关键词: l₂图, 高维数据, 空间投影, 噪声, 子空间聚类

Abstract: With the advent of the era of big data,how to effectively cluster,analyze and effectively use massive amounts of high-dimensional data has become a hot research topic.When the traditional clustering algorithms are used to process high-dimensional data,the accuracy and stability of the clustering results are low.The subspace clustering algorithm can reduce the feature space of the original data to form different feature subsets,reduce the influence of uncorrelated features between data on clustering results.It can mine the information that is difficult to display in high-dimensional data,and has significant advantages in processing high-dimensional data.Aiming at the limitations of existing graph-based subspace clustering algorithms in dealing with unknown type noise and solving complex convex problems,based on subspace clustering algorithm,combined with spatial projection theory,this paper proposes a projection-based robust low-rank subspace clustering algorithm.Firstly,the original data is projected,the noise of the projection space is eliminated by coding and the missing data is compensated.Then a new method map is used to construct the sparse similarity l₂ graph,and finally the subspace clustering is performed on the basis of the l₂ graph.The algorithm does not need a priori knowledge of the type of noise,and the l₂ graph can well describe the characteristics of high-dimensional data sparsity and spatial dispersion.Three datasets of face recognition are selected as experimental datasets.Firstly,the optimal parameters affecting the clustering effect are determined,and then the algorithm is verified from three aspects:accuracy,robustness and time complexity.The experimental results show that the algorithm has high accuracy,low time complexity and good robustness,when the unknown type of noise is mixed in the datasets of face recognition.

Key words: l₂ graph, High dimensional data, Noise, Space projection, Subspace clustering