Supplementary Material for ' Causality Preserving Chaotic Transformation and Classification using Neurochaos Learning '

This is the supplementary information pertaining to the main manuscript. In this supplementary material, we provide the comparative performance of Neurochaos Learning with Deep Neural Network, 1DConvolutional Neural Network (1D CNN), and Long Short term Memory (LSTM) for evaluation of cause-effect classification of timeseries data generated from coupled chaotic master-slave system and autoregressive (AR) processes. We also check whether each of these architectures are able to preserve cause-effect relationship between the corresponding features extracted from the original cause and effect time series. To evaluate the efficacy of Neurochaos Learning (NL: ChaosNet) and deep learning algorithms for the classification of cause-effect, we used simulated datasets from (a) coupled autoregressive (AR) processes, and (b) coupled 1D chaotic skew tent-maps in master-slave configuration. The governing equations for the coupled AR processes are the following: M(t)=a1M(t 1)+γr(t), (1) S(t)=a2S(t 1)+ηM(t 1)+γr(t), (2) where M(t) and S(t) are the independent and the dependent (or the cause and effect) time series respectively; a1 = 0.8, a2 = 0.9, the noise intensity γ = 0.03 and r(t) is independent and identically distributed additive Gaussian noise drawn from a standard normal distribution.