Automatic Redshift Determination by Use of Principal Component Analysis. I. Fundamentals

Abstract

With the advent of very large redshift surveys of tens to hundreds of\nthousands of galaxies reliable techniques for automatically determining galaxy\nredshifts are becoming increasingly important. The most common technique\ncurrently in common use is the cross-correlation of a galactic spectrum with a\nset of templates. This series of papers presents a new method based on\nPrincipal Component Analysis. The method generalizes the cross-correlation\napproach by replacing the individual templates by a simultaneous linear\ncombination of orthogonal templates. This effectively eliminates the mismatch\nbetween templates and data and provides for the possibility of better error\nestimates. In this paper, the first of a series, the basic mathematics are\npresented along with a simple demonstration of the application.\n