Grad-CAM for Visualizing Attention Regions of PCA and SVM Layers in Convolutional Neural Networks

Convolutional Neural Networks (CNNs) are an effective approach for classification tasks, particularly when the training dataset is large. Although CNNs have long been considered a black-box classification method, they can be used as a white-box method through visualization techniques such as Grad-CAM. When the training samples are limited, incorporating a Principal Component Analysis (PCA) layer and/or a Support Vector Machine (SVM) classifier into a CNN can effectively improve the classification performance. However, a conventional Grad-CAM cannot be directly applied to PCA and/or SVM layers. Generating attention regions for PCA and/or SVM layers in CNNs is important to facilitate the development of white-box methods. Therefore, we propose ``PCA-Grad-CAM'', a method for visualizing attention regions in PCA feature vectors, and ``SVM-Grad-CAM'', a method for visualizing attention regions in an SVM classifier layer. Solving a closed-form Jacobian problem comprising partial derivatives from the last convolutional layer to the PCA and/or SVM layers is necessary to complete the proposed methods analytically. In this paper, we present the exact closed-form Jacobian and visualization results of the proposed methods applied to several major datasets. In addition, the insertion and deletion metrics, which are major evaluation metrics in explainable AI, were applied to PCA- and SVM-Grad-CAM. The results suggest that the proposed method can successfully visualize the attention regions of PCA and SVM.