An Improved Support Vector Machine Algorithm Based on Sparse Optimization

Considering the dimension catastrophe, high computational complexity, and feature redundancy issues faced by traditional Support Vector Machines (SVMs) in high-dimensional data environments, this study proposes two optimized sparse SVM algorithms: the Improved Sparse Adaptive Matching Pursuit SVM (Improved SAMP-SVM) and the Basis Pursuit SVM (BP-SVM). By constructing an adaptive feature selection mechanism and a basis-tracking optimization scheme based on the Alternating Direction Method of Multipliers (ADMM), we successfully achieve synergistic optimization of feature dimensionality reduction and classification performance. Using standard SVM and L1-SVM as benchmarks, comprehensive evaluations were conducted across three distinct synthetic datasets (high-dimensional small-sample, low-dimensional large-sample, and high-noise data) regarding accuracy, feature compression rate, training time, and robustness. Experimental results demonstrate that BP-SVM exhibits outstanding performance in feature compression ratio (average 0.2–0.3) and robustness, achieving an accuracy of up to 0.706. Compared to BP-SVM, Improved SAMP-SVM shows significant computational efficiency advantages, reducing training cycles by 30%–40%. Compared to traditional SVM, these two optimized algorithms provide more efficient strategies for high-dimensional data classification.