Generalized Gradient Learning on Time Series

Abstract

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 Euclidean spaces to time series spaces. Necessary conditions are sketched under which generalized gradient learning on time series is consistent. 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 pattern recognition on time series.