  Distance metric learning can be viewed as one of the fundamental interests in
pattern recognition and machine learning, which plays a pivotal role in the
performance of many learning methods. One of the effective methods in learning
such a metric is to learn it from a set of labeled training samples. The issue
of data imbalance is the most important challenge of recent methods. This
research tries not only to preserve the local structures but also covers the
issue of imbalanced datasets. To do this, the proposed method first tries to
extract a low dimensional manifold from the input data. Then, it learns the
local neighborhood structures and the relationship of the data points in the
ambient space based on the adjacencies of the same data points on the embedded
low dimensional manifold. Using the local neighborhood relationships extracted
from the manifold space, the proposed method learns the distance metric in a
way which minimizes the distance between similar data and maximizes their
distance from the dissimilar data points. The evaluations of the proposed
method on numerous datasets from the UCI repository of machine learning, and
also the KDDCup98 dataset as the most imbalance dataset, justify the supremacy
of the proposed approach in comparison with other approaches especially when
the imbalance factor is high.
