Exploring novel semi-inner product reproducing Kernels in Banach space for robust Kernel methods.

Kernel methods are widely applied across various domains; however, structural limitations of reproducing kernels in Hilbert spaces pose significant challenges. Many challenges inherent to Hilbert spaces can be effectively addressed within the framework of Banach spaces. In this work, we define the semi-inner product reproducing kernel Banach space and its reproducing kernels using semi-inner product and bilinear mapping, supported by rigorous proofs. Specific forms of semi-inner product reproducing kernels are derived within the theoretical framework of the semi-inner product reproducing kernel Banach space. This constitutes the core originality of our work and represents its primary contribution. Through illustrative experiments, we validate the effectiveness of semi-inner product reproducing kernels and demonstrate their superior performance compared to polynomial reproducing kernels.