Mean Polynomial Kernel and Its Application to Vector Sequence Recognition

SUMMARY Classification tasks in computer vision and brain-computer interface research have presented several applications such as biometrics and cognitive training. However, like in any other discipline, determining suitable representation of data has been challenging, and recent approaches have deviated from the familiar form of one vector for each data sample. This paper considers a kernel between vector sets, the mean polynomial kernel, motivated by recent studies where data are approximated by linear subspaces, in particular, methods that were formulated on Grassmann manifolds. This kernel takes a more general approach given that it can also support input data that can be modeled as a vector sequence, and not necessarily requiring it to be a linear subspace. We discuss how the kernel can be associated with the Projection kernel, a Grassmann kernel. Experimental results using face image sequences and physiological signal data show that the mean polynomial kernel surpasses existing subspace-based methods on Grassmann manifolds in terms of predictive performance and efficiency.