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

Yuto Omae; Hirotaka Takahashi

cs.LGAug 16, 2025

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

Authors: Yuto Omae, Hirotaka Takahashi

Organizations: Nihon University

Abstract

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.

Figures & tables

Figure 1: Overview of the existing method (conventional-Grad-CAM [ 8 ] ) and the proposed methods (PCA- and SVM-Grad-CAM).

Method [ref. no.]	Year	Citation*	Gradient?	Applied cases (detection or prediction target)
CAM [ 22 ] (Pioneer)	2015	13,409	No	Food localization [ 23 ] , Diabetic retinopathy [ 24 ] , Building defects [ 25 ]
Grad-CAM [ 8 ]	2016	31,032	Yes	Fall armyworm [ 9 ] , Microscopic algae [ 10 ] , Gas–liquid jet [ 11 ]
Grad-CAM++ [ 26 ]	2018	3,748	Yes	Lung Cancer [ 27 ] , Brain tumor [ 28 ] , Malignant skin diseases [ 29 ]
XGrad-CAM [ 30 ]	2020	397	Yes	SARS-COVID [ 31 ] , Brain tumor [ 32 ] , Specific emitter identification [ 33 ]
Relevance-CAM [ 34 ]	2021	101	Yes	Compression fracture [ 35 ] , Small bowel [ 36 ] , Cities identification [ 37 ]
HiRes-CAM [ 38 ]	2020	174	Yes	Endoscopic image [ 39 ] , Insect pests [ 40 ] , Ship detection [ 41 ]

Table 1: CAM family comprising various approaches.

Figure 2: PCA-Grad-CAM visualizations generated from a CNN trained on the CIFAR-10 dataset, as described in Section 6 .

Figure 3: Visualized Jacobian computed from a CNN trained on the Dog vs. Cat dataset, as described in Section 6 . The red and blue paths represent positive and negative gradients, respectively. The width of each path represents the absolute value of the gradient.

Figure 4: Effect of the distance between the PCA feature vector $\bm{p}$ and the $i$ -th support vector $\bm{p}_{i}$ , $\|\bm{p}_{i}-\bm{p}\|_{2}$ , on $E(\|\bm{p}_{i}-\bm{p}\|_{2})$ . $E(\|\bm{p}_{i}-\bm{p}\|_{2})$ represents the degree of effect on the SVM-Grad-CAM $\bm{S}$ and is defined in Equation 27 . From Theorem 2 , the distance that maximizes $E(\|\bm{p}_{i}-\bm{p}\|_{2})$ is $\|\bm{p}_{i}-\bm{p}\|_{2}=(2\gamma)^{-1/2}$ , and the $\bigcirc$ in the figure represents these locations.

Figure 5: Relationship between epoch and validation accuracies. A star marker $\bigstar$ represents an optimal epoch.

	Classes /	Macro F1 score (training/test)
Dataset	$N_{\mathrm{train}}$ / $N_{\mathrm{test}}$	CNN	Lin-SVM	RBF-SVM
MNIST [ 68 ]	10/60,000/10,000	.993/.991	.986/.980	.997/.989
F-MNIST [ 69 ]	10/60,000/10,000	.925/.903	.922/.897	.988/.943
B-MNIST [ 70 ]	8/11,959/3,421	.944/.877	.925/.873	.984/.909
CIFAR-10 [ 66 ]	10/50,000/10,000	.899/.767	.789/.735	.892/.794
Chest X-Ray [ 71 ]	3/5,144/1,288	.966/.956	.998/.975	.998/.975

Table 3: Dataset informations and estimation performances.

Figure 6: Contribution ratios of the eigenvectors $\bm{v}_{1}$ , $\bm{v}_{2}$ , and $\bm{v}_{3}$ . Here, $\lambda_{b}^{\prime}$ represents the normalized eigenvalues, defined as $\lambda_{b}^{\prime}=100\times\lambda_{b}/\sum_{b}\lambda_{b}$ .

Panel of Figure 7 — Figure 7: Three-dimensional PCA feature spaces comprising $\bm{p}=\begin{bmatrix}p_{1}\ p_{2}\ p_{3}\end{bmatrix}^{\top}$ . The meanings of the labels from 0 to 9 are described in the Appendix B . The top and bottom figures are scatter plots corresponding to the training and test data, respectively.

Figure 8: Conventional-Grad-CAM, PCA-Grad-CAM, and SVM-Grad-CAM (MNIST [ 68 ] , Fashion-MNIST [ 69 ] , Blood-MNIST [ 70 ] , and CIFAR-10 [ 66 ] ).

Figure 9: Conventional-Grad-CAM, PCA-Grad-CAM, and SVM-Grad-CAM (Chest X-Ray [ 71 ] and Dog vs. Cat [ 72 ] ).

Dataset	Method	Ins.	Rand. Ins.	Adj. $p$
MNIST	SVM-Grad-CAM (Linear)	.676	.496	**
[ 68 ]	SVM-Grad-CAM (RBF)	.518	.320	**
	PCA-Grad-CAM $\oplus$	.754	.441	**
	PCA-Grad-CAM $\ominus$	–	–	–
Fashion-	SVM-Grad-CAM (Linear)	.668	.546	**
MNIST	SVM-Grad-CAM (RBF)	.667	.588	**

Table 4: Medians of insertion AUC (Ins.) and random insertion AUC (Rand. Ins.) by test datasets. Bold values indicate statistically superior performance. Higher is better. For the meaning of “–”, see Subsection 7.1 .

Dataset	Method	Del.	Rand. Del.	Adj. $p$
MNIST	SVM-Grad-CAM (Linear)	.416	.532	**
[ 68 ]	SVM-Grad-CAM (RBF)	.316	.353	**
	PCA-Grad-CAM $\oplus$	.299	.488	**
	PCA-Grad-CAM $\ominus$	–	–	–
Fashion-	SVM-Grad-CAM (Linear)	.525	.555	**
MNIST	SVM-Grad-CAM (RBF)	.558	.599	**

Table 5: Medians of deletion AUC (Del.) and random deletion AUC (Rand. Del.) by test datasets. Bold values indicate statistically superior performance. Lower is better. For the meaning of “–”, see Subsection 7.1 .

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Class Activation Mapping in Explainable Computer Vision: A Method-Centered Review of CNN, Transformer, and Foundation-Model-Era Visual Explanations

AmirHossein Eshghi, Hamid Saadatfar, Seyyed Ali Hoseini, AmirMohsen Eshghi+1

Department of Computer Engineering, University of Birjand, Iran · Department of Applied Mathematics and Computer Science Visual Computing, Technical University of Denmark, Denmark

Gradient-Weighted Class Activation Mapping Class Activation Mapping Explainability Explainable Artificial Intelligence Explainable AI Methods Convolutional Neural Networks+1

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Class activation mapping (CAM) is one of the most widely used visual explanation families in explainable artificial intelligence. Its purpose is intuitive: it converts internal model evidence into a heatmap that highlights the image regions, convolutional channels, tokens, or patches that support a target class or concept. Since the first CAM formulation in 2016, the field has moved far beyond global-average-pooled CNN classifiers. CAM-style methods now include gradient-based post-hoc explanations, gradient-free score and ablation methods, high-resolution upscaling, weakly supervised localization and segmentation, transformer token attribution, causal and debiasing methods, and foundation-model-era approaches that use CLIP, DINO, SAM, or feature-distribution comparisons. This review synthesizes a strict corpus of 57 method-centered papers published from 2016 onward. The paper develops a taxonomy that separates methods by attribution mechanism, architectural dependence, and evaluation objective. It then reviews gradient-based CAMs, recent and hybrid CAM-style methods, and model-based or architecture-aware methods. Across the corpus, the main trend is clear: the field is shifting from explaining one class score in one low-resolution CNN layer toward comparative, multi-layer, probabilistic, token-aware, and foundation-model-aware explanations. At the same time, evaluation remains fragmented. Faithfulness, localization, robustness, computational cost, and human trust are often measured with different protocols. The review therefore emphasizes not only what each method contributes, but also which gap it leaves open and which later methods attempt to close that gap.

Abstract

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