# Seg-Eigen-CAM: Eigen-Value-Based Visual Explanations for Semantic Segmentation Models
## 1 Introduction
Despite significant advances in existing methods, several notable limitations remain. Gradient-based methods (e.g., Seg-Grad-CAM or Seg-XRes-CAM) are often susceptible to noise interference. Moreover, when dealing with complex backgrounds or high-density objects, these methods tend to highlight irrelevant background areas inappropriately. These limitations are particularly pronounced in multiple-object tasks requiring precise target localization, such as image segmentation and object detection, where the interpretability results often fail to accurately reflect the model's decision-making process, lacking sufficient focus on local regions. On the other hand, while non-gradient-based methods (e.g., Eigen-CAM) effectively mitigate noise interference, they also face challenges when dealing with complex backgrounds or dense targets in multi-objective tasks due to insufficient consideration of spatial information. Additionally, the sign ambiguity in the Singular Value Decomposition (SVD) process in Eigen-CAM can lead to unstable explanation results, especially when handling scenes with multiple target classes. This instability significantly affects the reliability of the explanation results. Therefore, this study aims to propose a novel XAI method to avoid the impact of noise on gradient information and provide a more stable and accurate explanation for segmentation models. Specifically, we first obtain spatial information by performing gradient backpropagation on feature maps and use it as a weighted sum in an element-wise product with the activation map to generate a weighted activation map. Then, following the approach of Eigen-CAM, we perform SVD on the weighted activation map and use the first principal component as the weight vector to generate the class-discriminative localization map. Finally, in the post-processing stage, we employ an innovative sign correction strategy designed to optimize the representation direction of saliency maps by selecting and preserving the contributions of the most relevant information directions. Furthermore, in response to the shortcomings of existing evaluation metrics for assessing the performance of different explanation methods, we also propose a new evaluation framework to objectively compare the performance of various explanation methods. In summary, the main contributions of this study can be summarized as follows:  
1. We propose a completely new XAI method, extending the widely used Eigen-CAM method to make it more suitable for semantic segmentation models. By applying a gradient weighting strategy, we can obtain more precise spatial information, thus generating fine-grained explanation results. 2. We perform SVD on the weighted activation map to extract its main feature representations and introduce a sign correction strategy to optimize the direction of the saliency map. This approach not only effectively suppresses noise issues but also enhances the stability of explanation results. 3. We introduce an evaluation framework specifically designed for the interpretation of multiple-object task models, allowing for a more objective assessment of the performance of different XAI methods and quantifying their explanatory effectiveness.