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This paper presents local spline regression for semi-supervised classification. The core idea in our approach is to introduce splines developed in Sobolev space to map the data points directly to be class labels. The spline is composed of polynomials and Green's functions. It is smooth, nonlinear, and able to interpolate the scattered data points with high accuracy. Specifically, in each neighborhood,...
In this paper, we propose a new nonlinear dimensionality reduction algorithm by adopting regularized least-square criterion on local areas of the data distribution. We first propose a local linear model to describe the characteristic of the low-dimensional coordinates of the neighborhood centered in each data point, and use regularized least-square criterion to evaluate the fitness of the low-dimensional...
We address the problem of blindly separating mixtures of multiple layer images with unknown spatial shifts and mixing coefficients. Our proposed method can handle the over-determined, determined and under-determined cases where mixtures are more than, as many as and fewer than layers, respectively. The method is fast in over-determined and determined cases, with the same complexity as the fast Fourier...
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