基于正则化的半监督等距映射数据降维方法

针对等距映射(ISOMAP)算法无监督，不能生成显式映射函数等局限性，该文提出一种正则化的半监督等距映射(Reg-SS-ISOMAP)算法。该算法首先利用训练样本的标签样本构建K联通图(K-CG)，得到近似样本间测地线距离，并作为矢量特征代替原始数据点；然后通过测地线距离计算核矩阵，用半监督正则化方法代替多维尺度分析(MDS)算法处理矢量特征；最后利用正则化回归模型构建目标函数，得到低维表示的显式映射。算法在多个数据集上进行了比较实验，结果表明，文中提出的算法降维效果稳定，识别率高，显示了算法的有效性。

Data Dimensionality Reduction Method of Semi-supervised Isometric Mapping Based on Regularization

This paper proposes Regularized Semi-Supervised ISOmetric MAPping (Reg-SS-ISOMAP) algorithm to solve the problem that ISOmetric MAPping (ISOMAP) algorithm is unsupervised and can not generate explicit mapping function. At first, this algorithm creates K-Connectivity Graph (K-CG) by labeled samples in training samples to get geodesic distance between approximate samples and takes it as feature vector substituting for original data. Then, it takes the geodesic distance as kernel and processes feature vector through semi-supervised regularization not MultiDimensional Scaling (MDS) algorithm. At last, it constructs objective function by regularization regression model which is low dimension and explicit mapping. The algorithm is simulated on different data sets, results show that it is stable in dimension reduction and high recognition rate.