Thresholded spectral algorithms for sparse approximations

Spectral algorithms form a general framework that unifies many regularization schemes in learning theory. In this paper, we propose and analyze a class of thresholded spectral algorithms that are designed based on empirical features. Soft thresholding is adopted to achieve sparse approximations. Our analysis shows that without sparsity assumption of the regression function, the output functions of thresholded spectral algorithms are represented by empirical features with satisfactory sparsity, and the convergence rates are comparable to those of the classical spectral algorithms in the literature.