Chapter

Advances in Self-Organizing Maps

Volume 5629 of the series Lecture Notes in Computer Science pp 325-333

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

  • Thomas VillmannAffiliated withUniversity of Applied Sciences Mittweida, Dept. of Mathematics
  • , Barbara HammerAffiliated withInst. of Computer Science, Clausthal University of Technology

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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.

Keywords

functional PCA neural gas Sobolev-norms