Robust Low-Rank Matrix Recovery as Mixed Integer Programming via $\ell _{0}$-Norm Optimization

Shi, Zhang-Lei; Li, Xiao Peng; Li, Weiguo; Yan, Tongjiang; Wang, Jian; Fu, Yaru

doi:10.1109/lsp.2023.3301244

Cited by 4 publications

(1 citation statement)

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“…To realize the rule selection (RS), the Group Lasso regularization is added to the objective function. Compared with other Lasso regularization [35][36][37], it can induce row or column sparsity, thus producing sparsity of rules in a grouped manner, which provides the possibility for rule selection [38]. Therefore, the following objective function of each SFNN-1 contains two parts, that is, the mean square error (MSE) and the Group Lasso penalty term:…”

Section: First-order Sparse Tsk Nonstationary Fuzzy Neural Network (S...mentioning

confidence: 99%

First-Order Sparse TSK Nonstationary Fuzzy Neural Network Based on the Mean Shift Algorithm and the Group Lasso Regularization

Zhang,

Wang,

Gong

et al. 2023

Mathematics

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Nonstationary fuzzy inference systems (NFIS) are able to tackle uncertainties and avoid the difficulty of type-reduction operation. Combining NFIS and neural network, a first-order sparse TSK nonstationary fuzzy neural network (SNFNN-1) is proposed in this paper to improve the interpretability/translatability of neural networks and the self-learning ability of fuzzy rules/sets. The whole architecture of SNFNN-1 can be considered as an integrated model of multiple sub-networks with a variation in center, variation in width or variation in noise. Thus, it is able to model both “intraexpert” and “interexpert” variability. There are two techniques adopted in this network: the Mean Shift-based fuzzy partition and the Group Lasso-based rule selection, which can adaptively generate a suitable number of clusters and select important fuzzy rules, respectively. Quantitative experiments on six UCI datasets demonstrate the effectiveness and robustness of the proposed model.

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