Physical Sciences and Mathematics Commons^™

Automated Classification Of Stellar Spectra. Ii: Two-Dimensional Classification With Neural Networks And Principal Components Analysis, Ted Von Hippel, Coryn A.L. Bailer-Jones, Mike Irwin

Publications

We investigate the application of neural networks to the automation of MK spec- tral classification. The data set for this project consists of a set of over 5000 optical (3800–5200°A) spectra obtained from objective prism plates from the Michigan Spec- tral Survey. These spectra, along with their two-dimensional MK classifications listed in the Michigan Henry Draper Catalogue, were used to develop supervised neural network classifiers. We show that neural networks can give accurate spectral type classifications (68 = 0.82 subtypes, rms= 1.09 subtypes) across the full range of spectral types present in the data set (B2–M7). We show also that …

Fast Discrete Polynomial Transforms With Applications To Data Analysis For Distance Transitive Graphs, J. R. Driscoll, D. M. Healy, D. N. Rockmore

Dartmouth Scholarship

Let $\poly = \{P_0,\dots,P_{n-1}\}$ denote a set of polynomials with complex coefficients. Let $\pts = \{z_0,\dots,z_{n-1}\}\subset \cplx$ denote any set of {\it sample points}. For any $f = (f_0,\dots,f_{n-1}) \in \cplx^n$, the {\it discrete polynomial transform} of f (with respect to $\poly$ and $\pts$) is defined as the collection of sums, $\{\fhat(P_0),\dots,\fhat(P_{n-1})\}$, where $\fhat(P_j) = \langle f,P_j \rangle = \sum_{i=0}^{n-1} f_iP_j(z_i)w(i)$ for some associated weight function w. These sorts of transforms find important applications in areas such as medical imaging and signal processing.

In this paper, we present fast algorithms for computing discrete orthogonal polynomial transforms. For a system …