Selection of Supervised Learning-based Sparse Matrix Reordering Algorithms

TL;DR

Sparse matrix reordering to minimize bandwidth is not universally solved by a single algorithm. The paper introduces a supervised learning framework that maps matrix features to one of four reordering algorithms (AMD, SCOTCH, ND, RCM) using a dataset of 936 matrices with solve-time labels, formalized as $f(x_1, x_2, ..., x_n) -> y_n$. A Random Forest classifier with standardized features achieves 86.7% accuracy and delivers a 55.37% reduction in solve time on average, with a 1.45× speedup over the AMD baseline on the Florida Matrix Collection when solving with MUMPS. This work demonstrates that automated, data-driven selection of reordering algorithms can substantially improve sparse solver performance and reduce manual tuning effort.

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.

Figures (4)

• Figure 1: Comparison of Solution Times for Sparse Matrix Reordering Algorithms
• Figure 2: Sparse Matrix Reordering Algorithm Prediction Model
• Figure 3: The parameter tuning process of the grid search method
• Figure 4: Prediction Accuracy of Different Machine Learning Algorithms