In many applications-latent semantic indexing, for example-it is required to obtain a reduced rank approximation to a sparse matrix A. Unfortunately, the approximations based on traditional decompositions, like the si...
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In many applications-latent semantic indexing, for example-it is required to obtain a reduced rank approximation to a sparse matrix A. Unfortunately, the approximations based on traditional decompositions, like the singular value and QR decompositions, are not in general sparse. Stewart [(1999), 313-323] has shown how to use a variant of the classical gram-schmidt algorithm, called the quasi-gram-schmidt-algorithm, to obtain two kinds of low-rank approximations. The first, the SPQR, approximation, is a pivoted, Q-less QR approximation of the form (XR11-1)(R-11 R-12), where X consists of columns of A. The second, the SCR approximation, is of the form the form A congruent to XTYT, where X and Y consist of columns and rows A and T, is small. In this article we treat the computational details of these algorithms and describe a MATLAB implementation.
We propose a new approach for recognizing human from images of low quality. An ortho-diffusion decomposition is used on graph representations of images. This is implemented by a recursive algorithm in three steps on e...
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ISBN:
(纸本)9781479983407
We propose a new approach for recognizing human from images of low quality. An ortho-diffusion decomposition is used on graph representations of images. This is implemented by a recursive algorithm in three steps on either the covariance matrix or on the correlation of the training set. The first stage consists of an orthonormal decomposition implemented through the modified gram-schmidt with pivoting the columns. The other two stages consists of the data reduction and diffusion on graph representations. The data reduction ensures that the most significant features are preserved and together with the diffusion step ensures robustness to a variety of data corruption factors. The proposed methodology produces a set of ortho-diffusion bases representing the quintessential information from the training data set. The resulting orhto-diffusion bases are used to model face images when considering low resolution and corruption by various noise distributions.
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