We investigate the use of dimensionality reduction techniques for the classification of stellar spectra selected from the SDSS. Using local linear embedding (LLE), a technique that preserves the local (and possibly non-linear) structure within high d
imensional data sets, we show that the majority of stellar spectra can be represented as a one dimensional sequence within a three dimensional space. The position along this sequence is highly correlated with spectral temperature. Deviations from this stellar locus are indicative of spectra with strong emission lines (including misclassified galaxies) or broad absorption lines (e.g. Carbon stars). Based on this analysis, we propose a hierarchical classification scheme using LLE that progressively identifies and classifies stellar spectra in a manner that requires no feature extraction and that can reproduce the classic MK classifications to an accuracy of one type.
The three-point correlation function (3PCF) provides an important view into the clustering of galaxies that is not available to its lower order cousin, the two-point correlation function (2PCF). Higher order statistics, such as the 3PCF, are necessar
y to probe the non-Gaussian structure and shape information expected in these distributions. We measure the clustering of spectroscopic galaxies in the Main Galaxy Sample of the Sloan Digital Sky Survey (SDSS), focusing on the shape or configuration dependence of the reduced 3PCF in both redshift and projected space. This work constitutes the largest number of galaxies ever used to investigate the reduced 3PCF, using over 220,000 galaxies in three volume-limited samples. We find significant configuration dependence of the reduced 3PCF at 3-27 Mpc/h, in agreement with LCDM predictions and in disagreement with the hierarchical ansatz. Below 6 Mpc/h, the redshift space reduced 3PCF shows a smaller amplitude and weak configuration dependence in comparison with projected measurements suggesting that redshift distortions, and not galaxy bias, can make the reduced 3PCF appear consistent with the hierarchical ansatz. The reduced 3PCF shows a weaker dependence on luminosity than the 2PCF, with no significant dependence on scales above 9 Mpc/h. On scales less than 9 Mpc/h, the reduced 3PCF appears more affected by galaxy color than luminosty. We demonstrate the extreme sensitivity of the 3PCF to systematic effects such as sky completeness and binning scheme, along with the difficulty of resolving the errors. Some comparable analyses make assumptions that do not consistently account for these effects.
