Functional Perceptron using Multi-dimensional Activation Functions

Abstract

We propose a new perceptron, called functional perceptron, which consists of a multi-dimensional activation function capable of learning a specific function. The functional perceptron does not use the traditional activation functions such as Sigmoid and ReLU. Instead, the proposed perceptron trains a function in a multi-dimensional space to accomplish a specific functionality and uses it as the learning task specific activation function. To realize this perceptron, we teach a comparison functionality to a multi-dimensional function by training two comparable inputs and producing a value of similarity as output. In order to show the efficacy of the functional perceptron, we apply the proposed perceptron to the XOR problem, the IRIS classification problem and an indoor positioning problem based on multi-signal fingerprints. Extensive experiments show that the proposed perceptron achieves about 96% accuracy in the IRIS classification and shows 1.737m accuracy in indoor positioning problem.