  In the last few years, various types of machine learning algorithms, such as
Support Vector Machine (SVM), Support Vector Regression (SVR), and Non-negative
Matrix Factorization (NMF) have been introduced. The kernel approach is an
effective method for increasing the classification accuracy of machine learning
algorithms. This paper introduces a family of one-parameter kernel functions
for improving the accuracy of SVM classification. The proposed kernel function
consists of a trigonometric term and differs from all existing kernel
functions. We show this function is a positive definite kernel function.
Finally, we evaluate the SVM method based on the new trigonometric kernel, the
Gaussian kernel, the polynomial kernel, and a convex combination of the new
kernel function and the Gaussian kernel function on various types of datasets.
Empirical results show that the SVM based on the new trigonometric kernel
function and the mixed kernel function achieve the best classification
accuracy. Moreover, some numerical results of performing the SVR based on the
new trigonometric kernel function and the mixed kernel function are presented.
