In this article we investigate the effects of conformal transformations on
kernel functions used in Support Vector Machines. Our focus lies in the task of
text document categorization, which involves assigning each document to a
particular category. We introduce a new Gaussian Cosine kernel alongside two
conformal transformations. Building upon previous studies that demonstrated the
efficacy of conformal transformations in increasing class separability on
synthetic and low-dimensional datasets, we extend this analysis to the
high-dimensional domain of text data. Our experiments, conducted on the Reuters
dataset on two types of binary classification tasks, compare the performance of
Linear, Gaussian, and Gaussian Cosine kernels against their conformally
transformed counterparts. The findings indicate that conformal transformations
can significantly improve kernel performance, particularly for sub-optimal
kernels. Specifically, improvements were observed in 60% of the tested
scenarios for the Linear kernel, 84% for the Gaussian kernel, and 80% for the
Gaussian Cosine kernel. In light of these findings, it becomes clear that
conformal transformations play a pivotal role in enhancing kernel performance,
offering substantial benefits.

本文研究了共形变换对支持向量机中使用的核函数的影响，着重于文本文档分类任务，并引入了新的高斯余弦核和两种共形变换。研究结果表明，共形变换可以显著改善核函数的性能，特别是对于次优核函数，在线性核函数的 60%、高斯核函数的 84% 和高斯余弦核函数的 80% 的测试场景中都观察到了改进，从而明确了共形变换在提高核函数性能方面发挥了关键作用。