用正态分布标定地球移动器的距离
Indexing the Earth Mover's Distance Using Normal Distributions
摘要：
查询不确定的数据集（表示为概率分布）提出了许多挑战，由于涉及大量的数据和比较分布之间的不确定性的困难。地球移动器距离（EMD）已越来越多地用于比较不确定的数据，由于其能够有效地捕捉两个分布之间的差异。计算EMD需要找到运输问题的解决方案，这是计算密集型的。在本文中，我们提出了一个新的下界的EMD和索引结构，显着提高性能的EMD为基础的K-最近邻（K-NN）查询不确定数据库。我们提出了一个新的EMD下界，该下界逼近投影向量上的EMD。每个分布都被投影到一个向量上，并近似为正态分布以及伴随的误差项。然后，我们将每个法线表示为Hough变换空间中的一个点。然后，我们使用随机优势的概念，实现一个有效的索引结构中的转换空间。我们表明，我们的方法显着减少K-NN查询时间不确定数据库。索引结构也可以很好地扩展数据库基数。它非常适合于异构数据集，有助于保持EMD为基础的查询易处理的不确定数据集变得更大，更复杂。
英文摘要：
Querying uncertain data sets (represented as probability distributions) presents many challenges due to the large amount of data involved and the difficulties comparing uncertainty between distributions. The Earth Mover's Distance (EMD) has increasingly been employed to compare uncertain data due to its ability to effectively capture the differences between two distributions. Computing the EMD entails finding a solution to the transportation problem, which is computationally intensive. In this paper, we propose a new lower bound to the EMD and an index structure to significantly improve the performance of EMD based K-nearest neighbor (K-NN) queries on uncertain databases. We propose a new lower bound to the EMD that approximates the EMD on a projection vector. Each distribution is projected onto a vector and approximated by a normal distribution, as well as an accompanying error term. We then represent each normal as a point in a Hough transformed space. We then use the concept of stochastic dominance to implement an efficient index structure in the transformed space. We show that our method significantly decreases K-NN query time on uncertain databases. The index structure also scales well with database cardinality. It is well suited for heterogeneous data sets, helping to keep EMD based queries tractable as uncertain data sets become larger and more complex.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
