning validation of nonqualifying qualifying data. We develop a new index structure called the U-tree for minimizing the query overhead. Our algorithmic findings are accompanied with a thorough theoretical analysis, which reveals valuable insight into the problem characteristics, and mathematically confirms the efficiency of our solutions. We verify the effectiveness of the proposed techniques with extensive experiments. We study the problem of answering spatial queries in databases where objects exist with some uncertainty and they are associated with an existential probability. The goal of a thresholding probabilistic spatial query is to retrieve the objects that qualify the spatial predicates with probability that exceeds a threshold. Accordingly, a ranking probabilistic spatial query selects the objects with the highest probabilities to qualify the spatial predicates. We propose adaptations of spatial access methods and search algorithms for probabilistic versions of range queries, nearest neighbors, spatial skylines, and reverse nearest neighbors and conduct an extensive experimental study, which evaluates the effectiveness of proposed solutions.