Adaptive basis functions for prototype-based classification of functional data

We present a framework for distance-based classification of functional data. We consider the analysis of labeled spectral data and time series by means of generalized matrix relevance learning vector quantization (GMLVQ) as an example. To take advantage of the functional nature, a functional expansion of the input data is considered. Instead of using a predefined set of basis functions for the expansion, a more flexible scheme of an adaptive functional basis is employed. GMLVQ is applied on the resulting functional parameters to solve the classification task. For comparison of the classification, a GMLVQ system is also applied to the raw input data, as well as on data expanded by a different predefined functional basis. Computer experiments show that the methods offer potential to improve classification performance significantly. Furthermore, the analysis of the adapted set of basis functions give further insights into the data structure and yields an option for a drastic reduction of dimensionality