Interpolated Discretized Embedding of Single Vectors and Vector Pairs for Classification, Metric Learning and Distance Approximation

TL;DR

This paper introduces a novel embedding technique for vectors and vector pairs that facilitates efficient classification, distance approximation, and non-Euclidean metric learning, enabling universal semimetric learning with high accuracy.

Contribution

It presents the first method capable of learning and approximating any general, non-Euclidean, semimetric, broadening the scope of metric learning applications.

Findings

Effective approximation of various distance functions

Supports non-Euclidean, semimetric learning

Achieves high accuracy in distance approximation

Abstract

We propose a new embedding method for a single vector and for a pair of vectors. This embedding method enables: a) efficient classification and regression of functions of single vectors; b) efficient approximation of distance functions; and c) non-Euclidean, semimetric learning. To the best of our knowledge, this is the first work that enables learning any general, non-Euclidean, semimetrics. That is, our method is a universal semimetric learning and approximation method that can approximate any distance function with as high accuracy as needed with or without semimetric constraints. The project homepage including code is at: http://www.ariel.ac.il/sites/ofirpele/ID