  This paper addresses classification tasks on a particular target domain in
which labeled training data are only available from source domains different
from (but related to) the target. Two closely related frameworks, domain
adaptation and domain generalization, are concerned with such tasks, where the
only difference between those frameworks is the availability of the unlabeled
target data: domain adaptation can leverage unlabeled target information, while
domain generalization cannot. We propose Scatter Component Analyis (SCA), a
fast representation learning algorithm that can be applied to both domain
adaptation and domain generalization. SCA is based on a simple geometrical
measure, i.e., scatter, which operates on reproducing kernel Hilbert space. SCA
finds a representation that trades between maximizing the separability of
classes, minimizing the mismatch between domains, and maximizing the
separability of data; each of which is quantified through scatter. The
optimization problem of SCA can be reduced to a generalized eigenvalue problem,
which results in a fast and exact solution. Comprehensive experiments on
benchmark cross-domain object recognition datasets verify that SCA performs
much faster than several state-of-the-art algorithms and also provides
state-of-the-art classification accuracy in both domain adaptation and domain
generalization. We also show that scatter can be used to establish a
theoretical generalization bound in the case of domain adaptation.
