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Riemannian Geometry on Graphs and its Application to Ranking and Classification

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Zhou,  D
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zhou, D. (2004). Riemannian Geometry on Graphs and its Application to Ranking and Classification. Talk presented at -. DIMACS Working Group on The Mathematics of Web Search and Meta-Search, Bertorino, Italy.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-B472-8
Abstract
We consider the problem of transductive inference. In many real-world problems, unlabeled data is far easier to obtain than labeled data. Hence transductive inference is very significant in many practical problems. According to Vapnik's point of view, one should predict the function value only on the given points directly rather than a function defined on the whole space, the latter being a more complicated problem. Inspired by this idea, we develop discrete calculus on finite discrete spaces, and then build discrete regularization. A family of transductive algorithms is naturally derived from this regularization framework. We validate the algorithms on both synthetic and real-world data from text/web categorization to bioinformatics problems. A significant by-product of this work is a powerful way of ranking data based on examples including images, documents, proteins and many other kinds of data.