ABSTRACT

Recently, sparse graph-based discriminant analysis (SGDA) and collaborative graph-based discriminant analysis (CGDA) have been developed for dimensionality reduction of hyperspectral imagery. In SGDA or CGDA, a graph is constructed by -norm minimization-based representation or -norm minimization-based representation, respectively, based on labeled samples. These two methods have shown success over traditional methods by reinforcing discriminative power, but are limited in within-class representation and distribution of representation coefficients. In order to preserve intrinsic geometrical structure of original data and improve the interpretability of the underlying graph, we propose an adaptive collaborative graph for discriminant analysis (ACGDA), which explicitly models the internal relationship among within-class pixels during graph construction. The proposed method couples distance-weighted Tikhonov regularization with -norm minimization-based representation, of which the coefficients are solutions to a closed-form expression. The graph adaptively adjusts the collaborative representation by using distance-weighted measurement, which produces stronger ability of discrimination. In addition, the graph weight matrix is designed in the form of a block-diagonal structure, reducing the computational cost and further improving discriminative power. The proposed approach is compared with several traditional and state-of-the-art methods on two benchmark datasets. Experimental results demonstrate that the proposed approach can yield superior classification performance.

摘要

最近，已经开发了基于稀疏图的判别分析（SGDA）和基于协作图的判别分析（CGDA）来减少高光谱图像的维数。在SGDA或CGDA中，通过-基于规范最小化的表示形式或 -norm最小化基于表示，分别基于标记的样本。这两种方法通过增强判别力已显示出优于传统方法的成功，但在类内表示和表示系数分布方面受到限制。为了保留原始数据的内在几何结构并提高基础图的可解释性，我们提出了一种用于判别分析的自适应协作图（ACGDA），该图明确地建模了图构建过程中类内像素之间的内部关系。所提出的方法将距离加权的Tikhonov正则化与-基于范数最小化的表示形式，其系数是闭合形式表达式的解。该图通过使用距离加权测量来自适应地调整协作表示，从而产生更强的区分能力。此外，图形权重矩阵以块对角线结构的形式设计，从而降低了计算成本并进一步提高了判别能力。在两个基准数据集上，将所提出的方法与几种传统的和最先进的方法进行了比较。实验结果表明，该方法可以产生更好的分类性能。