Neurochaos Learning for Classification using Composition of Chaotic Maps

Abstract

In the age of increasing data availability, there is a pressing need for fast and precise algorithms that can classify datasets. Traditional methods like Support Vector Machines, Random Forest, and Neural Networks are commonly used, but a novel approach known as Neurochaos Learning (NL) has demonstrated strong classification performance across various datasets by incorporating chaos theory. However, the original NL algorithm requires tuning three hyperparameters and involves extraction of multiple features, leading to significant training time. In this study, we propose a modified NL algorithm with only a single hyperparameter and a single feature, using two distinct compositions of 1D chaotic maps, the Skew Tent map with the Logistic map, and the Skew Tent map with $sin(\pi x)$, thereby drastically reducing training time while maintaining classification performance. This study also analyses the 1D chaotic properties of composition of these chaotic maps including Lyapunov Exponent and the stability of fixed points. Testing on ten datasets including Iris, Penguin, Haberman, and Bank Note Authentication, our method yields very competitive F1 scores. The composition of the Logistic Map and Skew Tent Map yields an F1 score of $0.569$ for the Haberman dataset and an impressive $0.968$ for the Penguin dataset using cosine similarity. Utilizing the composition of $sin(\pi x)$ and Skew Tent Map, the Ionosphere dataset achieves an F1 score of $0.876$. Our method's versatility is further demonstrated with the Random Forest Algorithm, achieving a perfect F1 score of $1.0$ on the Iris dataset with the Skew Tent and Logistic Map composition and the same score on the Penguin dataset using the $sin(\pi x)$ and Skew Tent Map composition. This streamlined approach meets the demand for faster and more efficient classification algorithms, offering reliable performance in data-rich environments.

Keywords

• Neurochaos learning
• Skew tent map
• Logistic map
• Tracemean
• Composition

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