在机器学习领域，半监督学习作为一种有力工具吸引了越来越多的关注，其利用少量带标签数据和大量无标签数据进行有效学习，其中基于图的半监督学习方法因其优雅的数学形式和良好的学习性能而引起更广泛的研究。针对现有基于图的半监督学习方法所存在的模型参数敏感和数据判别信息不充分等问题，提出一种稀疏特征空间嵌入正则化（Sparse Feature Space embedding Regularization ，SFSR ）半监督学习框架，其主要思想为：首先分别将原始数据嵌入到线性特征空间，然后利用特征空间嵌入投影点集来稀疏重构原始数据，随后在由原始数据线性张成的标签空间通过保留这种稀疏表示关系来构建一个Laplacian正则化项，或称SFSR ，最后提出一个鲁棒的基于SFSR的半监督学习框架，在几个实际基准数据库上的综合实验结果证实了所提框架的鲁棒有效性。%Semi-supervised learning(SSL) ,as a powerful tool to learn from a limited number of labeled data and a large number of unlabeled data ,has been attracting increasing attention in machine learning community .Of various SSL methods ,graph based approaches have attracted more extensive research due to their elegant mathematical formulation and good performance .How-ever ,there may exist several nontrivial concerns such as such as model parameters sensitiveness and insufficient discriminative infor-mation in data space ,etc ,in existing graph based SSL approaches .To these ends ,in this paper ,we propose a robust Sparse Feature Space embedding Regularization (SFSR )SSL framework .The main idea of the proposed SFSR includes three folds:(1 )linearly em-bedding input data into its feature spaces (2 )sparsely reconstructing input data using its feature space embedding projection images;and (3 )preserving the same sparse representation relationship among labels of data as that among data in some label space spanned linearly by input data ,thus constructing a novel sparse nearest feature space embedding regularizer ,coined as SFSR .The comprehen-sive experimental results on several real-world benchmark databases are presented to demonstrate the significantly robust effective-ness of our proposed method .
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