The convex-concave minimax problem, also known as the saddle-point problem, has been extensively studied from various aspects including the algorithm design, convergence condition and complexity. In this paper, we pro...
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The convex-concave minimax problem, also known as the saddle-point problem, has been extensively studied from various aspects including the algorithm design, convergence condition and complexity. In this paper, we propose a generalized asymmetric forward-backward-adjoint algorithm (G-AFBA) to solve such a problem by utilizing both the proximal techniques and the extrapolation of primal-dual updates. Besides applying proximal primal-dual updates, G-AFBA enjoys a more relaxed convergence condition, namely, more flexible and possibly larger proximal stepsizes, which could result in significant improvements in numerical performance. We study the global convergence of G-AFBA as well as its sublinear convergence rate on both ergodic iterates and non-ergodic optimality error. The linear convergence rate of G-AFBA is also established under a calmness condition. By different ways of parameter and problem setting, we show that G-AFBA has close relationships with several well-established or new algorithms. We further propose an adaptive and a stochastic (inexact) versions of G-AFBA. Our numerical experiments on solving the robust principal component analysis problem and the 3D CT reconstruction problem indicate the efficiency of both the deterministic and stochastic versions of G-AFBA.
作者：
Chen, XiuhongZhu, XingyuJiangnan Univ
Sch Artificial Intelligence & Comp Sci Wuxi Jiangsu Peoples R China Jiangnan Univ
Jiangsu Key Lab Media Design & Software Technol Wuxi Jiangsu Peoples R China
Matrix regression model can directly take matrix data as input data, and its loss function is defined by left and right regression matrices. The spectral clustering-based matrix regression model can perform feature se...
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Matrix regression model can directly take matrix data as input data, and its loss function is defined by left and right regression matrices. The spectral clustering-based matrix regression model can perform feature selection for unsupervised images. However, the graph weight matrix used in the existing spectral clustering models is predefined, which is often inaccurate, especially for noisy images. Moreover, they do not consider the preservation of local structure of image samples in transformation space. To this end, we propose a nonnegative spectral clustering and adaptive graph-based matrix regression model for unsupervised image feature selection. This model can make the prediction label matrix as smooth as possible on the whole graph, and the graph weight matrix can be adaptively learned instead of being predefined as fixed matrix. Thus, the accurate local structure of the sample data is preserved in transformation space and the discriminative information of these pseudo class labels can be revealed. Finally, we devise an efficient optimization algorithm to solve the proposed problem and analyze the computational complexity and convergence of the algorithm. Some experimental results on several datasets also show the effectiveness and superiority of our proposed method.
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