Manifold learning has been widely used for dimensionality reduction and feature extraction of data recently. However, in the application of the related algorithms, it often suffers from noisy or unreliable data problems. For example, when the sample data have complex background, occlusions, and/or illuminations, the clustering of data is still a challenging task. To address these issues, we propose a family of novel algorithms for manifold regularized non-negative matrix factorization in this paper. In the algorithms, based on the alpha-beta-divergences, graph regularization with multiple segments is utilized to constrain the data transitivity in data decomposition. By adjusting two tuning parameters, we show that the proposed algorithms can significantly improve the robustness with respect to the images with complex background. The efficiency of the proposed algorithms is confirmed by the experiments on four different datasets. For different initializations and datasets, variations of cost functions and decomposition data elements in the learning are presented to show the convergent properties of the algorithms.