An approach combining a new weight initialization method and constructive algorithm to configure a single Feedforward Neural Network for multi-class classification. (November 2021) - Fontes, Cristiano Hora; Embiruçu, Marcelo
Abstract: This paper presents a new method for initializing weights in a Feedforward Neural Network (FNN) with a single hidden layer combined with a constructive approach to define the number of hidden units associated with the best classification performance. The strategy consists of defining an initial number of hidden units according to the classification problem, the linearization of the whole network around an equilibrium point and the determination of the initial weights and bias through the maximum approximation of the linearized model to the Optimal Linear Classifier (OLC) whose solution can be obtained analytically. The constructive algorithm comprises a gradual increase in the number of hidden units in such a way that at each training only the weights and bias associated with the new hidden units are initiated randomly while the weights and bias obtained from previous training are used as initial guesses. Additionally, the constructive algorithm seeks to ensure that the loss function of the trained networks decreases with the successive additions of hidden units. The proposed approach (Weight Initialization based on the Linearization of the Whole Neural Network combined with a new Constructive Algorithm, WILWNN-CA) is applied to synthetic and real datasets widely used as benchmark for multi-class classification problems. The comparison with conventional random weight initialization and other approaches involving different network topologies (and initialization strategies) shows that the proposed method is efficient and capable of providing success rates (correct classification rates) higher or similar to those achieved with existing methods. Highlights: Novel approach for initializing weights in a Single Feedforward Neural Network. Novel constructive algorithm to define the number of hidden units. The method performed better or similarly to other consolidated methods. Constructive approach ensures reduction of the loss function. The weight Initialization is based on the linearization of the NN as a whole.