Supervised Isomap Based on Pairwise Constraints

Abstract

Most existing typical dimension reduction methods, for example Isomap algorithm, are hard to deal with the problem of violation of pairwise constraint. In this paper, a pairwise-constraint supervised Isomap algorithm (PC-SIsomap) is proposed, in which the supervised information is taken on the form of pairwise constraint introduced to geodesic distance. Mapping high-dimensional and non-linear data points to low-dimensional embedding space, PC-SIsomap can effectively take advantage of pairwise constraint information to realize dimensionality reduction. At the same time in order to solve the out-of-sample problem in manifold learning, BP neural network is employed to build a nonlinear mapping relation from the high-dimensional original data space to a low-dimensional feature space. Consequentially, support vector machine (SVM) classifiers are designed for realizing pattern classification in the low-dimensional feature space. Some experiments are executed in UCI datasets and dataset of gas safety monitoring system in coal mine, the results show that PC-SIsomap not only reduces the residual value, but also improves the classification accuracy.