¹Neural Networks Research Centre, Helsinki University of Technology, PO Box 5400, FI-02015 HUT, Finland

Correspondence: Timo Similä, Neural Networks Research Centre, Helsinki University of Technology. E-mail: timo.simila@hut.fi

Received 20 August 2004; Revised 19 January 2005; Accepted 24 January 2005; Published online 3 March 2005.

Abstract

One of the main tasks in exploratory data analysis is to create an appropriate representation for complex data. In this paper, the problem of creating a representation for observations lying on a low-dimensional manifold embedded in high-dimensional coordinates is considered. We propose a modification of the Self-organizing map (SOM) algorithm that is able to learn the manifold structure in the high-dimensional observation coordinates. Any manifold learning algorithm may be incorporated to the proposed training strategy to guide the map onto the manifold surface instead of becoming trapped in local minima. In this paper, the Locally linear embedding algorithm is adopted. We use the proposed method successfully on several data sets with manifold geometry including an illustrative example of a surface as well as image data. We also show with other experiments that the advantage of the method over the basic SOM is restricted to this specific type of data.