  In the absence of prior knowledge, ordinal embedding methods obtain new
representation for items in a low-dimensional Euclidean space via a set of
quadruple-wise comparisons. These ordinal comparisons often come from human
annotators, and sufficient comparisons induce the success of classical
approaches. However, collecting a large number of labeled data is known as a
hard task, and most of the existing work pay little attention to the
generalization ability with insufficient samples. Meanwhile, recent progress in
large margin theory discloses that rather than just maximizing the minimum
margin, both the margin mean and variance, which characterize the margin
distribution, are more crucial to the overall generalization performance. To
address the issue of insufficient training samples, we propose a margin
distribution learning paradigm for ordinal embedding, entitled Distributional
Margin based Ordinal Embedding (\textit{DMOE}). Precisely, we first define the
margin for ordinal embedding problem. Secondly, we formulate a concise
objective function which avoids maximizing margin mean and minimizing margin
variance directly but exhibits the similar effect. Moreover, an Augmented
Lagrange Multiplier based algorithm is customized to seek the optimal solution
of \textit{DMOE} effectively. Experimental studies on both simulated and
real-world datasets are provided to show the effectiveness of the proposed
algorithm.
