Selection of Supervised Learning-based Sparse Matrix Reordering Algorithms

2025-11-13

AI Summary

Sparse matrix reordering algorithm selection traditionally relies on brute-force search or heuristic rules, leading to suboptimal performance and limited adaptability across diverse matrix structures. Method: This paper proposes the first supervised learning–based intelligent algorithm selection model. We construct a comprehensive structural feature set for sparse matrices and train a classification model to learn the mapping between these features and the performance of mainstream reordering algorithms (e.g., AMD, RCM), using the Florida Sparse Matrix Collection for training and evaluation. Contribution/Results: To our knowledge, this is the first work to systematically apply supervised learning to sparse matrix reordering selection. The model enables adaptive, structure-aware algorithm recommendation. Experiments demonstrate that our approach achieves an average 1.45× speedup over the single AMD strategy and reduces linear system solution time by 55.37% on the test set, significantly improving both efficiency and automation in sparse linear system solving.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Algorithm Configuration
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Sparse matrix ordering is a vital optimization technique often employed for solving large-scale sparse matrices. Its goal is to minimize the matrix bandwidth by reorganizing its rows and columns, thus enhancing efficiency. Conventional methods for algorithm selection usually depend on brute-force search or empirical knowledge, lacking the ability to adjust to diverse sparse matrix structures.As a result, we have introduced a supervised learning-based model for choosing sparse matrix reordering algorithms. This model grasps the correlation between matrix characteristics and commonly utilized reordering algorithms, facilitating the automated and intelligent selection of the suitable sparse matrix reordering algorithm. Experiments conducted on the Florida sparse matrix dataset reveal that our model can accurately predict the optimal reordering algorithm for various matrices, leading to a 55.37% reduction in solution time compared to solely using the AMD reordering algorithm, with an average speedup ratio of 1.45.

Problem

• Automating selection of sparse matrix reordering algorithms
• Reducing solution time through intelligent algorithm prediction
• Adapting to diverse matrix structures using supervised learning

Innovation

• Supervised learning model selects reordering algorithms
• Model learns matrix features to algorithm correlations
• Automates optimal algorithm choice for sparse matrices