Relative-Absolute Fusion: Rethinking Feature Extraction in Image-Based Iterative Method Selection for Solving Sparse Linear Systems
This work addresses a specific bottleneck in numerical linear algebra for researchers and practitioners, offering an incremental improvement over existing image-based selection methods.
The paper tackles the problem of feature ambiguity in image-based iterative method selection for sparse linear systems by introducing RAF, a feature extraction technique that fuses relative and absolute features, resulting in solution time reductions of 0.08s-0.29s (5.86%-11.50% faster) and achieving state-of-the-art performance.
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.