Loss Bounds for Online Category Ranking
Category ranking is the task of ordering labels with respect to their relevance to an input instance. In this paper we describe and analyze several algorithms for online category ranking where the instances are revealed in a sequential manner. We describe additive and multiplicative updates which constitute the core of the learning algorithms. The updates are derived by casting a constrained optimization problem for each new instance. We derive loss bounds for the algorithms by using the properties of the dual solution while imposing additional constraints on the dual form. Finally, we outline and analyze the convergence of a general update that can be employed with any Bregman divergence.