托勒密索引
Ptolemaic Indexing
摘要：
本文讨论了一个新的家庭的界限用于相似性搜索，相关的度量索引中使用的，但基于托勒密不等式，而不是度量公理。托勒密不等式适用于著名的欧几里得距离，但在这里也适用于一般的二次型度量，马氏距离是一个重要的特例。经验上的合成和现实世界的数据集的不平等检查，也被发现持有约，具有非常低的误差程度，重要的距离，如角伪度量和几个Lp规范。索引实验表明，与现有的三角形方法相比，过滤能力大大提高。它还表明，结合托勒密和三角滤波可以导致更好的结果比使用任何一种方法本身。
英文摘要：
This paper discusses a new family of bounds for use in similarity search, related to those used in metric indexing, but based on Ptolemy's inequality, rather than the metric axioms. Ptolemy's inequality holds for the well-known Euclidean distance, but is also shown here to hold for quadratic form metrics in general, with Mahalanobis distance as an important special case. The inequality is examined empirically on both synthetic and real-world data sets and is also found to hold approximately, with a very low degree of error, for important distances such as the angular pseudometric and several Lp norms. Indexing experiments demonstrate a highly increased filtering power compared to existing, triangular methods. It is also shown that combining the Ptolemaic and triangular filtering can lead to better results than using either approach on its own.
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