Using Self-Organising Mappings to Learn the Structure of Data Manifolds

Abstract

In this paper it is shown how to map a data manifold into a simpler form by progressively discarding small degrees of freedom. This is the key to self-organising data fusion, where the raw data is embedded in a very high-dimensional space (e.g. the pixel values of one or more images), and the requirement is to isolate the important degrees of freedom which lie on a low-dimensional manifold. A useful advantage of the approach used in this paper is that the computations are arranged as a feed-forward processing chain, where all the details of the processing in each stage of the chain are learnt by self-organisation. This approach is demonstrated using hierarchically correlated data, which causes the processing chain to split the data into separate processing channels, and then to progressively merge these channels wherever they are correlated with each other. This is the key to self-organising data fusion.