Rational Jacobi Kernel Functions: A novel massively parallelizable orthogonal kernel for support vector machines

Machine learning has recently seen a significant upsurge in its influence across diverse scientific domains. Among the array of machine learning techniques, the support vector machine (SVM) has emerged as a powerful supervised method. To enhance the SVM’s precision, the adoption of kernel methods has become commonplace. Notably, the integration of orthogonal functions as the SVM’s kernel has led to substantial improvements in accuracy. However, it is essential to note that the use of these functions also introduces heightened time complexity to the SVM along with imposing some limitations on data. In response to this challenge, a general formulation of orthogonal Jacobi kernel functions has been proposed. This formulation allows the user to choose classical Jacobi polynomial kernels, fractional or rational ones. Next, we develop a data-parallel technique implemented on heterogeneous computing systems to accelerate the computation of kernel matrix. The ensuing experimental results, conducted on the benchmark datasets, were founded on three distinctive rational mappings: algebraic, exponential, and logarithmic. Spanning data sizes from 700 to 3800, these mappings exhibited remarkable speedup factors of 3.967, 4.599, and 2.807, respectively.