Comparative analysis of CNNMVN and MLMVN as frequency domain CNN convolutions

Each convolutional layer in any convolutional neural network produces a feature map containing the most important information, which a network needs to recognize respective images. To further improve these neural networks and better understand their capabilities, it is essential to discover, which features are actually extracted and how the images to be recognized are transformed by convolutions resulted from the learning process. This paper presents a comparative analysis of convolutions obtained via two complex-valued neural networks based on multi-valued neurons. The first network is a convolutional neural network based on multi-valued neurons (CNNMVN) which has a traditional convolutional neural network topology except of that it employs complex-valued convolutional kernels in its convolutional part and multi-valued neurons in its fully connected part. The second one is the multi-valued neural network based on multi-valued neurons (MLMVN) which is a fully connected multilayer neural network employed as a convolutional network in the frequency domain. Considering that both neural networks are complex-valued and the obtained filters operate in the complex domain, the conducted research indicates that the kernels of both networks produce filters similar to existing digital image processing filters. The analysis of CNNMVN kernels revealed that they implement unsharp masking filters and edge detection filters for identifying shapes in images, while the MLMVN kernels enhance specific frequency sub-bands. The latter means that the respective filters are mostly not similar to the ones known as unsharp masking or sharpening filters. Thus, the kernels of both convolutional networks contribute to improving image recognition performance in their own ways.