An Alternating Minimization Method to Train Neural Network Models for Brain Wave Classification

Abstract

An alternating minimization (AM) method, which updates variables one-by-one while fixing the rest, is developed to train a neural network with low rank weights for brainwave classification. The training involves minimizing a non-smooth and nonconvex cross entropy loss function. The neural network model does a projection inside a hidden layer for low dimensional feature extraction. The sub-problem for each variable is shown to be either convex or piece-wise convex with a finite number of minima. The sub-problems are solved using the bisection method with bisection intervals analytically derived. The overall iterative AM method is descending and convergent, free of step size (learning parameter) in the standard gradient descent method. Experiments consist of noninvasive multiple electrode recordings and the classification of brain wave data. The AM method significantly outperforms the standard neural network model trained by the gradient descent method in classifying four thoughts for both normal and Alzheimer subjects.