Discriminative and Orthogonal Subspace Constraints-Based Nonnegative Matrix Factorization

Multi-Modal Curriculum Learning over Graphs

Curriculum Learning (CL) is a recently proposed learning paradigm that aims to achieve satisfactory performance by properly organizing the learning sequence from simple curriculum examples to more difficult ones. Up to now, few works have been done to explore CL for the data with graph structure. Therefore, this article proposes a novel CL algorithm that can be utilized to guide the Label Propagation (LP) over graphs, of which the target is to “learn” the labels of unlabeled examples on the graphs. Specifically, we assume that different unlabeled examples have different levels of difficulty for propagation, and their label learning should follow a simple-to-difficult sequence with the updated curricula. Furthermore, considering that the practical data are often characterized by multiple modalities, every modality in our method is associated with a “teacher” that not only evaluates the difficulties of examples from its own viewpoint, but also cooperates with other teachers to generate the overall simplest curriculum examples for propagation. By taking the curriculums suggested by the teachers as a whole, the common preference (i.e., commonality) of teachers on selecting the simplest examples can be discovered by a row-sparse matrix, and their distinct opinions (i.e., individuality) are captured by a sparse noise matrix. As a result, an accurate curriculum sequence can be established and the propagation quality can thus be improved. Theoretically, we prove that the propagation risk bound is closely related to the examples’ difficulty information, and empirically, we show that our method can generate higher accuracy than the state-of-the-art CL approach and LP algorithms on various multi-modal tasks.