Sobolev Metrics for Learning of Functional Data - Mathematical and Theoretical Aspects
نویسنده
چکیده
We study the utilization of functional metrics for learning of functional data. In particular we investigate the metrics based on the Sobelev metric which can be related top a respective inner product. This offers capabilities for adequate data processing of functional data taking into acccount the dependencies within the functional data vectors. We outline these possibilities and give the mathematical derivations as well as the theoretical basis for two basic applications: functional principal component analysis based on Oja’s algorithm and prototype based vector quantization. Machine Learning Reports,Research group on Computational Intelligence, http://www.uni-leipzig.de/̃compint Sobolev Metrics for Learning of Functional Data Mathematical and Theoretical Aspects
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