Parameter-Free Spectral Kernel Learning
This addresses the need for efficient kernel learning in semi-supervised settings, but it is incremental as it builds on existing manifold regularization and kernel alignment techniques.
The paper tackles the problem of semi-supervised kernel learning by proposing a method that combines manifold structure from unlabeled data with Regularized Least-Squares to learn a kernel analytically without optimization solvers, achieving comparable performance to fine-tuned methods on benchmark datasets.
Due to the growing ubiquity of unlabeled data, learning with unlabeled data is attracting increasing attention in machine learning. In this paper, we propose a novel semi-supervised kernel learning method which can seamlessly combine manifold structure of unlabeled data and Regularized Least-Squares (RLS) to learn a new kernel. Interestingly, the new kernel matrix can be obtained analytically with the use of spectral decomposition of graph Laplacian matrix. Hence, the proposed algorithm does not require any numerical optimization solvers. Moreover, by maximizing kernel target alignment on labeled data, we can also learn model parameters automatically with a closed-form solution. For a given graph Laplacian matrix, our proposed method does not need to tune any model parameter including the tradeoff parameter in RLS and the balance parameter for unlabeled data. Extensive experiments on ten benchmark datasets show that our proposed two-stage parameter-free spectral kernel learning algorithm can obtain comparable performance with fine-tuned manifold regularization methods in transductive setting, and outperform multiple kernel learning in supervised setting.