  Distance metric learning (DML) is a critical factor for image analysis and
pattern recognition. To learn a robust distance metric for a target task, we
need abundant side information (i.e., the similarity/dissimilarity pairwise
constraints over the labeled data), which is usually unavailable in practice
due to the high labeling cost. This paper considers the transfer learning
setting by exploiting the large quantity of side information from certain
related, but different source tasks to help with target metric learning (with
only a little side information). The state-of-the-art metric learning
algorithms usually fail in this setting because the data distributions of the
source task and target task are often quite different. We address this problem
by assuming that the target distance metric lies in the space spanned by the
eigenvectors of the source metrics (or other randomly generated bases). The
target metric is represented as a combination of the base metrics, which are
computed using the decomposed components of the source metrics (or simply a set
of random bases); we call the proposed method, decomposition-based transfer DML
(DTDML). In particular, DTDML learns a sparse combination of the base metrics
to construct the target metric by forcing the target metric to be close to an
integration of the source metrics. The main advantage of the proposed method
compared with existing transfer metric learning approaches is that we directly
learn the base metric coefficients instead of the target metric. To this end,
far fewer variables need to be learned. We therefore obtain more reliable
solutions given the limited side information and the optimization tends to be
faster. Experiments on the popular handwritten image (digit, letter)
classification and challenge natural image annotation tasks demonstrate the
effectiveness of the proposed method.
