Convolutional hyper basis function neural network and its online learning in the image recognition task
Yevgeniy V. Bodyanskiy, Anastasiia Deineko, Oleksandr Hontsa, Oleksandr Zeleniy · 2021
In the article hyper basic function neural network (HBFN) in convolutional neural networks instead of fully connected perceptron layers, which solve the problem of classification is proposed. HBFNs are generalization of traditional radial-basic function networks, which like multilayer perceptrons are also universal approximators. The peculiarity of hyper basic function neural networks is that their receptive fields are hyperellipsoids with arbitrary orientation of the axes in the feature space. It is assumed that, along with the synaptic weights, receptive field parameters are adjusted: their centers and matrices of the axis orientation. This approach allows to reduce the total number of synaptic weights, and accordingly the number of R-neurons (activation functions) of the network. Using multidimensional V. Epanechnikov’s functions with a hyperellipsoidal receptive field that can be adjusted during the learning process as activation functions permit to accelerate the learning process of investigated network. It should be noted that applying kernel functions in convolutional neural networks permits to avoid the undesirable effect of "exploiding gradient", which often occurs in fully connected layers. The computational experiment results on standard data sets confirm the effectiveness of the proposed approach and, first of all, the high learning speed.