The relationship between feature space and images in image classification tasks using CNN

It is known that the feature space of a Convolutional Neural Network (CNN) trained on a classification task is characterized by clusters distributed radially around the origin. In this study, to clarify the relationship between image characteristics and the norm of feature vectors, which is not directly involved in classification, we constructed a decoder to reconstruct images from these features and analyzed the feature space. Conventional decoders are trained by minimizing the Mean Squared Error (MSE) between the dataset and the reconstructed images. However, this approach does not allow for a sufficient investigation of the relationship with the norm and angle of the feature vectors. To address this, we propose a custom loss function, combining multiple loss terms, to train the decoder. Our results confirm that feature vectors with smaller norms reconstruct blurry images, whereas those with larger norms reconstruct sharp images. Furthermore, even in regions of the feature space where no training data exists, specifically on the vector of the cluster center, images were reconstructed that, despite some partial degradation, were still correctly classifiable.