Learning Wormholes for Sparsely Labelled Clustering

Distance functions are an important component in many learning applications. However, the correct function is context dependent, therefore it is advantageous to learn a distance function using available training data. Many existing distance functions is the requirement for data to exist in a space of constant dimensionality and not possible to be directly used on symbolic data. To address these problems, this paper introduces an alternative learnable distance function, based on multi-kernel distance bases or wormholes that connects spaces belonging to similar examples that were originally far away close together. This work only assumes the availability of a set data in the form of relative comparisons, avoiding the need for having labelled or quantitative information. To learn the distance function, two algorithms were proposed: 1) Building a set of basic wormhole bases using a Boosting-inspired algorithm. 2) Merging different distance bases together for better generalisation. The learning algorithms were then shown to successfully extract suitable distance functions in various clustering problems, ranging from synthetic 2D data to symbolic representations of unlabelled images.