560 research outputs found

    Multilevel approximate robust principal component analysis

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    Robust principal component analysis (RPCA) is currently the method of choice for recovering a low-rank matrix from sparse corruptions that are of unknown value and support by decomposing the observation matrix into low-rank and sparse matrices. RPCA has many applications including background subtraction, learning of robust subspaces from visual data, etc. Nevertheless, the application of SVD in each iteration of optimisation methods renders the application of RPCA challenging in cases when data is large. In this paper, we propose the first, to the best of our knowledge, multilevel approach for solving convex and non-convex RPCA models. The basic idea is to construct lower dimensional models and perform SVD on them instead of the original high dimensional problem. We show that the proposed approach gives a good approximate solution to the original problem for both convex and non-convex formulations, while being many times faster than original RPCA methods in several real world datasets

    Fast multilevel algorithms for compressive principal component pursuit

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    Recovering a low-rank matrix from highly corrupted measurements arises in compressed sensing of structured high-dimensional signals (e.g., videos and hyperspectral images among others). Robust principal component analysis (RPCA), solved via principal component pursuit (PCP), recovers a low-rank matrix from sparse corruptions that are of unknown value and support by decomposing the observation matrix into two terms: a low-rank matrix and a sparse one, accounting for sparse noise and outliers. In the more general setting, where only a fraction of the data matrix has been observed, low-rank matrix recovery is achieved by solving the compressive principal component pursuit (CPCP). Both PCP and CPCP are well-studied convex programs, and numerous iterative algorithms have been proposed for their optimisation. Nevertheless, these algorithms involve singular value decomposition (SVD) at each iteration, which renders their applicability challenging in the case of massive data. In this paper, we propose a multilevel approach for the solution of PCP and CPCP problems. The core principle behind our algorithm is to apply SVD in models of lower-dimensionality than the original one and then lift its solution to the original problem dimension. Hence, our methods rely on the assumption that the low rank component can be represented in a lower dimensional space. We show that the proposed algorithms are easy to implement, converge at the same rate but with much lower iteration cost. Numerical experiments on numerous synthetic and real problems indicate that the proposed multilevel algorithms are several times faster than their original counterparts, namely PCP and CPCP

    The Characteristics of Chronic Heart Failure in Rheumatoid Arthritis Review Article

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    <b><i>Review Article</b></i>In recent times there is an emerging evidence about the increased risk of cardiovascular disease (CVD) and rheumatic conditions. This review has been focused on the multiple relationships between rheumatoid arthritis (RA) and heart failure (HF) features.Cardiovascular (CV) system involvement is an extra-articular complication of RA and is a major cause of morbidity and mortality. All heart structures may be affected in RA and different clinical manifestations may be seen.HF is a complex clinical syndrome which represents universal end-stage of nearly every form of heart disease and has a poor prognosis. Patients with RA have almost 2-fold higher risk of HF development than non RA-subjects and this high risk is not explained entirely by traditional CV risk factors. RA patients with HF appear to have a more subtle presentation of HF, compared to HF patients without RA, while mortality from HF is significantly higher. In RA HF mostly is manifested by diastolic dysfunction (DD) which is revealed by echocardiography. In general, brain natriuretic peptide (BNP) is an important clinical and prognostic marker of HF, but there are no final data concerning its screening value in RA-subjects.Nevertheless, up to date HF is still being poorly revealed in most RA-patients, especially on early stages of the disease, which leads to HF treatment delay, thus contributing to mortality.These findings emphasize the role and need of further larger studies in this field, which will bring to early identification and treatment of RA-subjects with HF and a decrease in mortality rates
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