On the application of convex transforms to metric search

Funding: This research was supported by ERDF “CyberSecurity, CyberCrime and Critical Information Infrastructures Center of Excellence” (No.CZ.02.1.01/0.0/0.0/16 019/0000822) and by ESRC “Administrative Data Research Centres 2018” (No. ES/S007407/1).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.PostprintPeer reviewe

Metric Embedding into the Hamming Space with the n-Simplex Projection

Transformations of data objects into the Hamming space are often exploited to speed-up the similarity search in metric spaces. Techniques applicable in generic metric spaces require expensive learning, e.g., selection of pivoting objects. However, when searching in common Euclidean space, the best performance is usually achieved by transformations specifically designed for this space. We propose a novel transformation technique that provides a good trade-off between the applicability and the quality of the space approximation. It uses the n-Simplex projection to transform metric objects into a low-dimensional Euclidean space, and then transform this space to the Hamming space. We compare our approach theoretically and experimentally with several techniques of the metric embedding into the Hamming space. We focus on the applicability, learning cost, and the quality of search space approximation

Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised protons

Measurements of the Collins and Sivers asymmetries for charged pions and charged and neutral kaons produced in semi-inclusive deep-inelastic scattering of high energy muons off transversely polarised protons are presented. The results were obtained using all the available COMPASS proton data, which were taken in the years 2007 and 2010. The Collins asymmetries exhibit in the valence region a non-zero signal for pions and there are hints of non-zero signal also for kaons. The Sivers asymmetries are found to be positive for positive pions and kaons and compatible with zero otherwise. © 2015