A Sparse Optimal Scoring Model with Adherent Penalty  

基于依附惩罚的稀疏最优评分模型

作　　者：Hou Dandan Liu Yongjin 侯丹丹;刘勇进(福州大学数学与统计学院,福州350108)

机构地区：[1]School of Mathematics and Statistics,Fuzhou University,Fuzhou 350108,China

出　　处：《数学理论与应用》2024年第4期100-115,共16页Mathematical Theory and Applications

基　　金：supported by the National Natural Science Foundation of China(No.12271097);the Key Program of National Science Foundation of Fujian Province of China(No.2023J02007);the Central Guidance on Local Science and Technology Development Fund of Fujian Province(No.2023L3003);the Fujian Alliance of Mathematics(No.2023SXLMMS01)。

摘　　要：We consider the task of binary classification in the high-dimensional setting where the number of features of the given data is larger than the number of observations.To accomplish this task,we propose an adherently penalized optimal scoring(APOS)model for simultaneously performing discriminant analysis and feature selection.In this paper,an efficient algorithm based on the block coordinate descent(BCD)method and the SSNAL algorithm is developed to solve the APOS approximately.The convergence results of our method are also established.Numerical experiments conducted on simulated and real datasets demonstrate that the proposed model is more efficient than several sparse discriminant analysis methods.我们考虑在高维环境下的二分类问题,其中给定数据的特征数大于观测数.为此,我们提出一种基于依附惩罚的最优评分(APOS)模型,用于同时进行判别分析和特征选择.在本文中,我们设计一种基于块坐标下降(BCD)方法和SSNAL算法的高效算法来近似求解APOS模型,并给出该方法的收敛性结果.对模拟和真实数据集的数值实验结果表明,所提模型在性能上优于五种经典的稀疏判别方法.

关 键 词：Sparse discriminant analysis Optimal scoring Feature selection BCD method SSNAL algorithm 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]