Vebjorn Ljosa and Ambuj K. Singh:
APLA: Indexing Arbitrary Probability Distributions,”
in Proceedings of the 23rd International Conference on Data Engineering (ICDE), p. 946-955, April, 2007, doi:10.1109/ICDE.2007.367940.


The ability to store and query uncertain information is of great benefit to databases that infer values from a set of observations, including databases of moving objects, sensor readings, historical business transactions, and biomedical images. These observations are often inexact to begin with, and even if they are exact, a set of observations of an attribute of an object is better represented by a probability distribution than by a single number, such as a mean.

In this paper, we present adaptive, piecewise-linear approximations (APLAs), which represent arbitrary probability distributions compactly with guaranteed quality. We also present the APLA-tree, an index structure for APLAs. Because APLA is more precise than existing approximation techniques, the APLA-tree can answer probabilistic range queries twice as fast. APLA generalizes to multiple dimensions, and the APLA-tree can index multivariate distributions using either one-dimensional or multi-dimensional APLAs.

Finally, we propose a new definition of k-NN queries on uncertain data. The new definition allows APLA and the APLA-tree to answer k-NN queries quickly, even on arbitrary probability distributions. No efficient k-NN search was previously possible on such distributions.

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