一种基于Bhattacharyya核的SVM

包括图像识别在内的很多应用领域里,把单个样本表示成向量的集合的形式是很自然的想法,利用一个合适的核函数我们可以把这些向量映射到一个更高维的Hilbert空间,在这个高维空间里用Kernel PCA方法找到样本的高斯分布族,这样就可以把样本上的核函数定义成它们所服从的高斯分布密度函数的Bhattacharrya仿射.这样得到的核函数具有比较好的性质,比如说在各种变换下有稳定性表现,从而也说明了即使还有别的表示样本的方法,用向量集合的形式来表示单个的样本也是具有合理性的.

A SVM Based on Bhattacharyya Kernel

In various application domians,including image recognition.It is natural to represent each example as a set of vectors.With a base kernel we can implicitly map these vectors to a Hilbert space and fit a Gaussian distribution to the whole set using Kernel PCA.We define our kernel between examples as Bhattacharry's measure of affinity between such Gaussians.The resulting kernel is computable in closed form and enjoys many favorable properties,including graceful behavior under transformations,potentially justifying the vector set representation even in cases when more conventional representations also exist.