Learning Robust Distance Metric with Side Information via Ratio Minimization of
Orthogonally Constrained `2,1-Norm Distances
Abstract
Metric Learning, which aims at learning a distance metric for a given data set, plays an important role in measuring the distance or similarity between data objects. Due to its broad usefulness,
it has attracted a lot of interest in machine learning and related areas in the past few decades. This
paper proposes to learn the distance metric from
the side information in the forms of must-links and
cannot-links. Given the pairwise constraints, our
goal is to learn a Mahalanobis distance that minimizes the ratio of the distances of the data pairs
in the must-links to those in the cannot-links. Different from many existing papers that use the traditional squared `2-norm distance, we develop a
robust model that is less sensitive to data noise or
outliers by using the not-squared `2-norm distance.
In our objective, the orthonormal constraint is enforced to avoid degenerate solutions. To solve our
objective, we have derived an efficient iterative solution algorithm. We have conducted extensive experiments, which demonstrated the superiority of
our method over state-of-the-art