Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Semi-Supervised Learning on Riemannian Manifolds
Machine Learning
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Wavelet-based image estimation: an empirical Bayes approach using Jeffrey's noninformative prior
IEEE Transactions on Image Processing
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To estimate a possibly multivariate regression function g under the general regression setup, y=g+@e, one can use wavelet thresholding as an alternative to conventional nonparametric regression methods. Wavelet thresholding is a simple operation in the wavelet domain that selects a subset of coefficients corresponding to an estimator of g when back-transformed. We propose an enhancement to wavelet thresholding by selecting a subset in a semi-supervised fashion in which the neighboring structure and classification function appropriate for wavelet domains are utilized. Wavelet coefficients are classified into two types: labeled, which have either strong or weak magnitudes, and unlabeled, which have in-between magnitudes. Both are connected to neighboring coefficients and belong to a low-dimensional manifold within the set of all wavelet coefficients. The decision to include a coefficient in the model depends not only on its magnitude but also on the labeled and the unlabeled coefficients from its neighborhood. We discuss the theoretical properties of the method and demonstrate its performance in simulated examples.