Generalized Gradient Learning on Time Series under Elastic Transformations
This addresses the challenge of using standard machine learning algorithms on time series data for researchers in statistical pattern recognition, though it appears incremental as it extends existing linear classifiers.
The paper tackles the problem of applying gradient-based learning to time series under dynamic time warping, which is not straightforward due to the non-vector representation of time series. It introduces elastic functions to extend functions to matrix spaces and shows that generalized gradient learning is consistent, with results on benchmark datasets indicating potential to complement state-of-the-art methods.
The majority of machine learning algorithms assumes that objects are represented as vectors. But often the objects we want to learn on are more naturally represented by other data structures such as sequences and time series. For these representations many standard learning algorithms are unavailable. We generalize gradient-based learning algorithms to time series under dynamic time warping. To this end, we introduce elastic functions, which extend functions on time series to matrix spaces. Necessary conditions are presented under which generalized gradient learning on time series is consistent. We indicate how results carry over to arbitrary elastic distance functions and to sequences consisting of symbolic elements. Specifically, four linear classifiers are extended to time series under dynamic time warping and applied to benchmark datasets. Results indicate that generalized gradient learning via elastic functions have the potential to complement the state-of-the-art in statistical pattern recognition on time series.