[A novel method for the determination of redshifts of normal galaxies by non-linear dimensionality reduction]

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.