Scalable Probabilistic Similarity Ranking in Uncertain Databases

Abstract

Abstract-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 the Poisson binomial recurrence technique 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.

Efficient probabilistic reverse nearest neighbor query processing on uncertain data

“…For the verification step, we perform, for each remaining candidate B, a probabilistic nearest neighbor query using the algorithm proposed in [6] for probabilistic ranking queries (and setting k = 1). This algorithm takes Q, B and D \ B (in particular this set can be reduced, as shown in Appendix D) as input and returns P (N NB(Q)) which is equivalent to P (RN NQ(B)).…”

Continuous Inverse Ranking Queries in Uncertain Streams

“…These probabilities can be computed in a single database scan. We can process the p t j successively by means of the Poisson binomial recurrence [17], as proposed in [18]. Therefore, let P t i,j be the probability that, out of the j objects processed so far, exactly i objects have a higher score than q.…”

Top (<i>k</i>₁,<i>k</i>₂) Query in Uncertain Datasets

“…At the same time, uncertainty is inherent in many datasets due to various factors like noise [1], privacy protection strategy [2], incompleteness of data and delay or loss in data transfer [3]. In this paper, we connect top k query and uncertain data model, and propose a novel top (k 1 , k 2 ) query in uncertain datasets.…”