Generalized Gradient Learning on Time Series under Elastic Transformations

TL;DR

This paper extends gradient-based learning algorithms to time series data using elastic functions under dynamic time warping, enabling the application of linear classifiers to time series for improved pattern recognition.

Contribution

It introduces elastic functions for gradient learning on time series, providing conditions for consistency and extending classifiers to handle elastic distance measures.

Findings

Extended four linear classifiers to time series with dynamic time warping.

Achieved promising results on benchmark datasets.

Potential to enhance time series pattern recognition methods.

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 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.