Time series classification using Hankel matrix based dissimilarity measures in Learning Vector Quantization

Lars Holdijk, Mohammad Mohammadi and Michael Biehl

Abstract

Time-series classification is an interesting and challenging sub-domain of classi-fication problems. In distance based classification algorithms, the informationhidden in the ordering of the time-series and the possibility of misalignment re-quire the use of specialized dissimilarity measures. In this thesis we look at threesuch measures, all of which are based on Hankel matrices and the assumptionthat Hankel matrices with the same subspace originate from the same LTI-seriesand consequently from the same class. In previous work all three dissimilaritymeasures have shown competitive results when combined with k-Nearest Neigh-bours. In our work we combine two of the three dissimilarity measure withGeneralized Learning Vector Quantization (GLVQ) using a rewriting of deriva-tives presented in earlier work. The results presented show promise for thedissimilarity measures to be applied in GLVQ.