Fast Low-Rank Matrix Learning with Nonconvex Regularization

Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better recovery performance. However, the resultant optimization problem is much more challenging. A very recent state-of-the-art is based on the proximal gradient algorithm. However, it requires an expensive full SVD in each proximal step. In this paper, we show that for many commonly-used nonconvex low-rank regularizers, a cutoff can be derived to automatically threshold the singular values obtained from the proximal operator. This allows the use of power method to approximate the SVD efficiently. Besides, the proximal operator can be reduced to that of a much smaller matrix projected onto this leading subspace. Convergence, with a rate of O(1/T) where T is the number of iterations, can be guaranteed. Extensive experiments are performed on matrix completion and robust principal component analysis. The proposed method achieves significant speedup over the state-of-the-art. Moreover, the matrix solution obtained is more accurate and has a lower rank than that of the traditional nuclear norm regularizer.Comment: Long version of conference paper appeared ICDM 201

Decoupling Representation and Classifier for Noisy Label Learning

Since convolutional neural networks (ConvNets) can easily memorize noisy labels, which are ubiquitous in visual classification tasks, it has been a great challenge to train ConvNets against them robustly. Various solutions, e.g., sample selection, label correction, and robustifying loss functions, have been proposed for this challenge, and most of them stick to the end-to-end training of the representation (feature extractor) and classifier. In this paper, by a deep rethinking and careful re-examining on learning behaviors of the representation and classifier, we discover that the representation is much more fragile in the presence of noisy labels than the classifier. Thus, we are motivated to design a new method, i.e., REED, to leverage above discoveries to learn from noisy labels robustly. The proposed method contains three stages, i.e., obtaining the representation by self-supervised learning without any labels, transferring the noisy label learning problem into a semisupervised one by the classifier directly and reliably trained with noisy labels, and joint semi-supervised retraining of both the representation and classifier. Extensive experiments are performed on both synthetic and real benchmark datasets. Results demonstrate that the proposed method can beat the state-of-the-art ones by a large margin, especially under high noise level