Using the Choquet Integral in the Pooling Layer in Deep Learning Networks

Abstract

This paper aims to introduce the proposal of replacing the usual pooling functions by the Choquet integral in Deep Learning Networks. The Choquet integral is an aggregation function studied and applied in several areas, as, e.g., in classification problems. Its importance is related to the fact that it considers the relationship between the data to be aggregated by means of a fuzzy measure, unlike other aggregation functions such as the arithmetic mean and the maximum. The idea of this paper is to use the Choquet integral to reduce the size of an image, obtaining an abstract form of representation, that is, reducing the perception of the network corresponding to small changes in the image. The use of this aggregation function in the place of the max-pooling and mean-pooling functions of Convolutional Neural Networks presented promising results. This assertion is based on the Normalized Cross-Correlation and Structural Content quality measures applied to the original images and resulting images. It is important to emphasize that this preliminary study of Choquet integral as a pool layer has not yet been implemented on Convolutional Neural Networks until the present moment.