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 relative-comparisons 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.