PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Self-organizing map learning nonlinearly embedded manifolds
Timo Similä
Information Visualization Volume 4, Number 1, pp. 22-31, 2005. ISSN 1473-8716


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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:1740
Deposited By:Timo Similä
Deposited On:28 November 2005