Warped-Linear Models for Time Series Classification

TL;DR

This paper introduces warped-linear models for time series classification that are invariant to time warping, providing a theoretical link to polyhedral classifiers and demonstrating improved performance over traditional methods.

Contribution

It presents a novel class of time-warp invariant models, establishes their theoretical equivalence to polyhedral classifiers, and offers solutions to key learning challenges.

Findings

Warped-linear models are more efficient than nearest-neighbor methods.

They achieve better trade-offs between accuracy and computation time.

Empirical results validate their effectiveness in time series classification.

Abstract

This article proposes and studies warped-linear models for time series classification. The proposed models are time-warp invariant analogues of linear models. Their construction is in line with time series averaging and extensions of k-means and learning vector quantization to dynamic time warping (DTW) spaces. The main theoretical result is that warped-linear models correspond to polyhedral classifiers in Euclidean spaces. This result simplifies the analysis of time-warp invariant models by reducing to max-linear functions. We exploit this relationship and derive solutions to the label-dependency problem and the problem of learning warped-linear models. Empirical results on time series classification suggest that warped-linear functions better trade solution quality against computation time than nearest-neighbor and prototype-based methods.