Classification of ternary data using the ternary Allen–Cahn system for small datasets

Abstract

In this study, we present a classification method for ternary small data using the modified ternary Allen–Cahn (tAC) system. The governing system is the tAC equation with the fidelity term, which keeps the solution as close as possible to the given data. To solve the tAC system with the fidelity term, we apply an operator splitting method. We use an implicit-explicit finite difference method for solving the split equations. To validate the robust and superior performance of the proposed numerical algorithm, we perform the comparison tests with other widely used classifiers such as logistic regression, decision tree, support vector machine, random forest, and artificial neural network for small datasets.