Formulating context-dependent similarity functions

Tasks of information retrieval depend on a good distance function for measuring similarity between data instances. The most effective distance function must be formulated in a context-dependent (also application-, data-, and user-dependent) way. In this paper, we present a novel method, which learns a distance function by capturing the nonlinear relationships among contextual information provided by the application, data, or user. We show that through a process called the "kernel trick," such nonlinear relationships can be learned efficiently in a projected space. In addition to using the kernel trick, we propose two algorithms to further enhance efficiency and effectiveness of function learning. For efficiency, we propose a SMO-like solver to achieve O(N2) learning performance. For effectiveness, we propose using unsupervised learning in an innovative way to address the challenge of lack of labeled data (contextual information). Theoretically, we substantiate that our method is both sound and optimal. Empirically, we demonstrate that our method is effective and useful.