  Dictionary learning is an effective tool for pattern recognition and
classification of time series data. Among various dictionary learning
techniques, the dynamic time warping (DTW) is commonly used for dealing with
temporal delays, scaling, transformation, and many other kinds of temporal
misalignments issues. However, the DTW suffers overfitting or information loss
due to its discrete nature in aligning time series data. To address this issue,
we propose a generalized time warping invariant dictionary learning algorithm
in this paper. Our approach features a generalized time warping operator, which
consists of linear combinations of continuous basis functions for facilitating
continuous temporal warping. The integration of the proposed operator and the
dictionary learning is formulated as an optimization problem, where the block
coordinate descent method is employed to jointly optimize warping paths,
dictionaries, and sparseness coefficients. The optimized results are then used
as hyperspace distance measures to feed classification and clustering
algorithms. The superiority of the proposed method in terms of dictionary
learning, classification, and clustering is validated through ten sets of
public datasets in comparing with various benchmark methods.
