A Novel Method for the Determination of Redshifts of Normal Galaxies by Non-Linear Dimensionality Reduction
XU Xin1,2, WU Fu-chao1, HU Zhan-yi1, LUO A-li2
1. Robot Vision Group, National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China 2. National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China
摘要： 提出了一种确定正常星系红移的有效方法，该方法分为以下3个步骤：(1)利用四阶小波系数作为正常星系的特征表示，它能较好地反映吸收线、跳变点和吸收带的信息;(2)利用非线性降维方法LLE(locally linear embedding)将特征数据映射到三维空间中一维流形;(3)由一维流形上的红移分布数据，根据最近邻方法得到正常星系的红移值。实验表明，文中所给的方法较文献中通常使用的PCA方法对于红移的确定具有更高的精度。
关键词：正常星系;红移;LLE(locally linear embedding);流形;PCA(principal component analysis)
Abstract：It is difficult to determine the redshifts of normal galaxies (NG) from their spectra because of their common weak absorption property. In the present work, a novel method is proposed to effectively deal with this issue. The proposed method is composed of the following three parts: At first, the wavelet transform coefficients at the fourth scaling are experimentally found to be appropriate and used as our features to represent the absorption information from NG absorption lines, break points, and absorption bands. Then, the features are mapped by a non-linear method, LLE(locally linear embedding)，onto an one-dimensional manifold in the 3D space; Finally, the NG redshifts are obtained by the nearest neighborhood technique from the redshift distribution on the manifold. Besides, the proposed method is compared with widely used PCA method in the literature with SDSS database, and is shown to be more accurate for the redshifts determination.
许 馨1, 2，吴福朝1，胡占义1，罗阿理2 . 一种基于非线性降维求正常星系红移的新方法[J]. 光谱学与光谱分析, 2006, 26(01): 182-186.
XU Xin1,2, WU Fu-chao1, HU Zhan-yi1, LUO A-li2 . A Novel Method for the Determination of Redshifts of Normal Galaxies by Non-Linear Dimensionality Reduction . SPECTROSCOPY AND SPECTRAL ANALYSIS, 2006, 26(01): 182-186.
