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- W3201941059 abstract "Multinomial logistic regression (MLR) is a useful tool for solving multi-classification problems. The lq,0 (q⩾1) norm is an ideal regularization term for characterizing group sparsity in multinomial logistic regression and selecting important features in the high dimensional data. However, lq,0 regularized multinomial logistic regression (lq,0-MLR) is nonconvex, discontinuous, and NP-hard. Thus, most prior studies adopted a continuous approximation of the lq,0 norm. In this paper, we present a novel lq,0-proximal Newton algorithm (lq,0-PNA) to solve the lq,0-MLR. We first define a strong α-stationary point and prove that this point is a local minimizer of lq,0-MLR. We then convert such a point into a stationary equation and solve it by lq,0-PNA, which is a Newton-type method running on a group sparse subspace with a low computational cost. Furthermore, we establish a locally quadratic convergence of lq,0-PNA. Finally, numerical experiments on simulated and real data show the superiority of lq,0-PNA in terms of computational time and accuracy, when compared with six state-of-the-art solvers, especially for high dimensional data." @default.
- W3201941059 created "2021-10-11" @default.
- W3201941059 creator A5000919042 @default.
- W3201941059 creator A5070812231 @default.
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- W3201941059 date "2022-01-01" @default.
- W3201941059 modified "2023-09-27" @default.
- W3201941059 title "Multinomial logistic regression classifier via <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si64.svg><mml:mrow><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mi>q</mml:mi><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>-proximal Newton algorithm" @default.
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- W3201941059 doi "https://doi.org/10.1016/j.neucom.2021.10.005" @default.
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