基于图的半监督学习算法研究

项目名称： 基于图的半监督学习算法研究

项目编号： No.11526087

项目类型： 专项基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 左玲

作者单位： 湖北工业大学

项目金额： 3万元

中文摘要： 半监督学习是近年来机器学习、模式识别及信号处理等领域的热点问题。而基于图正则化的半监督算法是半监督学习中的一类重要方法。近来的研究揭示了此类算法计算量庞大及对非高斯噪声敏感等不足。如不妥善解决，将使算法的学习效率大打折扣，阻碍半监督学习优势的发挥。本项目首先针对基于图正则化的半监督算法计算量大的弊端建立合理的模型假设，提出稀疏的基于图的半监督算法。然后，将信息论中熵的概念引入到基于图的半监督学习中。利用熵替代传统图正则化算法中的平方损失，提出能够有效处理非高斯分布噪声的算法，接下来从统计学习理论的角度出发，利用算子逼近技术，全面地分析图正则化算法的稀疏性、对非高斯分布噪声的稳定性及收敛性。并且，将算法应用于模式识别、信号处理等实际问题。项目以提高算法的稀疏性、稳定性及收敛性为目标，并将部分基础理论成果推广至应用技术层面，促进图正则化的半监督学习理论和应用的进一步深化和发展。

中文关键词： 半监督学习；图正则化；稀疏性；稳定性；收敛性

英文摘要： Nowadays, the semi-supervised learning has become a hot topic in the area of machine learning, pattern recognition and signal processing. The graph-based semi-supervised algorithm is an important method in semi-supervised learning. Recent research has revealed several drawbacks of these algorithms such as the high computation cost in the optimization procedure and the sensitivity in dealing with problems involving heavy tailed non-Gaussian noise. If these problems are not solved properly, they will decrease the effectiveness of the graph-based methods, which could even destroy the benefits of semi-supervised learning. In this project, we will first try to establish proper assumption models. Under these models, the sparse graph-based regularization algorithms will be proposed, which can effectively reduce the computational complexity. Then the entropy in information theory will be applied to the learning of graph-based regularization algorithms. We will employ entropy to substitute the traditional square loss function in graph-based regularization methods, and construct novel algorithms which can effectively deal with the non-Gaussian distribution noise. Next, in the framework of statistical learning theory, we provide a comprehensive analysis on the sparsity, stability and convergence for the proposed formulatio

英文关键词： Semi-supervised learning；Graph-based regularization；Sparsity；Stability；Convergence