Relative-Absolute Fusion: Rethinking Feature Extraction in Image-Based Iterative Method Selection for Solving Sparse Linear Systems

2025-10-01

AI Summary

To address the ambiguity in iterative solver selection caused by feature distortion during matrix-to-image conversion—leading to indistinguishable image representations for distinct sparse matrices and suboptimal method choices—this paper proposes a relative-absolute multimodal feature fusion framework. It preserves the visual representation of matrices as images while explicitly incorporating critical numerical features (e.g., condition number, sparsity pattern statistics) and aligns them across modalities via weighted fusion to construct a more discriminative joint matrix representation. This design effectively mitigates representation collapse and significantly improves both accuracy and robustness in iterative solver selection. Experiments on SuiteSparse and BMCMat benchmarks demonstrate that our approach reduces average solution time by 0.08–0.29 seconds and achieves speedups of 5.86%–11.50%, attaining state-of-the-art performance.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Computer Vision: Multi-modal Vision
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

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.

Problem

• Enhancing image-based iterative method selection for sparse linear systems
• Preventing feature ambiguity in matrix representations through fusion technique
• Improving selection accuracy to reduce solution time for linear equations

Innovation

• RAF fuses relative image features with absolute numerical values
• It prevents feature ambiguity across distinct sparse matrices
• This enhances image-based iterative method selection accuracy