Data-Driven Optimal Shrinkage of Singular Values under High-Dimensional Noise with Separable Covariance Structure

We develop a data-driven optimal shrinkage algorithm for matrix denoising in the presence of high-dimensional noise with separable covariance structure; that is, the nose is colored and dependent. The algorithm, coined extended OptShrink (eOptShrink), involves a new imputation and rank estimation and we do not need to estimate the separable covariance structure of the noise. On the theoretical side, we study the asymptotic behavior of singular values and singular vectors of the random matrix associated with the noisy data, including the sticking property of non-outlier singular values and delocalization of the non-outlier singular vectors with a convergence rate. We apply these results to establish the guarantee of the imputation, rank estimation and eOptShrink algorithm with a convergence rate. On the application side, in addition to a series of numerical simulations with a comparison with various state-of-the-art optimal shrinkage algorithms, we apply eOptShrink to extract fetal electrocardiogram from the single channel trans-abdominal maternal electrocardiogram.Comment: arXiv admin note: text overlap with arXiv:1905.13060 by other author

Assessment of thermal-stable polymer nanocomposite techniques by patent citation network analysis

Nanocomposite material with new functions or properties superior to traditional composite materials opens a door to transform the way that material is currently applied. This study aims to provide 1) a systematic and quantitative method for obtaining global patent overview, 2) a global patent-citation overview on thermal-stable polymer nanocomposite patents retrieved from the United States Patent and Trademark Office (USPTO). The systematic method provided in this paper is integration of basic patent statistics, technology-function classification, standard industrial classification, patent citation and network properties calculation. All of these contribute not only to a systematic approach for obtaining a quantitative overview of large amount of selected patents, but also bridge the gap between patented techniques and business management activities, e.g. R&D resource allocation, performance evaluation, patent map visualization, patent valuation, in business and industry.<br

A new regularized least squares support vector regression for gene selection

<p>Abstract</p> <p>Background</p> <p>Selection of influential genes with microarray data often faces the difficulties of a large number of genes and a relatively small group of subjects. In addition to the curse of dimensionality, many gene selection methods weight the contribution from each individual subject equally. This equal-contribution assumption cannot account for the possible dependence among subjects who associate similarly to the disease, and may restrict the selection of influential genes.</p> <p>Results</p> <p>A novel approach to gene selection is proposed based on kernel similarities and kernel weights. We do not assume uniformity for subject contribution. Weights are calculated via regularized least squares support vector regression (RLS-SVR) of class levels on kernel similarities and are used to weight subject contribution. The cumulative sum of weighted expression levels are next ranked to select responsible genes. These procedures also work for multiclass classification. We demonstrate this algorithm on acute leukemia, colon cancer, small, round blue cell tumors of childhood, breast cancer, and lung cancer studies, using kernel Fisher discriminant analysis and support vector machines as classifiers. Other procedures are compared as well.</p> <p>Conclusion</p> <p>This approach is easy to implement and fast in computation for both binary and multiclass problems. The gene set provided by the RLS-SVR weight-based approach contains a less number of genes, and achieves a higher accuracy than other procedures.</p

Association between chronic viral hepatitis infection and breast cancer risk: a nationwide population-based case-control study

<p>Abstract</p> <p>Background</p> <p>In Taiwan, there is a high incidence of breast cancer and a high prevalence of viral hepatitis. In this case-control study, we used a population-based insurance dataset to evaluate whether breast cancer in women is associated with chronic viral hepatitis infection.</p> <p>Methods</p> <p>From the claims data, we identified 1,958 patients with newly diagnosed breast cancer during the period 2000-2008. A randomly selected, age-matched cohort of 7,832 subjects without cancer was selected for comparison. Multivariable logistic regression models were constructed to calculate odds ratios of breast cancer associated with viral hepatitis after adjustment for age, residential area, occupation, urbanization, and income. The age-specific (<50 years and ≥50 years) risk of breast cancer was also evaluated.</p> <p>Results</p> <p>There were no significant differences in the prevalence of hepatitis C virus (HCV) infection, hepatitis B virus (HBV), or the prevalence of combined HBC/HBV infection between breast cancer patients and control subjects (<it>p </it>= 0.48). Multivariable logistic regression analysis, however, revealed that age <50 years was associated with a 2-fold greater risk of developing breast cancer (OR = 2.03, 95% CI = 1.23-3.34).</p> <p>Conclusions</p> <p>HCV infection, but not HBV infection, appears to be associated with early onset risk of breast cancer in areas endemic for HCV and HBV. This finding needs to be replicated in further studies.</p

極端水文事件土砂量對陳有蘭溪河川型態演變影響分析

The total sediment yield from the 1999 Chichi earthquake to Typhoon Morakot in 2009 in the Chenyoulan River watershed is around 158.1×106 m3. The excess sediment yield has resulted in serious sediment deposition, widening river width and river meandering in the Chenyoulan River. By comparison of DEMs from 2004 and 2010, sediment deposits are obvious at the convergences of the tributaries and the in main river. Especially apparent are the deposited depth of 2.9 m at the convergence of the Junkeng River and the main river and the deposited depth of 2.6 m at the convergence of the Shibachong River and the main river. The serious sediment deposition has also resulted in river meandering and serious scouring upstream from the convergence of the Shibachong River and the main river, and widening river width and scouring in the main channel downstream from the convergence of the Shibachong River and the main river.陳有蘭溪集水區由1999 年集集地震至2009 年莫拉克颱風約產生158.1×106 m3 土砂量，巨量土砂產出在主河段造成河段淤積、拓寬及擺盪；以2004 年及2010 年DEM 比較結果，支流匯入溪處是主要土砂堆積處，又以郡坑溪匯入處之淤積2.9 m 及十八重溪匯入處之淤積2.6m 為最；受土砂淤積影響，在十八重溪上游匯入處上游河段以河道擺盪及河岸淘刷為主，在十八重溪匯入處下游河段則以河道拓寬及主深槽刷深為主