Incomplete observations in the data are always troublesome to data clustering algorithms. In fact, most of the well-received techniques are not designed to encounter such imperative scenarios. Hence, clustering of images under incomplete samples is an inquisitive yet unaddressed area of research. Therefore, the aim of this article is to design a single-stage optimization procedure for clustering as well as simultaneous reconstruction of images without breaking the intrinsic spatial structure. The method employs the self-expressiveness property of submodules, and images are stacked as the lateral slices of a three-dimensional tensor. The proposed optimization method is designed to extract a sparse t -linear combination tensor with low multirank constraint, consisting of a unique set of linear coefficients in the form of mode-3 fibers and the spectral clustering is performed on these fibers. Simultaneously, the recovery of lost samples is accomplished by twisting the entire lateral slices of the data tensor and applying a low-rank approximation on each slice. The prominence of the proposed method lies in the simultaneous execution of data clustering and reconstruction of incomplete observations in a single step. Experimental results reveal the excellence of the proposed method over state-of-the-art clustering algorithms in the context of incomplete imaging data.

中文翻译：

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用于不完整成像数据聚类和同时重建的统一张量框架

数据中的不完整观察对于数据聚类算法来说总是很麻烦。事实上，大多数广受欢迎的技术都不是为遇到这种命令式场景而设计的。因此，不完整样本下的图像聚类是一个好奇但尚未解决的研究领域。因此，本文的目的是在不破坏固有空间结构的情况下设计一种用于聚类和同时重建图像的单阶段优化程序。该方法利用子模块的自表达特性，将图像堆叠为三维张量的横向切片。所提出的优化方法旨在提取稀疏吨- 具有低多秩约束的线性组合张量，由模式 3 光纤形式的一组唯一线性系数组成，并且在这些光纤上执行光谱聚类。同时，通过扭曲数据张量的整个横向切片并在每个切片上应用低秩近似来完成丢失样本的恢复。所提出的方法的突出之处在于在一个步骤中同时执行数据聚类和重建不完整的观察。实验结果表明，在不完整的成像数据的情况下，所提出的方法优于最先进的聚类算法。