PCA- and SVM-Grad-CAM for Convolutional Neural Networks: Closed-form Jacobian Expression
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912539705606144 |
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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 |