Robust Local Learning and Discriminative Concept Factorization for Data Representation

Concept factorization (CF), as a matrix factorization method, has been applied widely in obtaining an optimal data representation and has yielded impressive results. However, some shortcomings exist in the existing CF method. 1) The standard concept factorization uses the squared loss function that is sensitive to outlier points and noises. 2) The graph generated by the original data does not reflect the real geometric structure of the data distribution. 3) The discriminant information is ignored. Herein, we propose a novel method, called robust local learning and discriminative concept factorization (RLLDCF) for data representation. Specifically, RLLDCF adopts the ℓ
_2,1
-norm-based loss function to improve its robustness against noises and outliers, and exploits the discriminative information by local linear regression constraints. In addition, the method obtains the topology structure of the data distribution during learning rather than known a priori and fixed. Anew iterative multiplicative updating rule is derived to solve RLLDCF's objective function. The convergence of the optimization algorithm is proved both theoretically and empirically. Numerous experiments on both synthetic and real-world datasets are conducted, and the results indicate that our proposed method is significantly better than all the comparison methods, thus validating the effectiveness and robustness of RLLDCF.