Dataset Information

Sparse Regression by Projection and Sparse Discriminant Analysis.

ABSTRACT: Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high dimensional data. The unique nature of this framework is that the directions of the regression coefficients are inferred first, and the lengths and the tuning parameters are determined by a cross validation procedure to achieve the largest prediction accuracy. We provide a theoretical result for simultaneous model selection consistency and parameter estimation consistency of our method in high dimension. This new framework is then generalized such that it can be applied to principal components analysis, partial least squares and canonical correlation analysis. We also adapt this framework for discriminant analysis. Compared to the existing methods, where there is relatively little control of the dependency among the sparse components, our method can control the relationships among the components. We present efficient algorithms and related theory for solving the sparse regression by projection problem. Based on extensive simulations and real data analysis, we demonstrate that our method achieves good predictive performance and variable selection in the regression setting, and the ability to control relationships between the sparse components leads to more accurate classification. In supplemental materials available online, the details of the algorithms and theoretical proofs, and R codes for all simulation studies are provided.

SUBMITTER: Qi X

PROVIDER: S-EPMC4560121 | biostudies-literature | 2015 Apr

REPOSITORIES: biostudies-literature

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Publications

Sparse Regression by Projection and Sparse Discriminant Analysis.

Qi Xin X Luo Ruiyan R Carroll Raymond J RJ Zhao Hongyu H

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America 20150401 2

Recent years have seen active developments of various penalized regression methods, such as LASSO and elastic net, to analyze high dimensional data. In these approaches, the direction and length of the regression coefficients are determined simultaneously. Due to the introduction of penalties, the length of the estimates can be far from being optimal for accurate predictions. We introduce a new framework, regression by projection, and its sparse version to analyze high dimensional data. The uniq ...[more]

PMID: 26345204

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Project description:BackgroundComputed tomography (CT) is an advanced medical imaging technology. The images obtained by CT are helpful for improving diagnostic accuracy. Currently, CT is widely used in clinical settings for diagnosis and health examinations. However, full angle CT scanning has the disadvantage of causing radiation damage to the human body. Sparse angle projection CT scanning is the most effective way to minimize this damage, but the quality of the reconstructed image is reduced. Therefore, it is important to improve the reconstructed image quality produced by sparse angle projection.MethodsIn this paper, we focused on the algebraic reconstruction algorithm. To reduce the accumulation of random noise, we formulated a modified algebraic reconstruction algorithm. Firstly, the algebraic reconstruction algorithm was used to compute two consecutive results, and then the weighted sum of these two results was used to correct the reconstructed image, and an iterative result was obtained. Using this method, we aimed to reduce the noise accumulation caused by iteration.ResultsIn this study, 20 angle projections were used for the reconstruction. The experimental object was the Shepp-Logan phantom test image. The experiments were implemented under two conditions: without noise and with noise. The peak signal to noise ratio (PSNR) and the mean squared error (MSE) of the reconstructed image from projections without noise were 76.0896 and 0.0016, respectively. The PSNR and MSE of the reconstructed image from projections with noise were 75.8263 and 0.0017, respectively. The reconstructed performance was superior to the previous algebraic reconstruction algorithm.ConclusionsThe performance of the proposed method was superior to other algorithms, which confirms that noise accumulation caused by iteration can be effectively reduced by the weighted summation of two consecutive reconstruction results. Moreover, the reconstruction performance under noisy projection is superior to other algorithms, which demonstrates that the proposed method improves anti-noise performance.

Dataset Information

Sparse Regression by Projection and Sparse Discriminant Analysis.

Publications

Sparse Regression by Projection and Sparse Discriminant Analysis.

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