Chen Li

Junhang Li, Jiao Wei, Can Tong et al.

Traditional nonnegative matrix factorization (NMF) learns a new feature representation on the whole data space, which means treating all features equally. However, a subspace is often sufficient for accurate representation in practical applications, and redundant features can be invalid or even harmful. For example, if a camera has some sensors destroyed, then the corresponding pixels in the photos from this camera are not helpful to identify the content, which means only the subspace consisting of remaining pixels is worthy of attention. This paper proposes a new NMF method by introducing adaptive weights to identify key features in the original space so that only a subspace involves generating the new representation. Two strategies are proposed to achieve this: the fuzzier weighted technique and entropy regularized weighted technique, both of which result in an iterative solution with a simple form. Experimental results on several real-world datasets demonstrated that the proposed methods can generate a more accurate feature representation than existing methods. The code developed in this study is available at https://github.com/WNMF1/FWNMF-ERWNMF.

Tingting Shen, Junhang Li, Can Tong et al.

Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. However, the traditional NMF does not properly handle outliers, so that it is sensitive to noise. In order to improve the robustness of NMF, this paper proposes an adaptive weighted NMF, which introduces weights to emphasize the different importance of each data point, thus the algorithmic sensitivity to noisy data is decreased. It is very different from the existing robust NMFs that use a slow growth similarity measure. Specifically, two strategies are proposed to achieve this: fuzzier weighted technique and entropy weighted regularized technique, and both of them lead to an iterative solution with a simple form. Experimental results showed that new methods have more robust feature representation on several real datasets with noise than exsiting methods.

Tielang Gong, Yuxin Dong, Hong Chen et al.

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical behavior can be fundamental in learning theory. Despite significant progress in characterizing its statistical property, the majority of the results are based on the assumption that samples are independent and identical distributed (i.i.d.), which is too restrictive for real-world applications. This paper concerns the statistical property of regularized modal regression (RMR) within an important dependence structure - Markov dependent. Specifically, we establish the upper bound for RMR estimator under moderate conditions and give an explicit learning rate. Our results show that the Markov dependence impacts on the generalization error in the way that sample size would be discounted by a multiplicative factor depending on the spectral gap of underlying Markov chain. This result shed a new light on characterizing the theoretical underpinning for robust regression.