Neurons With Paraboloid Decision Boundaries for Improved Neural Network Classification Performance.

Tsapanos, Nikolaos; Tefas, Anastasios; Nikolaidis, Nikolaos; Pitas, Ioannis · IEEE Trans Neural Netw Learn Syst · 2019

basic_science · Level V

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Abstract

In mathematical terms, an artificial neuron computes the inner product of a d -dimensional input vector x with its weight vector w , compares it with a bias value w<sub>0</sub> and fires based on the result of this comparison. Therefore, its decision boundary is given by the equation w<sup>T</sup>x+w<sub>0</sub>=0 . In this paper, we propose replacing the linear hyperplane decision boundary of a neuron with a curved, paraboloid decision boundary. Thus, the decision boundary of the proposed paraboloid neuron is given by the equation (h<sup>T</sup>x+h<sub>0</sub>)<sup>2</sup>-||x-p||<sub>2</sub><sup>2</sup>=0 , where h and h<sub>0</sub> denote the parameters of the directrix and p denotes the coordinates of the focus. Such paraboloid neural networks are proven to have superior recognition accuracy in a number of applications.