Neurons With Paraboloid Decision Boundaries for Improved Neural Network Classification Performance
Nikolaos Tsapanos, Anastasios Tefas, Nikos Nikolaidis, Ioannis Pitas · IEEE Transactions on Neural Networks and Learning Systems · 2018
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 w0and fires based on the result of this comparison. Therefore, its decision boundary is given by the equation wTx + w0= 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 (hTx + h0)2- ||x - p||22= 0, where h and h0denote 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.