Normalized determinant pooling layer in CNNs for multi-label classification

Convolutional neural networks (CNNs) are a widely researched neural network architecture that has demonstrated exemplary performance in image processing tasks and applications compared to other popular deep learning and machine learning methods resulting in state-of-the-art performance in many image processing tasks such as image classification and segmentation. CNNs operate on the principle of automated learning of filters or kernels in contrast with hand-crafted digital filters to extrapolate features from images effectively. This paper aims to investigate whether a matrix's determinant can be used to preserve information in CNN convolutional layers. Geometrically the absolute value of the determinant is defined as a scaling factor of the linear transformation resulting from matrix multiplication. When an image's size is reduced into a feature space through a convolutional layer of a CNN, some information is lost. The intuition is that the scaling factor that results from the determinant of the pooling layer matrix can enhance the feature space introducing scaling as a piece of information in the feature space as well as lost relations between adjacent pixels.