Unsupervised Ranking of Multi-Attribute Objects Based on Principal Curves

Unsupervised ranking faces one critical challenge in evaluation applications, that is, no ground truth is available. When PageRank and its variants show a good solution in related subjects, they are applicable only for ranking from link-structure data. In this work, we focus on unsupervised ranking from multi-attribute data which is also common in evaluation tasks. To overcome the challenge, we propose five essential meta-rules for the design and assessment of unsupervised ranking approaches: scale and translation invariance, strict monotonicity, linear/nonlinear capacities, smoothness, and explicitness of parameter size. These meta-rules are regarded as high level knowledge for unsupervised ranking tasks. Inspired by the works in [8] and [14], we propose a ranking principal curve (RPC) model, which learns a one-dimensional manifold function to perform unsupervised ranking tasks on multi-attribute observations. Furthermore, the RPC is modeled to be a cubic B\'ezier curve with control points restricted in the interior of a hypercube, thereby complying with all the five meta-rules to infer a reasonable ranking list. With control points as the model parameters, one is able to understand the learned manifold and to interpret the ranking list semantically. Numerical experiments of the presented RPC model are conducted on two open datasets of different ranking applications. In comparison with the state-of-the-art approaches, the new model is able to show more reasonable ranking lists.