  Kernel methods have been successfully applied to the areas of pattern
recognition and data mining. In this paper, we mainly discuss the issue of
propagating labels in kernel space. A Kernel-Induced Label Propagation
(Kernel-LP) framework by mapping is proposed for high-dimensional data
classification using the most informative patterns of data in kernel space. The
essence of Kernel-LP is to perform joint label propagation and adaptive weight
learning in a transformed kernel space. That is, our Kernel-LP changes the task
of label propagation from the commonly-used Euclidean space in most existing
work to kernel space. The motivation of our Kernel-LP to propagate labels and
learn the adaptive weights jointly by the assumption of an inner product space
of inputs, i.e., the original linearly inseparable inputs may be mapped to be
separable in kernel space. Kernel-LP is based on existing positive and negative
LP model, i.e., the effects of negative label information are integrated to
improve the label prediction power. Also, Kernel-LP performs adaptive weight
construction over the same kernel space, so it can avoid the tricky process of
choosing the optimal neighborhood size suffered in traditional criteria. Two
novel and efficient out-of-sample approaches for our Kernel-LP to involve new
test data are also presented, i.e., (1) direct kernel mapping and (2) kernel
mapping-induced label reconstruction, both of which purely depend on the kernel
matrix between training set and testing set. Owing to the kernel trick, our
algorithms will be applicable to handle the high-dimensional real data.
Extensive results on real datasets demonstrate the effectiveness of our
approach.
