一种改进的ISOMAP分类算法

AN IMPROVED ISOMAP CLASSIFICATION ALGORITHM

传统的等距特征映射算法在降维时未考虑数据的类别标签,降维后不能够产生从高维到低维的映射矩阵,且不适用于多个类簇的情况,不能直接用于分类。针对这几个问题利用近邻元分析方法取代多维尺度分析法,并且引入特征向量作为输入矩阵,提出一种以分类为目的的等距特征映射算法(NC-ISOMAP)。降维时获取理想的低维投影矩阵,使降维后类间数据更加分开,类内数据更加紧凑。实验结果表明NC-ISOMAP算法能够取得很好的降维效果和分类性能,并在不同的数据集中有着较好的鲁棒性。

Traditional isometric feature mapping algorithm does not consider the classification labels of data when reducing the dimensionality,and cannot produce a mapping matrix ranging from high dimensions to lower dimensions after the dimensionality being reduced,and it cannot fit the situation of multi-class clusters as well,so it cannot be directly used for classification. In light of these problems,we use neighbourhood component analysis（ NCA） to replace the multidimensional scaling analysis（ MDS）,introduce eigenvector as the input matrix,and propose an isometric feature mapping algorithm aiming at classification,called NC-ISOMAP. In the process of dimensionality reduction,NC-ISOMAP can obtain an ideal low dimensional project matrix,which makes the data become more separate between classes and more compact within a class after lowering the dimensionality. Experimental results show that NC-ISOMAP is able to achieve quite good dimensionality reduction result and classification performance,and has a better robustness in different datasets.