Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the ambient space. Thus, the information of the observational density is lost by the state-of-art LRR models, as they take a constant number of adjacent neighbors into account. This, as a result, degrades the subspace clustering accuracy in such situations. To cope with deficiency, in this paper, we propose to consider a hypergraph model to facilitate having a variable number of adjacent nodes and incorporating the locality information of the data. The sparsity of the number of subspaces is also taken into account. To do so, an optimization problem is defined based on a set of regularization terms and is solved by developing a tensor Laplacian-based algorithm. Extensive experiments on artificial and real datasets demonstrate the higher accuracy and precision of the proposed method in subspace clustering compared to the state-of-the-art methods. The outperformance of this method is more revealed in presence of inherent structure of the data such as nonlinearity, geometrical overlapping, and outliers.
翻译:低射线代表系统(LRR)在高度上由于丢弃了子空间组群中数据点的定位信息而蒙受了高度痛苦,因为它可能没有纳入数据结构非线性和环境空间观测分布不统一的情况,因此,最先进的LRR模型丢失了观测密度信息,因为它们考虑到相邻邻居的常数,从而降低了这类情况下的子空间群集的准确性。为了应对缺陷,我们在本文件中建议考虑一个高射模型,以便于拥有相邻节点的变量数并纳入数据的位置信息。还考虑到子空间数的广度。要做到这一点,一个优化问题是根据一套正规化条件来界定的,通过开发一个以数以拉多拉平方计为基础的算法来解决。关于人工和真实数据集的广泛实验表明,与最新方法相比,拟议中的子空间群集方法的准确性和准确性更高。这一方法的不完善性更多地表现在存在数据固有的结构上,例如非直线性、测量性、外径直径直径直等。