Subspace detection in a kernel space: The missing data case

This paper studies the problem of matched subspace detection in high-dimensional feature space where the signal in the input space is partially observed. We present a test statistic for our detection problem using kernel functions and provide kernel function value estimators with missing data for different kernels. The test statistic can be calculated approximately with estimated kernel function values. We also give theoretical results regarding the kernel function value and test statistic estimation. Numerical experiments involving both Gaussian and polynomial kernels show the efficacy of the proposed kernel function value estimator and resulting subspace detector.