Stability analysis for ranking algorithms

In this paper, the stability of ranking algorithms is studied by adopting a strategy which adjusts the sample set by deleting one or two element from it. Relationship between uniform loss stability and uniform score stability is investigated. A sufficient condition for uniform score stability is given. The result of our work shows that if a uniform score stability ranking algorithm use γ ranking loss, then it has uniform loss stability; also, if for any x, a kernel function K(x, x) has a limited upper bound, then the ranking algorithm which minimizes the regularization empirical l-error will have good uniform score stability.