  The performance of distance-based classifiers heavily depends on the
underlying distance metric, so it is valuable to learn a suitable metric from
the data. To address the problem of multimodality, it is desirable to learn
local metrics. In this short paper, we define a new intuitive distance with
local metrics and influential regions, and subsequently propose a novel local
metric learning method for distance-based classification. Our key intuition is
to partition the metric space into influential regions and a background region,
and then regulate the effectiveness of each local metric to be within the
related influential regions. We learn local metrics and influential regions to
reduce the empirical hinge loss, and regularize the parameters on the basis of
a resultant learning bound. Encouraging experimental results are obtained from
various public and popular data sets.
