A New Convolution for a Deep Learning using Two-dimensional Geometric Distance

Abstract

For deep learning classification, a new convolution called the Geometric Distance, which numerically evaluates the degree of likeness between the input image and the filter on the convolution layer is proposed. Traditionally, the convolution known as the cosine similarity has been used widely to measure likeness. Traditional method does not perform well in the presence of noise or pattern distortions. In this paper, a new mathematical model for a similarity is proposed which overcomes these limitations of the earlier model, and a new algorithm based on a one-to-many point mapping is proposed to realize the mathematical model. In the GD, when a “difference” occurs between peaks of the input image and the filter with a “wobble” due to noise, the “wobble” is absorbed and the distance metric increases monotonically according to the increase of the “difference”. We performed numerical experiments and confirmed the effectiveness of the GD.