On the Improvement of the Mapping Trustworthiness and Continuity of a Manifold Learning Model

Authors:
Raúl Cruz-Barbosa;Alfredo Vellido
Affiliations:
Universitat Politècnica de Catalunya, Barcelona, Spain 08034 and Universidad Tecnológica de la Mixteca, Huajuapan, México 69000;Universitat Politècnica de Catalunya, Barcelona, Spain 08034
Venue:
IDEAL '08 Proceedings of the 9th International Conference on Intelligent Data Engineering and Automated Learning
Year:
2008

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Abstract

Manifold learning methods model high-dimensional data through low-dimensional manifolds embedded in the observed data space. This simplification implies that their are prone to trustworthiness and continuity errors. Generative Topographic Mapping (GTM) is one such manifold learning method for multivariate data clustering and visualization, defined within a probabilistic framework. In the original formulation, GTM is optimized by minimization of an error that is a function of Euclidean distances, making it vulnerable to the aforementioned errors, especially for datasets of convoluted geometry. Here, we modify GTM to penalize divergences between the Euclidean distances from the data points to the model prototypes and the corresponding geodesic distances along the manifold. Several experiments with artificial data show that this strategy improves the continuity and trustworthiness of the data representation generated by the model.