Improved Prototype Embedding Based Generalized Median Computation by Means of Refined Reconstruction Methods

Abstract

Learning a prototype from a set of given objects is a core problem in machine learning and pattern recognition. A popular approach to consensus learning is to formulate it as an optimization problem in terms of generalized median computation. Recently, a prototype-embedding approach has been proposed to transform the objects into a vector space, compute the geometric median, and then inversely transform back into the original space. This approach has been successfully applied in several domains, where the generalized median problem has inherent high computational complexity (typically \(\mathcal {NP}\)-hard) and thus approximate solutions are required. In this work we introduce three new methods for the inverse transformation. We show that these methods significantly improve the generalized median computation compared to previous methods.