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In this paper, we study the heterogeneous domain adaptation (HDA) problem, in which the data from the source domain and the target domain are represented by heterogeneous features with different dimensions. By introducing two different projection matrices, we first transform the data from two domains into a common subspace such that the similarity between samples across different domains can be measured. We then propose a new feature mapping function for each domain, which augments the transformed samples with their original features and zeros. Existing supervised learning methods (e.g., SVM and SVR) can be readily employed by incorporating our newly proposed augmented feature representations for supervised HDA. As a showcase, we propose a novel method called Heterogeneous Feature Augmentation (HFA) based on SVM. We show that the proposed formulation can be equivalently derived as a standard Multiple Kernel Learning (MKL) problem, which is convex and thus the global solution can be guaranteed. To additionally utilize the unlabeled data in the target domain, we further propose the semi-supervised HFA (SHFA) which can simultaneously learn the target classifier as well as infer the labels of unlabeled target samples. Comprehensive experiments on three different applications clearly demonstrate that our SHFA and HFA outperform the existing HDA methods.