Description
The Karhunen-Loeve (KL) transform can compactly represent the information contained in large, complex datasets, cleanly eliminating noise from the data and identifying elements of the dataset with extreme or inconsistent characteristics. We develop techniques to apply the KL transform to the 4000-5700{AA} region of 9800 QSO spectra with z<0.619 from the SDSS archive. Up to 200 eigenspectra are needed to fully reconstruct the spectra in this sample to the limit of their signal-to-noise (S/N). We propose a simple formula for selecting the optimum number of eigenspectra to use to reconstruct any given spectrum, based on the S/N of the spectrum, but validated by formal cross-validation tests.
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