Classification and redshift estimation by principal component analysis

R. A. Cabanac; V. de Lapparent; P. Hickson

doi:doi:10.1051/0004-6361:20020665

Free access

Issue		A&A Volume 389, Number 3, July III 2002


Page(s)		1090 - 1116
Section		Instruments, observational techniques and data processing
DOI		http://dx.doi.org/10.1051/0004-6361:20020665

A&A 389, 1090-1116 (2002)
DOI: 10.1051/0004-6361:20020665

Classification and redshift estimation by principal component analysis

R. A. Cabanac^{1, 2}, V. de Lapparent¹ and P. Hickson³

¹ Institut d'Astrophysique de Paris, CNRS / Univ. Pierre et Marie Curie, 98 bis Bd. Arago, 75014 Paris, France
² European Southern Observatory, Vitacura, Alonso de Cordova, 3107, casilla 19001, Santiago, Chile
³ Dept. of Physics & Astronomy, Univ. British Columbia, 2219 Main Mall, Vancouver, BC V6T1Z4, Canada

(Received 3 April 2001 / Accepted 22 April 2002)

Abstract
We show that the first 10 eigencomponents of the Karhunen-Loève expansion or Principal Component Analysis (PCA) provide a robust classification scheme for the identification of stars, galaxies and quasi-stellar objects from multi-band photometry. To quantify the efficiency of the method, realistic simulations are performed which match the planned Large Zenith Telescope survey. This survey is expected to provide spectral energy distributions with a resolution $R\simeq40$ for ~ 10⁶ galaxies to $R\le23$ ( $z\sim 1$ ), $\sim 10^4$ QSOs, and $\sim 10^5$ stars.

We calculate that for a median signal-to-noise ratio of 6, 98% of stars, 100% of galaxies and 93% of QSOs are correctly classified. These values increase to 100% of stars, 100% of galaxies and 100% of QSOs at a median signal-to-noise ratio of 10. The 10-component PCA also allows measurement of redshifts with an accuracy of $\sigma_{{\rm Res.}}\la0.05$ for galaxies with $z\la0.7$ , and to $\sigma_{{\rm Res.}}\la0.2$ for QSOs with $z\ga2$ , at a median signal-to-noise ratio of 6. At a median signal-to-noise ratio 20, $\sigma_{{\rm Res.}}\la0.02$ for galaxies with $z\la1$ and for QSOs with $z\ga2.5$ (note that for a median S/N ratio of 20, the bluest/reddest objects will have a signal-to-noise ratio of $\la$ 2 in their reddest/bluest filters). This redshift accuracy is inherent to the $R\simeq40$ resolution provided by the set of medium-band filters used by the Large Zenith Telescope survey. It provides an accuracy improvement of nearly an order of magnitude over the photometric redshifts obtained from broad-band BVRI photometry.

Key words: galaxies: fundamental parameters -- methods: data analysis -- Surveys -- galaxies: general

Offprint request: R. A. Cabanac, rcabanac@eso.org

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