On the Application of Convex Transforms to Metric Search

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Authors

CONNOR Richard DEARLE Alan MÍČ Vladimír ZEZULA Pavel

Year of publication 2020
Type Article in Periodical
Magazine / Source Pattern Recognition Letters
MU Faculty or unit

Faculty of Informatics

Citation
Web https://www.sciencedirect.com/science/article/abs/pii/S0167865520303068
Doi http://dx.doi.org/10.1016/j.patrec.2020.08.008
Keywords similarity search; transformation of distance function; metric space; convex transform
Description Scalable similarity search in metric spaces relies on using the mathematical properties of the space in order to allow efficient querying. Most important in this context is the triangle inequality property, which can allow the majority of individual similarity comparisons to be avoided for a given query. However many important metric spaces, typically those with high dimensionality, are not amenable to such techniques. In the past convex transforms have been studied as a pragmatic mechanism which can overcome this effect; however the problem with this approach is that the metric properties may be lost, leading to loss of accuracy. Here, we study the underlying properties of such transforms and their effect on metric indexing mechanisms. We show there are some spaces where certain transforms may be applied without loss of accuracy, and further spaces where we can understand the engineering tradeoffs between accuracy and efficiency. We back these observations with experimental analysis. To highlight the value of the approach, we show three large spaces deriving from practical domains whose dimensionality prevents normal indexing techniques, but where the transforms applied give scalable access with a relatively small loss of accuracy.
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