Functional Principal Component Learning Using Oja's Method and Sobolev Norms

Authors:
Thomas Villmann;Barbara Hammer
Affiliations:
University of Applied Sciences Mittweida, Dept. of Mathematics, Mittweida, Germany 09648;Inst. of Computer Science, Clausthal University of Technology, Clausthal, Germany 38678
Venue:
WSOM '09 Proceedings of the 7th International Workshop on Advances in Self-Organizing Maps
Year:
2009

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Abstract

In this paper we present a method for functional principal component analysis based on the Oja-learning and neural gas vector quantizer. However, instead of the Euclidean inner product the Sobolev counterpart is applied, which takes the derivatives of the functional data into account and, therefore, uses information contained in the functional shape of the data into account. We investigate the theoretical foundations of the algorithm for convergence and stability and give exemplary applications.