Robust Ordinal Embedding from Contaminated Relative Comparisons
This work addresses robust ordinal embedding for applications like recommendation systems or data visualization, but it is incremental as it builds on existing methods by integrating outlier detection and embedding into a single framework.
The paper tackles the problem of learning ordinal embeddings from contaminated relative comparisons by proposing a unified framework that jointly identifies outliers and learns embeddings, alleviating sub-optimality in traditional two-stage methods and demonstrating effectiveness through experiments on simulated and real-world data.
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.