Domain adaptation using the grassmann manifold

Modern data analysis is flush with large databases and high-dimensional inference problems. Often the size of these problems directly relates to the fact that given data may have variations that can be difficult to incorporate into well-known, classical methods. One of these sources of variation is that of differing data sources, often called domain adaptation. Many domain adaptation techniques use the notion of a shared representation to attempt to remove domain-specific variation in given observations. One way to obtain these representations is through dimension reduction using a linear projection onto a lower-dimensional subspace of the predictors. Estimating linear projections is intrinsically linked with parameters lying on the Grassmannian. We present some historical approaches and their relationship to recent advances in domain adaptation that exploit the Grassmannian through subspace estimation.