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A recent novel approach to the visualisation and analysis of datasets, and one which is particularly applicable to those of a high dimension, is discussed in the context of real applica- tions. A feed-forward neural network is utilised to effect a topographic, structure-preserving, dimension-reducing trans- formation of the data, with an additional facility to incorpo- rate different degrees of associated subjective information. The properties of this transformation are illustrated on synthetic and real datasets, including the 1992 UK Research Assessment Exercise for funding in higher education. The method is compared and contrasted to established tech- niques for feature extraction, and related to topographic map- pings, the Sammon projection and the statistical field of multi- dimensional scaling. 1I NTRODUCTION The visualisation and analysis of high-dimensional data is a difficult problem and one that may be helpfully viewed in the context of feature extraction, which pro- vides a useful common ground for exploring the relation- ships between neural network and more traditional ap- proaches. There is a well established repertory of tech- niques for the derivation of appropriate feature spaces (usually of reduced dimension), with the nature and util- ity of these spaces depending significantly on the crite- ria for their extraction. Amongst such methods, there is a natural dichotomy between those features whose pur- pose is representation of the data, and those whose pur- pose is its classification (4). There is a clear parallel here with the division into unsupervised and supervised learn- ing in the neural network domain. Feature extraction is perhaps the most generic of the pat- tern processing capabilities of neural networks, and its importance at the centre of developments is two-fold. Firstly, there is a significant advantage to be gained by ac- companying dimensionality reduction, and secondly it per- mits the construction of nonlinear representations of the data which may then be exploited for information analy- sis.

Feed-forward neural networks and topographic mappings for exploratory data analysis