Filtering with relational similarity

For decades, the success of the similarity search has been based on detailed quantifications of pairwise similarities of objects. Currently, the search features have become much more precise but also bulkier, and the similarity computations are more time-consuming. We show that nearly no precise similarity quantifications are needed to evaluate the $k$ nearest neighbours ($k$NN) queries that dominate real-life applications. Based on the well-known fact that a selection of the most similar alternative out of several options is a much easier task than deciding the absolute similarity scores, we propose the search based on an epistemologically simpler concept of relational similarity. Having arbitrary objects $q,o_1,o_2$ from the search domain, the $k$NN search is solvable just by the ability to choose the more similar object to $q$ out of $o_1,o_2$. To support the filtering efficiency, we also consider a neutral option, i.e., equal similarities of $q,o_1$ and $q,o_2$. We formalise such concept and discuss its advantages with respect to similarity quantifications, namely the efficiency, robustness and scalability with respect to the dataset size. Our pioneering implementation of the relational similarity search for the Euclidean and Cosine spaces demonstrates robust filtering power and efficiency compared to several contemporary techniques.