Circular Bayesian classifiers using wrapped Cauchy distributions.

Capturing the dependences among circular variables within supervised classification models is a challenging task. In this paper, we propose four different supervised Bayesian classification algorithms where the predictor variables follow all circular wrapped Cauchy distributions. For this purpose, we introduce four wrapped Cauchy classifiers. The bivariate wrapped Cauchy distribution is the only bivariate circular distribution whose marginals and conditionals are also wrapped Cauchy distributions, a property that makes it possible to define these models easily. Furthermore, the wrapped Cauchy tree-augmented naive Bayes classifier requires the definition of a conditional circular mutual information measure between variables that follow wrapped Cauchy distributions. Synthetic data is used to illustrate, compare and evaluate the classification algorithms (including a comparison with the Gaussian TAN classifier, decision tree, random forest, multinomial logistic regression, support vector machine and simple neural network), leading to satisfactory predictive results. We also use a real neuromorphological dataset obtained from juvenile rat somatosensory cortex cells, where we measure the bifurcation angles of the dendritic basal arbors. • An adaptation of Bayesian network classifiers to circular domain is proposed. • The classifiers are suitable for wrapped Cauchy distributions. • A conditional circular mutual information for wrapped Cauchy is presented • Wrapped Cauchy classifiers outperform linear Bayesian network classifiers. • Neuron layer identification is appropriate for wrapped Cauchy classifiers. [ABSTRACT FROM AUTHOR]