提出融合相对与绝对特征的图像选择方法，提升稀疏线性系统求解效率。
Relative-Absolute Fusion: Rethinking Feature Extraction in Image-Based Iterative Method Selection for Solving Sparse Linear Systems
- 同时提取矩阵图像的相对关系与数值绝对特征，融合生成完整表示。
- 在真实数据集上实现0.08~0.29秒加速，比传统方法快5.86%~11.50%。
- 适合需要高效求解稀疏系统的科研与工程应用，尤其关注模型可解释性。
迭代法求解稀疏线性系统时，方法选择至关重要，因其固有鲁棒性不足。尽管基于图像的选择方法已有进展，但现有特征提取方式可能将不同矩阵映射为相同图像表示，导致错误选择和次优结果。本文提出RAF（Relative-Absolute Fusion）——一种高效的特征提取技术，通过同步提取图像的相对特征与对应数值的绝对特征并进行融合，构建全面的矩阵表示，有效避免不同矩阵间的特征混淆，从而提升选择准确率，释放图像方法潜力。我们在SuiteSparse及自建的BMCMat（Balanced Multi-Classification Matrix dataset）上进行了全面评估，结果显示稀疏线性系统求解时间减少0.08秒至0.29秒，相较传统图像方法提速5.86%~11.50%，达到当前最优（SOTA）性能。BMCMat数据集已开源：https://github.com/zkqq/BMCMat。
原文摘要 · Abstract (English)
Iterative method selection is crucial for solving sparse linear systems because these methods inherently lack robustness. Though image-based selection approaches have shown promise, their feature extraction techniques might encode distinct matrices into identical image representations, leading to the same selection and suboptimal method. In this paper, we introduce RAF (Relative-Absolute Fusion), an efficient feature extraction technique to enhance image-based selection approaches. By simultaneously extracting and fusing image representations as relative features with corresponding numerical values as absolute features, RAF achieves comprehensive matrix representations that prevent feature ambiguity across distinct matrices, thus improving selection accuracy and unlocking the potential of image-based selection approaches. We conducted comprehensive evaluations of RAF on SuiteSparse and our developed BMCMat (Balanced Multi-Classification Matrix dataset), demonstrating solution time reductions of 0.08s-0.29s for sparse linear systems, which is 5.86%-11.50% faster than conventional image-based selection approaches and achieves state-of-the-art (SOTA) performance. BMCMat is available at https://github.com/zkqq/BMCMat.
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