Improved data visualisation through nonlinear dissimilarity modelling

- Elastic MDS is extended to learn observation dissimilarities from a dictionary.
- The dictionary of dissimilarities is nonlinearly combined with an RBF network.
- Four standard datasets show the improvement over standard Elastic MDS.

Inherent to state-of-the-art dimension reduction algorithms is the assumption that global distances between observations are Euclidean, despite the potential for altogether non-Euclidean data manifolds. We demonstrate that a non-Euclidean manifold chart can be approximated by implementing a universal approximator over a dictionary of dissimilarity measures, building on recent developments in the field. This approach is transferable across domains such that observations can be vectors, distributions, graphs and time series for instance. Our novel dissimilarity learning method is illustrated with four standard visualisation datasets showing the benefits over the linear dissimilarity learning approach.