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Enhancing classification accuracy through chaos

Panos Stinis

Abstract

We propose a novel approach which exploits chaos to enhance classification accuracy. Specifically, the available data that need to be classified are treated as vectors that are first lifted into a higher-dimensional space and then used as initial conditions for the evolution of a chaotic dynamical system for a prescribed temporal interval. The evolved state of the dynamical system is then fed to a trainable softmax classifier which outputs the probabilities of the various classes. As proof-of-concept, we use samples of randomly perturbed orthogonal vectors of moderate dimension (2 to 20), with a corresponding number of classes equal to the vector dimension, and show how our approach can both significantly accelerate the training process and improve the classification accuracy compared to a standard softmax classifier which operates on the original vectors, as well as a softmax classifier which only lifts the vectors to a higher-dimensional space without evolving them. We also provide an explanation for the improved performance of the chaos-enhanced classifier.

Enhancing classification accuracy through chaos

Abstract

We propose a novel approach which exploits chaos to enhance classification accuracy. Specifically, the available data that need to be classified are treated as vectors that are first lifted into a higher-dimensional space and then used as initial conditions for the evolution of a chaotic dynamical system for a prescribed temporal interval. The evolved state of the dynamical system is then fed to a trainable softmax classifier which outputs the probabilities of the various classes. As proof-of-concept, we use samples of randomly perturbed orthogonal vectors of moderate dimension (2 to 20), with a corresponding number of classes equal to the vector dimension, and show how our approach can both significantly accelerate the training process and improve the classification accuracy compared to a standard softmax classifier which operates on the original vectors, as well as a softmax classifier which only lifts the vectors to a higher-dimensional space without evolving them. We also provide an explanation for the improved performance of the chaos-enhanced classifier.
Paper Structure (8 sections, 14 equations, 8 figures, 1 table, 3 algorithms)

This paper contains 8 sections, 14 equations, 8 figures, 1 table, 3 algorithms.

Table of Contents

  1. Chaos-enhanced classification
  2. Results
  3. Numerical experiments setup
  4. Observations from results
  5. Reason for improvement over the baseline model
  6. Robustness
  7. Complexity
  8. Discussion and future work

Figures (8)

  • Figure 1: $m=2.$ Comparison of the baseline model, the lifting-enhanced model, and the lifting- and chaos-enhanced model (with the optimal lifting dimension). (a) Evolution of loss (cross-entropy) with epochs. (b) Evolution of accuracy with epochs.
  • Figure 2: $m=10.$ Comparison of the baseline model, the lifting-enhanced model, and the lifting- and chaos-enhanced model (with the optimal lifting dimension). (a) Evolution of loss (cross-entropy) with epochs. (b) Evolution of accuracy with epochs.
  • Figure 3: $m=20.$ Comparison of the baseline model, the lifting-enhanced model, and the lifting- and chaos-enhanced model (with the optimal lifting dimension). (a) Evolution of loss (cross-entropy) with epochs. (b) Evolution of accuracy with epochs.
  • Figure 4: $m=20.$ Evolution of training and testing accuracy with the lifting dimension for the lifting- and chaos-enhanced model for two different values of the Adam optimizer learning rate $\eta.$
  • Figure 5: $m=20.$ (a) Evolution of training and testing accuracy with the lifting dimension for the lifting- and chaos-enhanced model for two different values of the chaotic evolution temporal interval $T.$ (b) Evolution of training and testing accuracy with epochs for the optimal lifting dimension of the lifting- and chaos-enhanced model for two different values of the chaotic evolution temporal interval $T.$
  • ...and 3 more figures