检索结果-内蒙古大学图书馆

sparse principal component analysis With Preserved Sparsity Pattern

IEEE TRANSACTIONS ON IMAGE PROCESSING 2019年第7期28卷 3274-3285页

作者： Seghouane, Abd-Krim Shokouhi, Navid Koch, Inge Univ Melbourne Dept Elect & Elect Engn Melbourne Vic 3010 Australia Univ Western Australia Dept Math & Stat Perth WA 6009 Australia

principal component analysis (PCA) is widely used for feature extraction and dimension reduction in pattern recognition and data analysis. Despite its popularity, the reduced dimension obtained from the PCA is difficult to interpret due to the dense structure of principal loading vectors. To address this issue, several methods have been proposed for sparse PCA, all of which estimate loading vectors with few non-zero elements. However, when more than one principal component is estimated, the associated loading vectors do not possess the same sparsity pattern. Therefore, it becomes difficult to determine a small subset of variables from the original feature space that have the highest contribution in the principal components. To address this issue, an adaptive block sparse PCA method is proposed. The proposed method is guaranteed to obtain the same sparsity pattern across all principal components. Experiments show that applying the proposed sparse PCA method can help improve the performance of feature selection for image processing applications. We further demonstrate that our proposed sparse PCA method can he used to improve the performance of blind source separation for functional magnetic resonance imaging data.

关键词： sparse principal component analysis structured sparsity group lasso

来源：评论

学校读者我要写书评

暂无评论

sparse principal component analysis for Natural Language Processing

引用

Annals of Data Science 2023年第1期10卷 25-41页

作者： Drikvandi, Reza Lawal, Olamide Department of Computing and Mathematics Manchester Metropolitan University Manchester United Kingdom

High dimensional data are rapidly growing in many different disciplines, particularly in natural language processing. The analysis of natural language processing requires working with high dimensional matrices of word embeddings obtained from text data. Those matrices are often sparse in the sense that they contain many zero elements. sparse principal component analysis is an advanced mathematical tool for the analysis of high dimensional data. In this paper, we study and apply the sparse principal component analysis for natural language processing, which can effectively handle large sparse matrices. We study several formulations for sparse principal component analysis, together with algorithms for implementing those formulations. Our work is motivated and illustrated by a real text dataset. We find that the sparse principal component analysis performs as good as the ordinary principal component analysis in terms of accuracy and precision, while it shows two major advantages: faster calculations and easier interpretation of the principal components. These advantages are very helpful especially in big data situations. © 2020, The Author(s).

关键词： Classification Dimensionality reduction Ensemble learning High dimensional data Natural language processing sparse principal component analysis

来源：评论

学校读者我要写书评

暂无评论

sparse principal component analysis by choice of norm

引用

JOURNAL OF MULTIVARIATE analysis 2013年第1期114卷 127-160页

作者： Qi, Xin Luo, Ruiyan Zhao, Hongyu Georgia State Univ Dept Math & Stat Atlanta GA 30303 USA Yale Univ Dept Epidemiol & Publ Hlth New Haven CT 06520 USA

Recent years have seen the developments of several methods for sparse principal component analysis due to its importance in the analysis of high dimensional data. Despite the demonstration of their usefulness in practical applications, they are limited in terms of lack of orthogonality in the loadings (coefficients) of different principal components, the existence of correlation in the principal components, the expensive computation needed, and the lack of theoretical results such as consistency in high-dimensional situations. In this paper, we propose a new sparse principal component analysis method by introducing a new norm to replace the usual norm in traditional eigenvalue problems, and propose an efficient iterative algorithm to solve the optimization problems. With this method, we can efficiently obtain uncorrelated principal components or orthogonal loadings, and achieve the goal of explaining a high percentage of variations with sparse linear combinations. Due to the strict convexity of the new norm, we can prove the convergence of the iterative method and provide the detailed characterization of the limits. We also prove that the obtained principal component is consistent for a single component model in high dimensional situations. As illustration, we apply this method to real gene expression data with competitive results. (C) 2012 Elsevier Inc. All rights reserved.

关键词： sparse principal component analysis High-dimensional data Uncorrelated or orthogonal principal components Iterative algorithm Consistency in high dimension

来源：评论

学校读者我要写书评

暂无评论

sparse principal component analysis with measurement errors

引用

JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2016年 175卷 87-99页

作者： Shi, Jianhong Song, Weixing Shanxi Normal Univ Sch Math & Comp Sci Linfen 041000 Shanxi Peoples R China Kansas State Univ Dept Stat Manhattan KS 66503 USA

Traditional principal component analysis often produces non-zero loadings, which makes it hard to interpret the principal components. This drawback can be overcome by the sparse principal component analysis procedures developed in the past decade. However, similar work has not been done when the random variables or vectors are contaminated with measurement errors. Simply applying the existing sparse principal component analysis procedure to the error-contaminated data might lead to biased loadings. This paper tries to modify an existing sparse principal component procedure to accommodate the measurement error setup. Similar to error-free cases, we show that the sparse principal component for the latent variables can be formulated as a bias-corrected lasso (elastic net) regression problem based on the observed surrogates, efficient algorithms are also developed to implement the procedure. Numerical simulation studies are conducted to illustrate the finite sample performance of the proposed method. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Lasso Elastic net sparse principal component analysis Measurement error Bias correction

来源：评论

学校读者我要写书评

暂无评论

sparse principal component analysis VIA VARIABLE PROJECTION

引用

SIAM JOURNAL ON APPLIED MATHEMATICS 2020年第2期80卷 977-1002页

作者： Erichson, N. Benjamin Zheng, Peng Manohar, Krithika Brunton, Steven L. Kutz, J. Nathan Aravkin, Aleksandr Y. Univ Calif Berkeley Dept Stat Berkeley CA 94720 USA Univ Washington Dept Appl Math Seattle WA 98195 USA Univ Washington Dept Mech Engn Seattle WA 98195 USA

sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating between distinct time scales. We demonstrate a robust and scalable SPCA algorithm by formulating it as a value-function optimization problem. This viewpoint leads to a flexible and computationally efficient algorithm. The approach can further leverage randomized methods from linear algebra to extend SPCA to the large-scale (big data) setting. Our proposed innovation also allows for a robust SPCA formulation which obtains meaningful sparse principal components in spite of grossly corrupted input data. The proposed algorithms are demonstrated using both synthetic and real world data, and show exceptional computational efficiency and diagnostic performance.

关键词： dimension reduction sparse principal component analysis randomized algorithms variable projection

来源：评论

学校读者我要写书评

暂无评论

sparse principal component analysis in medical shape modeling

Sparse principal component analysis in medical shape modelin...

引用

Medical Imaging 2006 Conference

作者： Sjostrand, Karl Stegmann, Mikkel B. Larsen, Rasmus Tech Univ Denmark Informat & Math Modelling Richard Petersens Plads DK-2800 Lyngby Denmark

ISBN: (纸本)0819464236

principal component analysis (PCA) is a widely used tool in medical image analysis for data reduction, model building, and data understanding and exploration. While PCA is a holistic approach where each new variable is a linear combination of all original variables, sparse PCA (SPCA) aims at producing easily interpreted models through sparse loadings, i.e. each new variable is a linear combination of a subset of the original variables. One of the aims of using SPCA is the possible separation of the results into isolated and easily identifiable effects. This article introduces SPCA for shape analysis in medicine. Results for three different data sets are given in relation to standard PCA and sparse PCA by simple thresholding of small loadings. Focus is on a recent algorithm for computing sparse principal components, but a review of other approaches is supplied as well. The SPCA algorithm has been implemented using Matlab and is available for download. The general behavior of the algorithm is investigated, and strengths and weaknesses are discussed. The original report on the SPCA algorithm argues that the ordering of modes is not an issue. We disagree on this point and propose several approaches to establish sensible orderings. A method that orders modes by decreasing variance and maximizes the sum of variances for all modes is presented and investigated in detail.

关键词： sparse principal component analysis PCA evaluation of principal components shape modeling corpus callosum

来源：评论

学校读者我要写书评

暂无评论

Clustering and feature selection using sparse principal component analysis

引用

OPTIMIZATION AND ENGINEERING 2010年第1期11卷 145-157页

作者： Luss, Ronny d'Aspremont, Alexandre Princeton Univ ORFE Dept Princeton NJ 08544 USA

In this paper, we study the application of sparse principal component analysis (PCA) to clustering and feature selection problems. sparse PCA seeks sparse factors, or linear combinations of the data variables, explaining a maximum amount of variance in the data while having only a limited number of nonzero coefficients. PCA is often used as a simple clustering technique and sparse factors allow us here to interpret the clusters in terms of a reduced set of variables. We begin with a brief introduction and motivation on sparse PCA and detail our implementation of the algorithm in d'Aspremont et al. (SIAM Rev. 49(3):434-448, 2007). We then apply these results to some classic clustering and feature selection problems arising in biology.

关键词： sparse principal component analysis Semidefinite programming Clustering Feature selection

来源：评论

学校读者我要写书评

暂无评论

Demixed sparse principal component analysis Through Hybrid Structural Regularizers

引用

IEEE ACCESS 2021年 9卷 103075-103090页

作者： Zhang, Yan Xu, Haoqing Southeast Univ Sch Comp Sci & Engn Nanjing 211189 Jiangsu Peoples R China Southeast Univ Sch Artificial Intelligence Nanjing 211189 Jiangsu Peoples R China

Recently, the sparse representation of multivariate data has gained great popularity in real-world applications like neural activity analysis. Many previous analyses for these data utilize sparse principal component analysis (SPCA) to obtain a sparse representation. However, l(0)-norm based SPCA suffers from non-differentiability and local optimum problems due to non-convex regularization. Additionally, extracting dependencies between task parameters and feature responses is essential for further analysis while SPCA usually generates components without demixing these dependencies. To address these problems, we propose a novel approach, demixed sparse principal component analysis (dSPCA), that relaxes the non-convex constraints into convex regularizers, e.g., l(1)-norm and nuclear norm, and demixes dependencies of feature response on various task parameters by optimizing the loss function with marginalized data. The sparse and demixed components greatly improve the interpretability of the multivariate data. We also develop a parallel proximal algorithm to accelerate the optimization for hybrid regularizers based on our method. We provide theoretical analyses for error bound and convergency. We apply our method on simulated datasets to evaluate its time cost, the ability to explain the demixed information, and the ability to recover sparsity for the reconstructed data. Finally, we successfully separate the neural activity into different task parameters like stimulus or decision, and visualize the demixed components based on the real-world dataset.

关键词： Task analysis principal component analysis Optimization Neurons Neural activity Decoding Matrix decomposition Dimensionality reduction sparse principal component analysis demixed principal component analysis parallel proximal algorithms

来源：评论

学校读者我要写书评

暂无评论

Projection algorithms for nonconvex minimization with application to sparse principal component analysis

引用

JOURNAL OF GLOBAL OPTIMIZATION 2016年第4期65卷 657-676页

作者： Hager, William W. Phan, Dzung T. Zhu, Jiajie Univ Florida Dept Math POB 118105 Gainesville FL 32611 USA IBM TJ Watson Res Ctr Yorktown Hts NY 10598 USA Boston Coll Dept Comp Sci Chestnut Hill MA 02167 USA

We consider concave minimization problems over nonconvex sets. Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where the Hessian approximation is a multiple of the identity. Convergence results are established. In numerical experiments arising in sparse principal component analysis, it is seen that the performance of the gradient projection algorithm is very similar to that of the truncated power method and the generalized power method. In some cases, the approximate Newton algorithm with a Barzilai-Borwein Hessian approximation and a nonmonotone line search can be substantially faster than the other algorithms, and can converge to a better solution.

关键词： sparse principal component analysis Gradient projection Nonconvex minimization Approximate Newton Barzilai-Borwein method

来源：评论

学校读者我要写书评

暂无评论

A novel super-resolution image and video reconstruction approach based on Newton-Thiele's rational kernel in sparse principal component analysis

引用

MULTIMEDIA TOOLS AND APPLICATIONS 2017年第7期76卷 9463-9483页

作者： He, Lei Tan, Jieqing Huo, Xing Xie, Chengjun Hefei Univ Technol Sch Comp & Informat Sch Math Hefei 230009 Peoples R China Chinese Acad Sci Inst Intelligent Machines Hefei Peoples R China

In this paper, we propose a new image and video sequences reconstruction approach, where the Newton-Thiele's vector valued rational interpolation is combined with the sparse principal component analysis. Through observation of the degraded model, the reconstruction scheme is performed by two steps. Firstly, the sparse principal component analysis and the linear minimum mean square-error estimation method are used to remove the noise from the degraded image. And then, the Newton-Thiele's vector valued rational interpolation is used to magnify the denoising result, by which the details and texture regions of image can be well preserved. By using this novel reconstruction model by Newton-Thiele's rational kernel in sparse principal component analysis, the final reconstructed results not only have good visual effect, but also have rich texture details. In order to show the effectiveness and robustness of the proposed method, we have done plenty of experiments on images and video sequences, and the experimental results show that the proposed method can produce better high-quality resolution results, as compared with the state-of-the-art methods.

关键词： Newton-thiele Super-resolution Linear minimum mean square-error estimation sparse principal component analysis

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：