Ranking a Set of Objects: A Graph Based Least-Square Approach

We consider the problem of ranking $N$ objects starting from a set noisy pairwise comparisons provided by crowd equal workers. assume that are endowed with intrinsic qualities and probability which an object is preferred to another depends only on difference between two competitors. propose class non-adaptive algorithms rely least-squares optimization criterion for estimation qualities. Such shown be asymptotically optimal (i.e., they require $O(\frac{N}{\epsilon ^2}\log \frac{N}{\delta })$ $(\epsilon, \delta)$ -PAC). Numerical results show our schemes very efficient also in many non-asymptotic scenarios exhibiting performance similar maximum-likelihood algorithm. Moreover, we how can extended adaptive test them real-world datasets.