一种新的有监督流形学习方法

A New Supervised Manifold Learning Method

提出了一种新的有监督流形学习方法,目的是提供将流形学习降维方法高效应用于有监督学习问题的全新策略.算法的核心思想是集成流形学习方法对高维流形结构数据的降维有效性与支撑向量机(SVM)在中小规模分类数据集上的优良特性实现高效有监督流形学习.算法具体实现步骤为:首先利用SVM在流形学习降维数据中选出对分类决策最重要的数据集,即支撑向量集;按标号返回可得到原空间的支撑向量集;在这个集合上再次使用SVM即可得到原空间的分类决策,从而完成有监督流形学习.在一系列人工与实际数据集上的实验验证了方法的有效性.

A new supervised manifold learning method is proposed in this paper, in order to present a new strategy to efficiently apply manifold learning and nonlinear dimensionality reduction methods to supervised learning problems. The new method realizes efficient supervised learning mainly based on integrating the topology preserving property of the manifold learning methods （Isomap and LLE） and some prominent properties of support vector machine such as efficiency on middle and small sized data sets and essential capability of support vectors calculated from support vector machine. The method is realized via the following steps： first to apply Isomap or LLE to get the embeddings of the original data set in the low dimensional space; then to obtain support vectors, which are the most significant and intrinsic data for the final classification result, by using support vector machine on these low dimensional embedding data; subsequently to get support vectors in the original high dimensional space based on the corresponding labels of the obtained low dimensional support vectors; finally to apply support vector machine again on these high dimensional support vectors to gain the final classification discriminant function. The good performance of the new method on a series of synthetic and real world data sets verifies the feasibility and efficiency of the method.