Hyperspectral images (HSIs) are typical high-dimensional and complex data. As such, the clustering of HSIs is a challenging task. Out of the motivation to find the low-dimensional structure representation of the high-dimensional data, sparse subspace clustering (SSC) methods have been proposed in recent studies. Sparse representation is an important technique in SSC, which is aimed at obtaining the sparse coefficient matrix of the HSI data. Generally speaking, the acquisition of the sparse coefficient matrix is an ill-posed problem, and the existing methods introduce an extra condition as a regularization term to resolve it. However, the regularization parameter is determined manually, which is difficult and lacks self-adaptability. Hence, in this article, a multi-objective SSC method for hyperspectral imagery is proposed, which simultaneously optimizes the sparse term and the data fidelity term. In addition, the spatial structure information of the HSIs is often neglected in the processing model, and thus, a spatial prior term, as the third optimization objective function, is also tested in this article. As a result, there is no need to manually set a regularization parameter. Furthermore, by using the $l_{0}$ norm as the sparse term, this reduces the error caused by the convex relaxation of the other norms. In the proposed method, a multi-objective optimization model is first used to acquire the sparse coefficient matrix, in which a strategy for constructing the dictionary is proposed for more precise and efficient multi-objective optimization. In addition, a knee point-based selection method is utilized to automatically select the optimal sparse representation solution from the Pareto front. The adjacency matrix is then constructed according to the sparse coefficient matrix. Finally, a spectral clustering method is used to obtain clustering results. Experiments undertaken with four HSI data sets confirm the effectiveness of the proposed method.

中文翻译：

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高光谱图像的多目标稀疏子空间聚类

高光谱图像 (HSI) 是典型的高维复杂数据。因此，HSI 的聚类是一项具有挑战性的任务。出于寻找高维数据的低维结构表示的动机，最近的研究提出了稀疏子空间聚类（SSC）方法。稀疏表示是 SSC 中的一项重要技术，旨在获得 HSI 数据的稀疏系数矩阵。一般来说，稀疏系数矩阵的获取是一个不适定的问题，现有的方法引入了一个额外的条件作为正则化项来解决它。然而，正则化参数是手动确定的，难度大，缺乏自适应性。因此，在本文中，提出了一种用于高光谱图像的多目标 SSC 方法，同时优化稀疏项和数据保真度项。此外，HSI的空间结构信息在处理模型中经常被忽略，因此本文还测试了空间先验项作为第三个优化目标函数。因此，无需手动设置正则化参数。此外，通过使用 $l_{0}$ 范数作为稀疏项，这减少了由其他范数的凸松弛引起的误差。该方法首先采用多目标优化模型获取稀疏系数矩阵，提出了一种构建字典的策略，以实现更精确、更高效的多目标优化。此外，利用基于拐点的选择方法从帕累托前沿自动选择最佳稀疏表示解决方案。然后根据稀疏系数矩阵构造邻接矩阵。最后，使用谱聚类方法获得聚类结果。使用四个 HSI 数据集进行的实验证实了所提出方法的有效性。