  Reproducing Kernel Hilbert Space (RKHS) is the common mathematical platform
for various kernel methods in machine learning. The purpose of kernel learning
is to learn an appropriate RKHS according to different machine learning
scenarios and training samples. Because RKHS is uniquely generated by the
kernel function, kernel learning can be regarded as kernel function learning.
This paper proposes a Domain Adaptive Learning method based on Sample-Dependent
and Learnable Kernels (SDLK-DAL). The first contribution of our work is to
propose a sample-dependent and learnable Positive Definite Quadratic Kernel
function (PDQK) framework. Unlike learning the exponential parameter of
Gaussian kernel function or the coefficient of kernel combinations, the
proposed PDQK is a positive definite quadratic function, in which the symmetric
positive semi-definite matrix is the learnable part in machine learning
applications. The second contribution lies on that we apply PDQK to Domain
Adaptive Learning (DAL). Our approach learns the PDQK through minimizing the
mean discrepancy between the data of source domain and target domain and then
transforms the data into an optimized RKHS generated by PDQK. We conduct a
series of experiments that the RKHS determined by PDQK replaces those in
several state-of-the-art DAL algorithms, and our approach achieves better
performance.
