  Existing ordinal embedding methods usually follow a two-stage routine:
outlier detection is first employed to pick out the inconsistent comparisons;
then an embedding is learned from the clean data. However, learning in a
multi-stage manner is well-known to suffer from sub-optimal solutions. In this
paper, we propose a unified framework to jointly identify the contaminated
comparisons and derive reliable embeddings. The merits of our method are
three-fold: (1) By virtue of the proposed unified framework, the sub-optimality
of traditional methods is largely alleviated; (2) The proposed method is aware
of global inconsistency by minimizing a corresponding cost, while traditional
methods only involve local inconsistency; (3) Instead of considering the
nuclear norm heuristics, we adopt an exact solution for rank equality
constraint. Our studies are supported by experiments with both simulated
examples and real-world data. The proposed framework provides us a promising
tool for robust ordinal embedding from the contaminated comparisons.
