基于成对约束的自适应半监督降维方法研究

With the rapid accumulation of high dimensional data, dimensionality reduction plays a more and more important role in practical data processing and learning tasks such as computer vision, speech recognition, natural language processing, bioinformatics, and so on. This project focuses on semi-supervised dimensionality reduction based on pairwise constraints. In this setting, domain knowledge is given in the form of pairwise constraint. pairwise constraint is a kind of side information, which specifies whether a pair of samples belongs to the same class or not. However, there are two serious problems existing in the current pairwise constraint based semi-supervised dimensionality reduction methods. First, all the pairwise constraints are equally treated which ignores the fact of unequally amount of information owned by different pairwise constraints. second, neighborhood graph construction methods are usually unsupervised which ignores the guiding function of pairwise constraints to graph construction. To solve the above problems, this project will propose an adaptive semi-supervised dimensionality reduction framework which can implement adaptive pairwise constraint weighting and adaptive graph optimizing to promote the learning ability of the high dimensional data with pairwise constraints.

随着高维数据的快速增长，降维在机器视觉、语音识别、自然语言处理、生物信息学等领域当中扮演着越来越重要的作用。本项目的研究对象为基于成对约束的半监督降维，其中领域知识是以成对约束的形式给出的，成对约束是边信息的一种，可用来指示一对样本是否属于同一类别。然而，现有的基于成对约束的半监督降维方法，存在着两个不可忽视的问题：其一，所有成对约束都被看成同等重要，忽视了不同成对约束所包含的信息量也可能不同的事实；其二，邻域图的构造是一个无监督的过程，忽视了成对约束对邻域图构造的指导作用。针对上述问题，本项目拟在自适应成对约束加权和自适应图优化等方面展开研究，提出一种基于成对约束加权和图优化的自适应半监督降维框架，并根据框架设计若干半监督降维方法，以此提升成对约束条件下对高维数据的学习能力。

随着大数据时代高维数据的快速增长，降维技术在机器学习、人工智能等领域中发挥的作用越来越大。针对基于成对约束的半监督降维方法中存在的问题，本项目在自适应成对约束加权和自适应图优化等方面展开了研究，提出了一种基于成对约束加权与图优化的自适应半监督降维框架，并根据该框架设计了若干半监督降维新方法，这些新方法在真实数据集上的实验结果表明了其先进性。该课题的成功实施有利于提升在成对约束情况下对高维数据的学习能力，对填补相关领域研究的空白，具有重要的理论意义和应用价值。