Eficient Machine Learning Methods over Pairwise Space (keynote) Hung Son Nguyen University of Warsaw Keywords Rough sets, Support Vector Machine, Factorization Machine, Distance Metric Learning, Context-Aware Recommendation Extended Abstract In recent years many machine learning concepts and methods were developed on the set of pairs of objects. In this paper, the set of all pairs of objects is called the pairwise space. Let us notice that if the set of objects X = {x 1 , x 2 ,..., x n } consists of n instances, then the pairwise space contains O(n 2 ) pairs. Thus why the straightforward implementations of those methods are not applicable for big data sets with millions of objects. The main concepts in rough set theory (RS) such as reducts, lower and upper approximations, decision rules or discretizations have been defned in term of the discernibility matrix, which is a form of the pairwise space [1]. For example, in minimal decision reduct problem, we are looking for the minimal subset of features that preserves the discernibility between objects from diferent decision classes [2]. Support Vector Machine (SVM) is also a classifcation method described as an optimization problem over the pairwise space [3]. The initial idea of looking for the linear classifer with the maximal margin were transformed into the problem of looking for a set of coefcients α =(α 1 ,α 2 , ··· ,α n ) related to objects that maximizes an objective function W (α)= ∑ i α i - 1 2 ∑ i,j y i y j α i α j K(x i ,x j ). defned on the set of dot products of all pairs of objects. In the above formula y i denotes the decision class of the object x i and K is a kernel function chosen by the user. Distance Metric Learning (DML) [4] is a machine learning discipline that looks for the best distance function (also divergence or similarity ) from certain available information about similarity measures between diferent pairs or triplets of data. These similarities are determined 29th International Workshop on Concurrency, Specifcation and Programming (CS&P’21)  son@mimuw.edu.pl (H. S. Nguyen)  0000-0002-3236-5456 (H. S. Nguyen) © 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings http://ceur-ws.org ISSN1613-0073 CEUR Workshop Proceedings (CEUR-WS.org)