  Kernel methods have had great success in Statistics and Machine Learning.
Despite their growing popularity, however, less effort has been drawn towards
developing kernel based classification methods on Riemannian manifolds due to
difficulty in dealing with non-Euclidean geometry. In this paper, motivated by
the extrinsic framework of manifold-valued data analysis, we propose a new
positive definite kernel on planar Kendall shape space $\Sigma_2^k$, called
extrinsic Veronese Whitney Gaussian kernel. We show that our approach can be
extended to develop Gaussian kernels on any embedded manifold. Furthermore,
kernel ridge regression classifier (KRRC) is implemented to address the shape
classification problem on $\Sigma_2^k$, and their promising performances are
illustrated through the real data analysis.
