Symmetry-Augmented Representation for Time Series

Amine Mohamed Aboussalah, Chi-Guhn Lee

Keywords: Time Series, Symmetry, Homology, Augmentation, Machine Learning, Reinforcement Learning

Abstract: We examine the hypothesis that the concept of symmetry augmentation is fundamentally linked to learning. Our focus in this study is on the augmentation of symmetry embedded in 1-dimensional time series (1D-TS). Motivated by the duality between 1D-TS and networks, we augment the symmetry by converting 1D-TS into three 2-dimensional representations: temporal correlation (GAF), transition dynamics (MTF), and recurrent events (RP). This conversion does not require a priori knowledge of the types of symmetries hidden in the 1D-TS. We then exploit the equivariance property of CNNs to learn the hidden symmetries in the augmented 2-dimensional data. We show that such conversion only increases the amount of symmetry, which may lead to more efficient learning. Specifically, we prove that a direct sum based augmentation will never decrease the amount of symmetry. We also attempt to measure the amount of symmetry in the original 1D-TS and augmented representations using the notion of persistent homology, which reveals symmetry increase after augmentation quantitatively. We present empirical studies to confirm our findings using two cases: reinforcement learning for financial portfolio management and classification with the CBF data set. Both cases demonstrate significant improvements in learning efficiency.

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One-sentence Summary: Symmetry-based augmentation improves machine learning.

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