Improving approximate inverses based on Frobenius norm minimization

[EN]Approximate inverses, based on Frobenius norm minimization, of real nonsingular matrices are analyzed from a purely theoretical point of view. In this context, this paper provides several sufficient conditions, that assure us the possibility of improving (in the sense of the Frobenius norm) some given approximate inverses. Moreover, the optimal approximate inverses of matrix A ∈ R n×n , among all matrices belonging to certain subspaces of R n×n , are obtained. Particularly, a natural generalization of the classical normal equations of the system Ax = b is given, when searching for approximate inverses N 6= AT such that AN is symmetric and kAN − IkF < AAT − I F …

Robust Tensor Analysis With L1-Norm

Tensor analysis plays an important role in modern image and vision computing problems. Most of the existing tensor analysis approaches are based on the Frobenius norm, which makes them sensitive to outliers. In this paper, we propose L1-norm-based tensor analysis (TPCA-L1), which is robust to outliers. Experimental results upon face and other datasets demonstrate the advantages of the proposed approach.

Robust tensor analysis with L1-norm

Tensor analysis plays an important role in modern image and vision computing problems. Most of the existing tensor analysis approaches are based on the Frobenius norm, which makes them sensitive to outliers. In this paper, we propose L1-norm-based tensor analysis (TPCA-L1), which is robust to outliers. Experimental results upon face and other datasets demonstrate the advantages of the proposed approach. © 2006 IEEE.

Improved image set classification via joint sparse approximated nearest subspaces

Existing multi-model approaches for image set classification extract local models by clustering each image set individually only once, with fixed clusters used for matching with other image sets. However, this may result in the two closest clusters to represent different characteristics of an object, due to different undesirable environmental conditions (such as variations in illumination and pose). To address this problem, we propose to constrain the clustering of each query image set by forcing the clusters to have resemblance to the clusters in the gallery image sets. We first define a Frobenius norm distance between subspaces over Grassmann manifolds based on reconstruction error. We then extract local linear subspaces from a gallery image set via sparse representation. For each local linear subspace, we adaptively construct the corresponding closest subspace from the samples of a probe image set by joint sparse representation. We show that by minimising the sparse representation reconstruction error, we approach the nearest point on a Grassmann manifold. Experiments on Honda, ETH-80 and Cambridge-Gesture datasets show that the proposed method consistently outperforms several other recent techniques, such as Affine Hull based Image Set Distance (AHISD), Sparse Approximated Nearest Points (SANP) and Manifold Discriminant Analysis (MDA).

Topics in randomized numerical linear algebra

This thesis studies three classes of randomized numerical linear algebra algorithms, namely: (i) randomized matrix sparsification algorithms, (ii) low-rank approximation algorithms that use randomized unitary transformations, and (iii) low-rank approximation algorithms for positive-semidefinite (PSD) matrices.

Randomized matrix sparsification algorithms set randomly chosen entries of the input matrix to zero. When the approximant is substituted for the original matrix in computations, its sparsity allows one to employ faster sparsity-exploiting algorithms. This thesis contributes bounds on the approximation error of nonuniform randomized sparsification schemes, measured in the spectral norm and two NP-hard norms that are of interest in computational graph theory and subset selection applications.

Low-rank approximations based on randomized unitary transformations have several desirable properties: they have low communication costs, are amenable to parallel implementation, and exploit the existence of fast transform algorithms. This thesis investigates the tradeoff between the accuracy and cost of generating such approximations. State-of-the-art spectral and Frobenius-norm error bounds are provided.

The last class of algorithms considered are SPSD "sketching" algorithms. Such sketches can be computed faster than approximations based on projecting onto mixtures of the columns of the matrix. The performance of several such sketching schemes is empirically evaluated using a suite of canonical matrices drawn from machine learning and data analysis applications, and a framework is developed for establishing theoretical error bounds.

In addition to studying these algorithms, this thesis extends the Matrix Laplace Transform framework to derive Chernoff and Bernstein inequalities that apply to all the eigenvalues of certain classes of random matrices. These inequalities are used to investigate the behavior of the singular values of a matrix under random sampling, and to derive convergence rates for each individual eigenvalue of a sample covariance matrix.

A criterion for unitary similarity of upper triangular matrices in general position

Each square complex matrix is unitarily similar to an upper triangular matrix with diagonal entries in any prescribed order. Let A = [a(ij)] and B = [b(ij)] be upper triangular n x n matrices that are not similar to direct sums of square matrices of smaller sizes, or are in general position and have the same main diagonal. We prove that A and B are unitarily similar if and only if parallel to h(A(k))parallel to = parallel to h(B(k))parallel to for all h is an element of C vertical bar x vertical bar and k = 1, ..., n, where A(k) := [a(ij)](i.j=1)(k) and B(k) := [b(ij)](i.j=1)(k) are the leading principal k x k submatrices of A and B, and parallel to . parallel to is the Frobenius norm. (C) 2011 Elsevier Inc. All rights reserved.

Estabilidade, desempenho e observação de estado de sistemas chaveados afins: aplicações aos conversores CC-CC

Pós-graduação em Engenharia Elétrica - FEIS

A generalization of the Moore-Penrose inverse related to matrix subspaces of C(nxm)

[EN]A natural generalization of the classical Moore-Penrose inverse is presented. The so-called S-Moore-Penrose inverse of a m x n complex matrix A, denoted by As, is defined for any linear subspace S of the matrix vector space Cnxm. The S-Moore-Penrose inverse As is characterized using either the singular value decomposition or (for the nonsingular square case) the orthogonal complements with respect to the Frobenius inner product. These results are applied to the preconditioning of linear systems based on Frobenius norm minimization and to the linearly constrained linear least squares problem.

A generalization of the optimal diagonal approximate inverse preconditioner

[EN ]The classical optimal (in the Frobenius sense) diagonal preconditioner for large sparse linear systems Ax = b is generalized and improved. The new proposed approximate inverse preconditioner N is based on the minimization of the Frobenius norm of the residual matrix AM − I, where M runs over a certain linear subspace of n × n real matrices, defined by a prescribed sparsity pattern. The number of nonzero entries of the n×n preconditioning matrix N is less than or equal to 2n, and n of them are selected as the optimal positions in each of the n columns of matrix N. All theoretical results are justified in detail…

Data-driven impostor selection for T-norm score normalisation and the background dataset in SVM-based speaker verification

A data-driven background dataset refinement technique was recently proposed for SVM based speaker verification. This method selects a refined SVM background dataset from a set of candidate impostor examples after individually ranking examples by their relevance. This paper extends this technique to the refinement of the T-norm dataset for SVM-based speaker verification. The independent refinement of the background and T-norm datasets provides a means of investigating the sensitivity of SVM-based speaker verification performance to the selection of each of these datasets. Using refined datasets provided improvements of 13% in min. DCF and 9% in EER over the full set of impostor examples on the 2006 SRE corpus with the majority of these gains due to refinement of the T-norm dataset. Similar trends were observed for the unseen data of the NIST 2008 SRE.

Broad Bean Mottle Virus: Identification, Serology, Host Range, and Occurrence on Faba Bean (Vicia Faba) in West Asia and Norm Africa

One of the faba bean viruses found in West Asia and North Africa was identified as broad bean mottle virus (BBMV) by host reactions, particle morphology and size, serology, and granular, often vesiculated cytoplasmic inclusions. Detailed research on four isolates, one each from Morocco, Tunisia, Sudan and Syria, provided new information on the virus. The isolates, though indistinguishable in ELISA or gel-diffusion tests, differed slightly in host range and symptoms. Twenty-one species (12 legumes and 9 non-legumes) out of 27 tested were systemically infected, and 14 of these by all four isolates. Infection in several species was symptomless, but major legumes such as chickpea, lentil and especially pea, suffered severely from infection. All 23 genotypes of faba bean, 2 of chickpea, 4 of lentil, 11 out of 21 of Phaseolus bean, and 16 out of 17 of pea were systemically sensitive to the virus. Twelve plant species were found to be new potential hosts and cucumber a new local-lesion test plant of the virus. BBMV particles occurred in faba bean plants in very high concentrations and seed transmission in this species (1.37%) was confirmed. An isolate from Syria was purified and two antisera were produced, one of which was used in ELISA to detect BBMV in faba bean field samples. Two hundred and three out of the 789 samples with symptoms suggestive of virus infection collected in 1985, 1986 and 1987, were found infected with BBMV: 4 out of 70 (4/70) tested samples from Egypt, 0/44 from Lebanon, 1/15 from Morocco, 46/254 from Sudan, 72/269 from Syria and 80/137 from Tunisia. This is the first report on its occurrence in Egypt, Syria and Tunisia. The virus is a potential threat to crop improvement in the region.

The responsibility to protect and the Arab Spring : Libya as the exception, Syria as the norm?

On March 17 2011 the UN Security Council passed resolution 1973 authorising the use of force for civilian protection purposes in Libya.1 This resolution was hailed by many supporters of the responsibility to protect (R2P) as a crucial step towards the consolidation of the concept’s normative standing.2 Gareth Evans described the intervention as ‘a textbook case of the R2P norm working exactly as it was supposed to’.3 For Lloyd Axworthy the Libya episode signalled a move towards a ‘more humane world’.4 UN Secretary-General Ban Ki-Moon declared that it ‘affirms, clearly and unequivocally, the international community’s determination to fulfil its responsibility to protect civilians from violence perpetrated by their own government.’5 At first glance, the Security Council’s rapid, decisive response to escalating violence in Libya might well have suggested a new willingness on the part of the international community to take collective action to avert intra-state humanitarian crises. However, a closer examination of the text of resolution 1973 and statements by Security Council member states reveals a less than complete endorsement of R2P. Disagreements between states over the scope of the mandate for the use of force in Libya quickly emerged. Long-standing fears among Russia, China and other non-Western states that R2P could be used as a pretext for regime change returned to the fore as the legality and legitimacy of NATO’s military action were called into question. This post-Libya backlash against R2P has been a central factor in the international community’s subsequent inability to agree on effective civilian protection measures in Syria. Much of the optimism that surrounded R2P in the immediate aftermath of resolution 1973 has given way to a sober realization that achieving international consensus on civilian protection measures will rarely be straightforward.

Life-history constraints in grassland plant species : a growth-defence trade-off is the norm

Plant growth can be limited by resource acquisition and defence against consumers, leading to contrasting trade-off possibilities. The competition-defence hypothesis posits a trade-off between competitive ability and defence against enemies (e.g. herbivores and pathogens). The growth-defence hypothesis suggests that strong competitors for nutrients are also defended against enemies, at a cost to growth rate. We tested these hypotheses using observations of 706 plant populations of over 500 species before and following identical fertilisation and fencing treatments at 39 grassland sites worldwide. Strong positive covariance in species responses to both treatments provided support for a growth-defence trade-off: populations that increased with the removal of nutrient limitation (poor competitors) also increased following removal of consumers. This result held globally across 4 years within plant life-history groups and within the majority of individual sites. Thus, a growth-defence trade-off appears to be the norm, and mechanisms maintaining grassland biodiversity may operate within this constraint.

Epithelial-mesenchymal interconversions in normal ovarian surface epithelium and ovarian carcinomas : an exception to the norm

Cancer that arises from the ovarian surface epithelium (OSE) accounts for approximately 90% of human ovarian cancer, and is the fourth leading cause of cancer-related deaths among women in developed countries. The pathophysiology of epithelial ovarian cancer is still unclear because of the poor understanding of the complex nature of its development and the unusual mechanism(s) of disease progression. Recent studies have reported epithelial-mesenchymal transition (EMT) in cultured OSE and ovarian cancer cell lines in response to various stimuli, but our understanding of the importance of these observations for normal ovarian physiology and cancer progression is not well established. This review highlights the current literature on EMT-associated events in normal OSE and ovarian cancer cell lines, and discusses its implication for normal ovarian function as well as acquisition of neoplastic phenotypes. The pathological changes in OSE in response to EMT during neoplastic transformation and the contribution of hormones, growth factors, and cytokines that initiate and drive EMT to sustain normal ovarian function, as well as cancer development and progression are also discussed. Finally, emphasis is placed on the clinical implications of EMT and potential therapeutic opportunities that may arise from these observations have been proposed.