Analysis of logistic map based neurons in neurochaos learning architectures for data classification

Abstract

Artificial neurons used in Artificial Neural Networks and Deep Learning architectures do not mimic the chaotic behavior of biological neurons found in the brain. Recently, a chaos based learning algorithm namely Neurochaos Learning (NL) for classification has been proposed that gives comparable performance with state-of-the-art Machine Learning methods and sometimes exceeding them, especially in the low training sample regime. NL uses 1D chaotic maps namely Generalized Lüroth Series (GLS) as neurons and the success of NL owes to the rich properties of these chaotic GLS maps. In this study, we propose for the first time, two extensions to NL: (a) 1D Logistic map neurons instead of GLS neurons, and (b) Heterogeneous Neurochaos Learning (HNL) architecture which incorporates both GLS and Logistic map neurons which is inspired by the presence of heterogeneous types of neurons in the human brain and central nervous system. We evaluate the performance of these proposed schemes on classification tasks on well known publicly available datasets such as Iris, Ionosphere, Wine, Bank Note Authentication, Haberman’s Survival, Breast Cancer Wisconsin, Statlog (Heart) and Seeds. We extract chaos-based features (ChaosFEX) from these NL architectures and feed them to SVM to further boost classification performance. Results indicate the superior performance of these proposed architecture over homogeneous NL (GLS neurons) architecture in most cases. We also investigate the relationship between the degree of chaos as measured by the Lyapunov exponent and the classification accuracies obtained by NL using logistic map (with different ‘r’ values) and heterogeneous neurons.