Typical graph-theoretic approaches for semisupervised classification infer labels of unlabeled instances with the help of graph Laplacians. Founded on the spectral decomposition of the graph Laplacian, this paper learns a kernel matrix via minimizing the leave-one-out classification error on the labeled instances. To this end, an efficient algorithm is presented based on linear programming, resulting in a transductive spectral kernel. The idea of our algorithm stems from regularization methodology and also has a nice interpretation in terms of spectral clustering. A simple classifier can be readily built upon the learned kernel, which suffices to give prediction for any data point aside from those in the available dataset. Besides this usage, the spectral kernel can be effectively used in tandem with conventional kernel machines such as SVMs. We demonstrate the efficacy of the proposed algorithm through experiments carried out on challenging classification tasks.

Authors

• Wei Liu Amazon AGI
• Buyue Qian
• Jingyu Cui
• Jianzhuang Liu Shenzhen Institute of Advanced Technology

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