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Heterogeneous domain adaptation (HDA) aims to solve the learning problems where the source- and the target-domain data are represented by heterogeneous types of features. The existing HDA approaches based on matrix completion or matrix factorization have proven to be effective to capture shareable information between heterogeneous domains. However, there are two limitations in the existing methods. First, a large number of corresponding data instances between the source domain and the target domain are required to bridge the gap between different domains for performing matrix completion. These corresponding data instances may be difficult to collect in real-world applications due to the limited size of data in the target domain. Second, most existing methods can only capture linear correlations between features and data instances while performing matrix completion for HDA. In this paper, we address these two issues by proposing a new matrix-factorization-based HDA method in a semisupervised manner, where only a few labeled data are required in the target domain without requiring any corresponding data instances between domains. Such labeled data are more practical to obtain compared with cross-domain corresponding data instances. Our proposed algorithm is based on matrix factorization in an approximated reproducing kernel Hilbert space (RKHS), where nonlinear correlations between features and data instances can be exploited to learn heterogeneous features for both the source and the target domains. Extensive experiments are conducted on cross-domain text classification and object recognition, and experimental results demonstrate the superiority of our proposed method compared with the state-of-the-art HDA approaches.