Abstract
We present a framework for distance-based classification of functional data. We consider the analysis of labeled spectral data by means of Generalized Matrix Relevance Learning Vector Quantization (GMLVQ) as an example. Feature vectors and prototypes are represented as functional expansions in order to take advantage of the functional nature of the data. Specifically, we employ truncated Chebyshev series in the context of several spectral datasets available in the public domain. GMLVQ is applied in the space of expansion coefficients and its performance is compared with the standard approach in original feature space, which ignores the functional nature of the data. Data smoothing by polynomial expansion alone is also considered for comparison. Computer experiments show that, beyond the reduction of dimensionality and computational effort, the method offers the potential to improve classification performance significantly.