  Pointwise matches between two time series are of great importance in time
series analysis, and dynamic time warping (DTW) is known to provide generally
reasonable matches. There are situations where time series alignment should be
invariant to scaling and offset in amplitude or where local regions of the
considered time series should be strongly reflected in pointwise matches. Two
different variants of DTW, affine DTW (ADTW) and regional DTW (RDTW), are
proposed to handle scaling and offset in amplitude and provide regional
emphasis respectively. Furthermore, ADTW and RDTW can be combined in two
different ways to generate alignments that incorporate advantages from both
methods, where the affine model can be applied either globally to the entire
time series or locally to each region. The proposed alignment methods
outperform DTW on specific simulated datasets, and one-nearest-neighbor
classifiers using their associated difference measures are competitive with the
difference measures associated with state-of-the-art alignment methods on real
datasets.
