Kernel optimization using nonparametric Fisher criterion in the subspace

• We solve the kernel optimization problem by creating an object function in the subspace instead of kernel space.
• We propose a new separability measure as the object function, named nonparametric Fisher criterion.
• We show that the KNDA algorithm with all parameters optimized can get the best performance.

Kernel optimization plays an important role in kernel-based dimensionality reduction algorithms, such as kernel principal components analysis (KPCA) and kernel discriminant analysis (KDA). In this paper, a nonparametric Fisher criterion is proposed as the objective function to find the optimized kernel parameters. Unlike other criterions that rooted in the kernel feature space, the proposed criterion works in the low-dimensional subspace to measure the separability of different patterns. Experiments on 13 different benchmark datasets show the effectiveness of the proposed method, in comparison with other criterions and the kernel space methods.