  In this paper, we propose a data-adaptive non-parametric kernel learning
framework in margin based kernel methods. In model formulation, given an
initial kernel matrix, a data-adaptive matrix with two constraints is imposed
in an entry-wise scheme. Learning this data-adaptive matrix in a
formulation-free strategy enlarges the margin between classes and thus improves
the model flexibility. The introduced two constraints are imposed either
exactly (on small data sets) or approximately (on large data sets) in our
model, which provides a controllable trade-off between model flexibility and
complexity with theoretical demonstration. In algorithm optimization, the
objective function of our learning framework is proven to be gradient-Lipschitz
continuous. Thereby, kernel and classifier/regressor learning can be
efficiently optimized in a unified framework via Nesterov's acceleration. For
the scalability issue, we study a decomposition-based approach to our model in
the large sample case. The effectiveness of this approximation is illustrated
by both empirical studies and theoretical guarantees. Experimental results on
various classification and regression benchmark data sets demonstrate that our
non-parametric kernel learning framework achieves good performance when
compared with other representative kernel learning based algorithms.
