Dimensionality Reduction via Regression in Hyperspectral Imagery
Dimensionality Reduction via Regression in Hyperspectral Imagery
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DOI：
10.1109/jstsp.2015.2417833
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发表时间：
2015-09-01
影响因子：
7.5
通讯作者：
Camps-Valls, Gustau
中科院分区：
文献类型：
--
作者：
Laparra, Valero;Malo, Jesus;Camps-Valls, Gustau
提出了一种新的无监督回归降维方法。该算法属于可逆变换家族，通过使用曲线而不是线性特征来推广主成分分析（PCA）。DRR通过多元回归识别非线性特征，以确保PCA系数之间的冗余减少，分数方差的减少以及重建误差的减少。更重要的是，与其他非线性降维方法不同，可逆性，体积保持和直接的样本外扩展使得DRR具有可解释性和易于应用。DRR的性质使学习更广泛的一类数据流形比最近提出的非线性主成分分析（NLPCA）和主多项式分析（PPA）。我们说明了表现在减少遥感数据的维数。特别是，我们解决两个常见的问题：处理非常高维的光谱信息，如在高光谱图像探测数据，和处理多光谱图像的空间光谱图像补丁。这两种设置造成共线性和不确定性问题。的功能的表达能力的评价进行评估截断误差，估计大气变量，地表土地覆盖分类误差。结果表明，DRR优于线性PCA和最近提出的基于神经网络（NLPCA）和单变量回归（PPA）的可逆扩展。
This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize principal component analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between the PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservation, and straightforward out-of-sample extension, makes DRR interpretable and easy to apply. The properties of DRR enable learning a more broader class of data manifolds than the recently proposed non-linear principal components analysis (NLPCA) and principal polynomial analysis (PPA). We illustrate the performance of the representation in reducing the dimensionality of remote sensing data. In particular, we tackle two common problems: processing very high dimensional spectral information such as in hyperspectral image sounding data, and dealing with spatial-spectral image patches of multispectral images. Both settings pose collinearity and ill-determination problems. Evaluation of the expressive power of the features is assessed in terms of truncation error, estimating atmospheric variables, and surface land cover classification error. Results show that DRR outperforms linear PCA and recently proposed invertible extensions based on neural networks (NLPCA) and univariate regressions (PPA).