Fuzzy Cluster Analysis: Application to Determining Metallicities for
  Very Metal-poor Stars
  This work presents a first attempt to apply fuzzy cluster analysis (FCA) to
analyzing stellar spectra. FCA is adopted to categorize line indices measured
from LAMOST low-resolution spectra, and automatically remove the least
metallicity-sensitive indices. The FCA-processed indices are then transferred
to the artificial neural network (ANN) to derive metallicities for 147 very
metal-poor (VMP) stars that have been analyzed by high-resolution spectroscopy.
The FCA-ANN method could derive robust metallicities for VMP stars, with a
precision of 0.2 dex compared with high-resolution analysis. The recommended
FCA threshold value \lambda for this test is between 0.9965 and 0.9975. After
reducing the dimension of the line indices through FCA, the derived
metallicities are still robust, with no loss of accuracy, and the FCA-ANN
method performs stably for different spectral quality from [Fe/H] from -1.8
down to -3.5. Compared with traditional classification methods, FCA considers
ambiguity in groupings and noncontinuity of data, and is thus more suitable for
observational data analysis. Though this early test uses FCA to analyze
low-resolution spectra, and feeds the input to the ANN method to derive
metallicities, FCA should be able to, in the large data era, also analyze
slitless spectroscopy and multiband photometry, and prepare the input for
methods not limited to ANN, in the field of stellar physics for other studies,
e.g., stellar classification, identification of peculiar objects. The
literature-collected high-resolution sample can help improve pipelines to
derive stellar metallicities, and systematic offsets in metallicities for VMP
stars for three published LAMOST catalogs have been discussed.
