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We show that the first 10 eigencomponents of the Karhunen-Lo\`eve expansionor Principal Component Analysis (PCA) provide a robust classification schemefor the identification of stars, galaxies and quasi-stellar objects frommulti-band photometry. To quantify the efficiency of the method, realisticsimulations are performed which match the planned Large Zenith Telescopesurvey. This survey is expected to provide spectral energy distributions with aresolution $R\simeq40$ for $\sim10^6$ galaxies to $R\le23$ ($z\sim 1$), $\sim10^4$ 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 to100% of stars, 100% of galaxies and 100% of QSOs at a median signal-to-noiseratio of 10. The 10-component PCA also allows measurement of redshifts with anaccuracy of $\sigma_\mathrm{Res.}\la0.05$ for galaxies with $z\la0.7$, and to$\sigma_\mathrm{Res.}\la0.2$ for QSOs with $z\ga2$, at a median signal-to-noiseratio of 6. At a median signal-to-noise ratio 20, $\sigma_\mathrm{Res.}\la0.02$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 ratioof $\la 2$ in their reddest/bluest filters). This redshift accuracy is inherentto the $R\simeq40$ resolution provided by the set of medium-band filters usedby the Large Zenith Telescope survey. It provides an accuracy improvement ofnearly an order of magnitude over the photometric redshifts obtained frombroad-band $BVRI$ photometry.

Classification and redshift estimation by principal component analysis