Perpendicular Bisector Constraint on Artificial Neural Network

A perpendicular bisector solution of perceptron and a perpendicular bisector constraint on artificial neural network(ANN) are studied in this paper. As is known, both Preceptron and multilayer ANN based on back-propagation algorithm suffer from similar issues of solution instability. The classical SVM can solve the solution instability of perceptron, yet in low efficiency. We use perpendicular bisector of two center vectors, which are composed of weighted positive and negative sample points respectively, as the solution of the perceptron(called PBP). The solution of PBP is stable and more efficient than SVM because of the uniqueness and stability of perpendicular bisector. Then we apply the perpendicular bisector as a constraint(PBC) for multilayer ANN. The solution of constrained ANN should near the perpendicular bisector, thus we can get a more stable solution compared with the one does not have the constraint. The main contributions are: 1. Put forward PBP as a new solver for perceptron with solution stability and less running time than SVM. For example, on data sets Heart Scale and Abalone, training speeds of PBP are at least 10 times faster than SVM. 2. The ANN with PBC improves the solution stability. For an instance, on the highly linear inseparable dataset Abalone, ANN with PBC keeps good convergence property while the one without PBC always oscillates.