A kernel optimization method based on the localized kernel Fisher criterion

It is widely recognized that whether the selected kernel matches the data determines the performance of kernel-based methods. Ideally it is expected that the data is linearly separable in the kernel induced feature space, therefore, Fisher linear discriminant criterion can be used as a cost function to optimize the kernel function. However, the data may not be linearly separable even after kernel transformation in many applications, e.g., the data may exist as multimodally distributed structure, in this case, a nonlinear classifier is preferred, and obviously Fisher criterion is not a suitable choice as kernel optimization rule. Motivated by this issue, we propose a localized kernel Fisher criterion, instead of traditional Fisher criterion, as the kernel optimization rule to increase the local margins between embedded classes in kernel induced feature space. Experimental results based on some benchmark data and measured radar high-resolution range profile (HRRP) data show that the classification performance can be improved by using the proposed method.