¹Department of Industrial Engineering and Management, Tokyo Institute of Technology, Japan

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Abstract—The present paper proposes new approaches for recommendation tasks based on one-class support vector machines (1-SVMs) with graph kernels generated from a Laplacian matrix. We introduce new formulations for the 1-SVM that can manipulate graph kernels quite efficiently. We demonstrate that the proposed formulations fully utilize the sparse structure of the Laplacian matrix, which enables the proposed approaches to be applied to recommendation tasks having a large number of customers and products in practical computational times. Results of various numerical experiments demonstrating the high performance of the proposed approaches are presented.

Index Terms—support vector machine, Laplacian matrix, graph kernel, quadratic programming problem, collaborative filtering, recommender system

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Cite: Yasutoshi Yajima, Tien-Fang Kuo, "Efficient Formulations for 1-SVM and their Application to Recommendation Tasks," Journal of Computers vol. 1, no.3, pp.27-34, 2006.