Discrete Classification with Principal Component Analysis: Discrimination of Giant and Dwarf Spectra in K-stars

We demonstrate the use of a variant of Principal Component Analysis (PCA) for discrimination problems in astronomy. This variant of PCA is shown to provide the best linear discrimination between data classes. As a test case, we present the problem of discrimination between K giant and K dwarf stars from intermediate resolution spectra near the Mg `b' feature. The discrimination procedure is trained on a set of 24 standard K giants and 24 standard K dwarfs, and then used to perform giant - dwarf classification on a sample of approximately 1500 field K stars of unknown luminosity class which were initially classified visually. For the highest S/N spectra, the automated classification agrees very well (at the 90 - 95% level) with the visual classification. Most importantly, however, the automated method is found to classify stars in a repeatable fashion, and, according to numerical experiments, is very robust to signal to noise (S/N) degradation.