摘要
半监督回归算法可以利用少量有标签样本和大量无标签样本进行回归建模,进而在一定程度上解决了获取标签样本成本高的问题.目前,已经提出了能利用邻接矩阵来挖掘数据潜在结构的图半监督回归算法.然而,这些方法存在两个问题.第一,现有半监督回归算法多使用全连接的图生成方式,很容易受到噪声或离群点的影响;第二,现有图半监督回归算法的稀疏性不足.为了解决上述问题,本文提出了一种新的半监督回归学习算法——基于局部邻接图的半监督稀疏回归算法.该算法构建了一种新的局部邻接图,在生成邻接矩阵时仅关注样本的局部信息,从而保留了数据的局部流形结构,缓解噪声样本对算法的影响.另外,利用1范数正则能诱导稀疏性的特性,本文在优化问题中引入模型系数的1范数正则项,有效地提高了模型的稀疏性.本文在9个真实数据集上对算法的半监督回归性能和稀疏性进行了实验验证.实验结果表明,本文所提算法在不同实验设置下均能获得较好的回归性能.
Semi-supervised regression(SSR)algorithms leverage a small amount of labeled samples along with a large pool of unlabeled samples for modeling regression functions,which can alleviate the high costs associated with obtaining labeled data to some extent.At present,graph-based SSR algorithms have been proposed,which can employ adjacency matrices to dig the underlying data structure.However,existing graph-based SSR methods are confronted with two primary challenges.First,existing methods rely on the fully-connected graph on data that is susceptible to noise and outliers.Second,the sparsity of current SSR algorithms leaves room for enhancement.To address these issues,this paper proposes a novel semi-supervised sparse regression algorithm.This algorithm designs a new graph,the local adjacency graph,which focuses on the local connectivity of samples.This graph generation method preserves the local manifold structure of the data and mitigates the impact of noisy samples.Furthermore,our algorithm capitalizes on the sparsity-inducing property of the 1-norm regularization by incorporating a 1-norm regularization term for the model coefficients into the optimization problem,effectively enhancing the model's sparsity.Empirical validation is performed on nine real-world datasets to evaluate the SSR performance and the sparsity of the proposed algorithm.Results demonstrate that our method achieves superior performance across various experimental setups.
作者
秦晓燕
郑晓晗
张莉
Qin Xiaoyan;Zheng Xiaohan;Zhang Li(School of Information and Software,Suzhou Global Institute,Suzhou 215163,China;School of Computer Science and Technology,Soochow University,Suzhou 215006,China)
出处
《南京师大学报(自然科学版)》
北大核心
2025年第4期96-105,共10页
Journal of Nanjing Normal University(Natural Science Edition)
基金
江苏省高校自然科学研究资助项目(19KJA550002)
江苏省六大人才高峰资助项目(XYDXX-054)
江苏省职业教育软件技术“双师型”名师工作室资助项目(苏教师函[2022]31号)。
关键词
半监督回归学习
图生成
邻接矩阵
稀疏性
1范数正则
semi-supervised regression learning
adjacency matrix
graph generation
sparsity
1-norm regularization
