Automatic classification for WDMS with Isomap and SVM

For the purpose of discovering White Dwarf + Main Sequence (WDMS) from massive spectra, in this paper, an unsupervised learning algorithm for Nonlinear Dimensionality Reduction (NLDR) named Isometric Feature Mapping (Isomap) is discussed. The applicability of Isomap to Sloan Digital Sky Survey Data Release 10 (SDSS-DR10) is confirmed. Furthermore, Particle Swarm Optimization (PSO) is implemented to increase Support Vector Machine (SVM) classification accuracy via optimizing its parameters. The experiment turns out (1)Compared with Principle Component Analysis (PCA), Isomap primely maintains the nonlinear structure of high-dimensional spectral data, which leads to a higher classification accuracy (2)Optimizing parameters for SVM with PSO helps to generate a more accurate classification hyper-plane. PSO is proved to be capable of finding an optimal solution faster than Grid Search (GS). Unlike PCA, Isomap measures the distance between two samples with a significant concept named geodesic distance, which is extremely important for manifold learning. Isomap estimates the geodesic distances between all pairs of samples on the manifold by computing their shortest path distances. Geodesic distance can better represent the topology structure of all samples. After being reconstructed by Isomap, high-dimensional spectral data can be visualized in a low-dimensional space without losing their nonlinear structures. More importantly, with the help of Isomap, a classification model is generated by training SVM with low-dimensional dataset from SDSS-DR10 and this model can be applied to carry out large scale data mining which aims to discover WDMS.