  Domain adaptation leverages the knowledge in one domain - the source domain -
to improve learning efficiency in another domain - the target domain. Existing
heterogeneous domain adaptation research is relatively well-progressed, but
only in situations where the target domain contains at least a few labeled
instances. In contrast, heterogeneous domain adaptation with an unlabeled
target domain has not been well-studied. To contribute to the research in this
emerging field, this paper presents: (1) an unsupervised knowledge transfer
theorem that guarantees the correctness of transferring knowledge; and (2) a
principal angle-based metric to measure the distance between two pairs of
domains: one pair comprises the original source and target domains and the
other pair comprises two homogeneous representations of two domains. The
theorem and the metric have been implemented in an innovative transfer model,
called a Grassmann-Linear monotonic maps-geodesic flow kernel (GLG), that is
specifically designed for heterogeneous unsupervised domain adaptation (HeUDA).
The linear monotonic maps meet the conditions of the theorem and are used to
construct homogeneous representations of the heterogeneous domains. The metric
shows the extent to which the homogeneous representations have preserved the
information in the original source and target domains. By minimizing the
proposed metric, the GLG model learns the homogeneous representations of
heterogeneous domains and transfers knowledge through these learned
representations via a geodesic flow kernel. To evaluate the model, five public
datasets were reorganized into ten HeUDA tasks across three applications:
cancer detection, credit assessment, and text classification. The experiments
demonstrate that the proposed model delivers superior performance over the
existing baselines.
