  We propose a new learning method for heterogeneous domain adaptation (HDA),
in which the data from the source domain and the target domain are represented
by heterogeneous features with different dimensions. Using two different
projection matrices, we first transform the data from two domains into a common
subspace in order to measure the similarity between the data from two domains.
We then propose two new feature mapping functions to augment the transformed
data with their original features and zeros. The existing learning methods
(e.g., SVM and SVR) can be readily incorporated with our newly proposed
augmented feature representations to effectively utilize the data from both
domains for HDA. Using the hinge loss function in SVM as an example, we
introduce the detailed objective function in our method called Heterogeneous
Feature Augmentation (HFA) for a linear case and also describe its
kernelization in order to efficiently cope with the data with very high
dimensions. Moreover, we also develop an alternating optimization algorithm to
effectively solve the nontrivial optimization problem in our HFA method.
Comprehensive experiments on two benchmark datasets clearly demonstrate that
HFA outperforms the existing HDA methods.
