Abstract: The Concept Factorization (CF) algorithm can not take into account the label information and the multi-relationship of samples simultaneously. In this paper, a novel algorithm called Hyper-graph regularized Constrained Concept Factorization (HCCF) is proposed, which extracts the multi-geometry information of samples by constructing an undirected weighted hyper-graph Laplacian regularize term, hence overcomes the deficiency that traditional graph model expresses pair-wise relationship only. Meanwhile, HCCF takes full advantage of the label information of labeled samples as hard constraints, and it preserves label consistent in low-dimensional space. The objective function of HCCF is solved by the iterative multiplicative updating algorithm and its convergence is also proved. The experimental results on TDT2, Reuters, and PIE data sets show that the proposed approach achieves better clustering performance in terms of accuracy and normalized mutual information, and the effectiveness of the proposed approach is verified.