Complex-valued online classifier

Abstract

In order to improve the identification accuracy of the online classifier in binary classification problems, we here propose complex-valued online machine learning algorithms. The Perceptron is commonly used in simple form of online machine learning. First, we extended it to the complex domain. The real-valued inputs are projected to points on the first quarter of unit circle on the complex plane. The real and imaginary parts of inputs are fed separately to two different Perceptrons. In each Perceptron, a real-valued weight vector is applied to the input vector. Outputs of two Perceptrons are plotted on a complex plane. The upper half of the plane is considered as the class 1 and the lower half as the class −1. If misclassified, the weight vectors are modified. We here term it the complex-valued Perceptron (CP). The results on some benchmarks showed that the identification accuracy of the online classifier with the CP was higher than that with the conventional Perceptron. Secondly, we adopted the Passive-Aggressive (PA) algorithm, as well as PA-I and PA-II with noise immunity. We term them CPA, CPA-I and CPA-II, respectively. For the benchmarks, the identification accuracies of the online classifier with these PA algorithms was higher than those with the conventional PA algorithms. Since the CP used here is simple in principle, complex-valued online classifiers, CP, CPA, CPA-I and CPA-II, can be applied to various practical problems.