IEEE Trans Image Process. 2015 Dec;24(12):4934-42. doi: 10.1109/TIP.2015.2472280. Epub 2015 Aug 24.
A sparse principal component analysis (PCA) seeks a sparse linear combination of input features (variables), so that the derived features still explain most of the variations in the data. A group sparse PCA introduces structural constraints on the features in seeking such a linear combination. Collectively, the derived principal components may still require measuring all the input features. We present a joint group sparse PCA (JGSPCA) algorithm, which forces the basic coefficients corresponding to a group of features to be jointly sparse. Joint sparsity ensures that the complete basis involves only a sparse set of input features, whereas the group sparsity ensures that the structural integrity of the features is maximally preserved. We evaluate the JGSPCA algorithm on the problems of compressed hyperspectral imaging and face recognition. Compressed sensing results show that the proposed method consistently outperforms sparse PCA and group sparse PCA in reconstructing the hyperspectral scenes of natural and man-made objects. The efficacy of the proposed compressed sensing method is further demonstrated in band selection for face recognition.
稀疏主成分分析 (PCA) 寻求输入特征（变量）的稀疏线性组合，以便派生特征仍能解释数据中的大部分变化。群组稀疏 PCA 在寻求这种线性组合时对特征施加了结构约束。总体而言，导出的主成分可能仍需要测量所有输入特征。我们提出了一种联合群组稀疏 PCA (JGSPCA) 算法，该算法强制一组特征对应的基本系数共同稀疏。联合稀疏性确保完整基仅涉及输入特征的稀疏集，而群组稀疏性确保特征的结构完整性得到最大保留。我们在压缩高光谱成像和人脸识别问题上评估了 JGSPCA 算法。压缩感知结果表明，与稀疏 PCA 和群组稀疏 PCA 相比，该方法在重建自然和人造物体的高光谱场景方面表现始终更好。该压缩感知方法的有效性在人脸识别的波段选择中得到了进一步证明。
