用于成像分类的空间加权主成分分析
Spatially Weighted Principal Component Analysis for Imaging Classification.
作者信息
Guo Ruixin, Ahn Mihye, Zhu Hongtu
机构信息
Department of Biostatistics and Informatics, University of Colorado School of Public Health, University of North Carolina at Chapel Hill.
Department of Biostatistics and Biomedical Research Imaging Center, University of North Carolina at Chapel Hill.
出版信息
J Comput Graph Stat. 2015 Jan;24(1):274-296. doi: 10.1080/10618600.2014.912135.
The aim of this paper is to develop a supervised dimension reduction framework, called Spatially Weighted Principal Component Analysis (SWPCA), for high dimensional imaging classification. Two main challenges in imaging classification are the high dimensionality of the feature space and the complex spatial structure of imaging data. In SWPCA, we introduce two sets of novel weights including global and local spatial weights, which enable a selective treatment of individual features and incorporation of the spatial structure of imaging data and class label information. We develop an e cient two-stage iterative SWPCA algorithm and its penalized version along with the associated weight determination. We use both simulation studies and real data analysis to evaluate the finite-sample performance of our SWPCA. The results show that SWPCA outperforms several competing principal component analysis (PCA) methods, such as supervised PCA (SPCA), and other competing methods, such as sparse discriminant analysis (SDA).
本文的目的是开发一种用于高维成像分类的监督降维框架，称为空间加权主成分分析（SWPCA）。成像分类中的两个主要挑战是特征空间的高维性以及成像数据复杂的空间结构。在SWPCA中，我们引入了两组新颖的权重，包括全局和局部空间权重，这使得能够对各个特征进行选择性处理，并纳入成像数据的空间结构和类别标签信息。我们开发了一种高效的两阶段迭代SWPCA算法及其惩罚版本以及相关的权重确定方法。我们使用模拟研究和实际数据分析来评估SWPCA的有限样本性能。结果表明，SWPCA优于几种竞争的主成分分析（PCA）方法，如监督主成分分析（SPCA），以及其他竞争方法，如稀疏判别分析（SDA）。
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