PCA- and SVM-Grad-CAM for Convolutional Neural Networks: Closed-form Jacobian Expression

Fuente: arXiv
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Autore principale: Omae, Yuto
Natura: Preprint
Pubblicazione: 2025
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author Omae, Yuto
author_facet Omae, Yuto
contents 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 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 classification performance. However, traditional Grad-CAM cannot be directly applied to PCA and/or SVM layers. It is important to generate attention regions for PCA and/or SVM layers in CNNs 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. To complete our methods analytically, it is necessary to solve the closed-form Jacobian consisting of partial derivatives from the last convolutional layer to the PCA and/or SVM layers. In this paper, we present the exact closed-form Jacobian and the visualization results of our methods applied to several major datasets.
format Preprint
id arxiv_https___arxiv_org_abs_2508_11880
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle PCA- and SVM-Grad-CAM for Convolutional Neural Networks: Closed-form Jacobian Expression
Omae, Yuto
Machine Learning
I.2.0; I.5.0
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 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 classification performance. However, traditional Grad-CAM cannot be directly applied to PCA and/or SVM layers. It is important to generate attention regions for PCA and/or SVM layers in CNNs 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. To complete our methods analytically, it is necessary to solve the closed-form Jacobian consisting of partial derivatives from the last convolutional layer to the PCA and/or SVM layers. In this paper, we present the exact closed-form Jacobian and the visualization results of our methods applied to several major datasets.
title PCA- and SVM-Grad-CAM for Convolutional Neural Networks: Closed-form Jacobian Expression
topic Machine Learning
I.2.0; I.5.0
url https://arxiv.org/abs/2508.11880