Robust Adaptive Graph Learning with Manifold Constraints for Subspace Clustering

Subspace clustering aims at grouping data into a number of partitions, which has become one of the most powerful tools to analyze and interpret big data, particularly for clustering high-dimensional data. Although a series of related approaches have been proposed, real data are often corrupted leading to the learned graph is inexact or unreliable. Meanwhile, constructing an informative graph is one of the most important steps, which can greatly affect the final performance of clustering approaches. To learn a robust graph, this paper presents a novel data representation approach called Robust Adaptive Graph Learning with Manifold Constraints (RAGLMC) for subspace clustering. RAGLMC introduces the l(2,1)-norm constraint on sparse coding coefficients for ensuring the learned coding coefficients would be optimal as adaptive graph weights. Moreover, in order to reduce the influence of noise points on the local structure in graph construction, we combine l(2,1)-norm with manifold constraints on the coding coefficients to learn a locality and smoothness representation. Therefore, the proposed approach can estimate the graph from data alone by using manifold constraint on coding coefficients, which is independent of a prior affinity matrix. Extensive experiments verify the effectiveness of the proposed approach over other state-of-the-art approaches.