Semi-supervised learning with manifold fitted graphs

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Conference Proceeding
International Joint Conference on Artificial Intelligence, 2013, pp. 1896 - 1902
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In this paper, we propose a locality-constrained and sparsity-encouraged manifold fitting approach, aiming at capturing the locally sparse manifold structure into neighborhood graph construction by exploiting a principled optimization model. The proposed model formulates neighborhood graph construction as a sparse coding problem with the locality constraint, therefore achieving simultane- ous neighbor selection and edge weight optimiza- tion. The core idea underlying our model is to per- form a sparse manifold fitting task for each data point so that close-by points lying on the same local manifold are automatically chosen to connect and meanwhile the connection weights are acquired by simple geometric reconstruction. We term the nov- el neighborhood graph generated by our proposed optimization model M - Fitted Graph since such a graph stems from sparse manifold fitting. To eval- uate the robustness and effectiveness of M -fitted graphs, we leverage graph-based semi-supervised learning as the testbed. Extensive experiments car- ried out on six benchmark datasets validate that the proposed M -fitted graph is superior to state- of-the-art neighborhood graphs in terms of classi- fication accuracy using popular graph-based semi- supervised learning methods.
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