CONFORMAL TRANSFORMATION OF KERNELS: A GEOMETRIC PERSPECTIVE ON TEXT CLASSIFICATION

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 classification, 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 data sets, we extend this analysis to the high-dimensional domain of text data. The novelty of this study resides in extending the use of conformal transformation techniques- a well-established concept in the literature- to the specialized task of text categorization, particularly for a real-world, high-dimensional dataset. Our experiments, conducted on the Reuters data set 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 transforma tions can significantly improve kernel performance, particularly for sub-optimal kernels. Specifically, improvements were observed in 60% of the tested scenarios for the linear ker nel, 84% for the Gaussian kernel, and 80% for the Gaussian cosine kernel. In light of these f indings, it becomes clear that conformal transformations play a pivotal role in enhancing kernel performance, offering substantial benefits.