Learning multi-kernel distance functions using relative comparisons

In this manuscript, a new form of distance function that can model spaces where a Mahalanobis distance cannot be assumed is proposed. Two novel learning algorithms are proposed to allow that distance function to be learnt, assuming only relativecomparisons training examples. This allows a distance function to be learnt in non-linear, discontinuous spaces, avoiding the need for labelled or quantitative information. The first algorithm builds a set of basic distance bases. The second algorithm improves generalisation capability by merging different distance bases together. It is shown how the learning algorithms produce a distance function for clustering multiple disjoint clusters belonging to the same class. Crucially, this is achieved despite the lack of any explicit form of class labelling on the training data. 2005 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.