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16th International Conference on Computer Analysis of Images and Patterns (CAIP)

作者： Gudivada, Sravan Bors, Adrian G. Univ York Dept Comp Sci York YO10 5GH N Yorkshire England

ISBN: (纸本)9783319231921;9783319231914

This paper describes a new classification method based on modeling data by embedding diffusions into orthonormal decompositions of graph-based data representations. The training data is represented by an adjacency matrix calculated using either the correlation or the covariance of the training set. The application of the modified gram-schmidt orthonormal decomposition alternating with diffusion and data reduction stages, is applied recursively at each scale level. The diffusion process is strengthening the representation pattern of representative features. Meanwhile, noise is removed together with non-essential detail during the data reduction stage. The proposed methodology is shown to be robust when applied to face recognition considering low image resolution and corruption by various types of noise.

关键词： Ortho-diffusion decompositions gram-schmidt algorithm Robust face recognition

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ORTHO-DIFFUSION DECOMPOSITIONS FOR FACE RECOGNITION FROM LOW QUALITY IMAGES

ORTHO-DIFFUSION DECOMPOSITIONS FOR FACE RECOGNITION FROM LOW...

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IEEE International Conference on Image Processing (ICIP)

作者： Gudivada, Sravan Bors, Adrian G. Univ York Dept Comp Sci York YO10 5GH N Yorkshire England

ISBN: (纸本)9781479983391

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.

关键词： gram-schmidt algorithm diffusion wavelets robust face recognition

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ORTHO-DIFFUSION DECOMPOSITIONS FOR FACE RECOGNITION FROM LOW QUALITY IMAGES

ORTHO-DIFFUSION DECOMPOSITIONS FOR FACE RECOGNITION FROM LOW...

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IEEE International Conference on Image Processing

作者： Sravan Gudivada Adrian G. Bors Department of Computer Science University of York

ISBN: (纸本)9781479983407

关键词： gram-schmidt algorithm Diffusion wavelets Robust face recognition Facial Recognition Graph representations images data reduction Face variance covariance matrix Recursive algorithms vandalism corruption Ensure data corruption diffusion

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Simple precoding algorithms using gram-schmidt orthonormalization process for multiuser relay communications with optimized power allocation

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ANNALS OF TELECOMMUNICATIONS 2013年第5-6期68卷 247-266页

作者： Meghdadi, Hamid Cances, Jean-Pierre Meghdadi, Vahid Univ Limoges ENSIL C2S2 XlimESTECNRSUMR 6172 F-87068 Limoges France

This paper proposes a new simple precoding solution based on the gram-schmidt orthonormalization to be used at the relay station of a multirelay wireless networks where the different mobile stations belong to the same network, in order to mitigate the multiuser interference at each mobile station. The strength of this method is that it only requires the knowledge of all channel impulse responses from a given relay to all the mobile stations. In other words, to compute its precoding vectors, each relay does not need to know the channel impulse responses of the channels of other relays. Unlike the centralized reference method where each mobile station benefits from the same diversity gain, using this algorithm, some mobile stations will improve their diversity gain at the cost of a loss in the diversity gain of other users. This constitutes a simple solution to supply different qualities of service in the case of a multiservices network. Furthermore, this work proposes an optimized power allocation between the relays. Analytical and accurate performance analyses for the different studied contexts are provided.

关键词： Cooperative diversity gain gram-schmidt algorithm Multiuser interference mitigation Expectation maximization Power allocation optimization

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SLOW INVARIANT MANIFOLDS AS CURVATURE OF THE FLOW OF DYNAMICAL SYSTEMS

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INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 2008年第11期18卷 3409-3430页

作者： Ginoux, Jean-Marc Rossetto, Bruno Chua, Leon O. Univ Sud Lab PROTEE IUT Toulon F-83957 La Garde France Univ Calif Berkeley Dept EECS Berkeley CA 94720 USA

Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e. the curvature of the trajectory curves of any n-dimensional dynamical system directly provides its slow manifold analytical equation the invariance of which will be then proved according to Darboux theory. Thus, it will be stated that the flow curvature method, which uses neither eigenvectors nor asymptotic expansions but only involves time derivatives of the velocity vector field, constitutes a general method simplifying and improving the slow invariant manifold analytical equation determination of high-dimensional dynamical systems. Moreover, it will be shown that this method generalizes the Tangent Linear System Approximation and encompasses the so-called Geometric Singular Perturbation Theory. Then, slow invariant manifolds analytical equation of paradigmatic Chua's piecewise linear and cubic models of dimensions three, four and five will be provided as tutorial examples exemplifying this method as well as those of high-dimensional dynamical systems.

关键词： Differential geometry curvature torsion gram-schmidt algorithm Darboux invariant

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Error analysis of the quasi-gram-schmidt algorithm

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SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS 2005年第2期27卷 493-506页

作者： Stewart, GW Univ Maryland Dept Comp Sci College Pk MD 20742 USA Univ Maryland Inst Adv Comp Studies College Pk MD 20742 USA

Let the n x p ( n >= p) matrix X have the QR factorization X = QR, where R is an upper triangular matrix of order p and Q is orthonormal. This widely used decomposition has the drawback that Q is not generally sparse even when X is. One cure is to discard Q, retaining only X and R. Products like a = Q(T)y = R(-T)X(T)y can then be formed by computing b = X(T)y and solving the system R(T)a = b. This approach can be used to modify the gram-schmidt algorithm for computing Q and R to compute R without forming Q or altering X. Unfortunately, this quasi-gram-schmidt algorithm can produce inaccurate results. In this paper it is shown that with reorthogonalization the inaccuracies are bounded under certain natural conditions.

关键词： gram-schmidt algorithm sparse matrix QR factorization orthogonalization rounding-error analysis

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BLOCK gram-schmidt ORTHOGONALIZATION

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SIAM JOURNAL ON SCIENTIFIC COMPUTING 2008年第1期31卷 761-775页

作者： Stewart, G. W. Univ Maryland Dept Comp Sci College Pk MD 20742 USA Univ Maryland Inst Adv Comp Studies College Pk MD 20742 USA

The classical gram-schmidt algorithm for computing the QR factorization of a matrix X requires at least one pass over the current orthogonalized matrix Q as each column of X is added to the factorization. When Q becomes so large that it must be maintained on a backing store, each pass involves the costly transfer of data from the backing store to main memory. However, if one orthogonalizes the columns of X in blocks of m columns, the number of passes is reduced by a factor of 1/m. Moreover, matrix-vector products are converted into matrix-matrix products, allowing level-3 BLAS cache performance. In this paper we derive such a block algorithm and give some experimental results that suggest it can be quite effective for large scale problems, even when the matrix X is rank degenerate.

关键词： orthogonalization gram-schmidt algorithm blocked algorithm QR factorization

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How many entries of a typical orthogonal matrix can be approximated by independent normals?

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ANNALS OF PROBABILITY 2006年第4期34卷 1497-1529页

作者： Jiang, Tiefeng Univ Minnesota Minneapolis MN 55455 USA

We solve an open problem of Diaconis that asks what are the largest orders of p(n) and q(n) such that Z(n), the p(n) x q(n) upper left block of a random matrix Gamma(n) which is uniformly distributed on the orthogonal group O(n), can be approximated by independent standard normals? This problem is solved by two different approximation methods. First, we show that the variation distance between the joint distribution of entries of Z(n) and that of p(n)q(n) independent standard normals goes to zero provided p(n) = o(root n) and q(n) = o(root n). We also show that the above variation distance does not go to zero if p(n) = [x root n] and q(n) = [y root n] for any positive numbers x and y. This says that the largest orders of p(n) and q(n) are o(n(1/2)) in the sense of the above approximation. Second, suppose Gamma(n) = (y(ij))(nxn) is generated by performing the gram-schmidt algorithm on the columns of Y-n = (y(ij))(nxn), where {y(ij);1 <= i, j <= n} are i.i.d. standard normals. We show that epsilon(n)(m) : = max(1 <= i <= n,1 <= j <= m)vertical bar root n center dot y(ij) - y(ij)vertical bar goes to zero in probability as long as m = m(n) = o(n/log n). We also prove that epsilon(n) (m(n)) -> 2 root alpha in probability when m(n) = [n alpha/log n] for any alpha > 0. This says that m(n) = o(n/log n) is the largest order such that the entries of the first m(n) columns of Gamma(n) can be approximated simultaneously by independent standard normals.

关键词： Haar measure gram-schmidt algorithm large deviation maxima product distribution random matrix theory variation distance

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algorithm 844: Computing sparse reduced-rank approximations to sparse matrices

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2005年第2期31卷 252-269页

作者： Berry, MW Pulatova, SA Stewart, GW Univ Tennessee Dept Comp Sci Knoxville TN 37996 USA Univ Maryland Dept Comp Sci College Pk MD 20742 USA Univ Maryland Inst Adv Comp Studies College Pk MD 20742 USA

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.

关键词： algorithms sparse approximations gram-schmidt algorithm MATLAB

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When modified gram-schmidt generates a well-conditioned set of vectors

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IMA JOURNAL OF NUMERICAL ANALYSIS 2002年第4期22卷 521-528页

作者： Giraud, L Langou, J CERFACS F-31057 Toulouse 1 France

In this paper, we show why the modified gram-schmidt algorithm generates a well-conditioned set of vectors. This result holds under the assumption that the initial matrix is not 'too ill-conditioned' in a way that is quantified. As a consequence we show that if two iterations of the algorithm are performed, the resulting algorithm produces a matrix whose columns are orthogonal up to machine precision. Finally, we illustrate through a numerical experiment the sharpness of our result.

关键词： gram-schmidt algorithm orthogonalization schemes floating point arithmetic

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