15 research outputs found
Spectral approximations in machine learning
In many areas of machine learning, it becomes necessary to find the
eigenvector decompositions of large matrices. We discuss two methods for
reducing the computational burden of spectral decompositions: the more
venerable Nystom extension and a newly introduced algorithm based on random
projections. Previous work has centered on the ability to reconstruct the
original matrix. We argue that a more interesting and relevant comparison is
their relative performance in clustering and classification tasks using the
approximate eigenvectors as features. We demonstrate that performance is task
specific and depends on the rank of the approximation.Comment: 11 pages, 4 figure
Semi-supervised Learning for Photometric Supernova Classification
We present a semi-supervised method for photometric supernova typing. Our
approach is to first use the nonlinear dimension reduction technique diffusion
map to detect structure in a database of supernova light curves and
subsequently employ random forest classification on a spectroscopically
confirmed training set to learn a model that can predict the type of each newly
observed supernova. We demonstrate that this is an effective method for
supernova typing. As supernova numbers increase, our semi-supervised method
efficiently utilizes this information to improve classification, a property not
enjoyed by template based methods. Applied to supernova data simulated by
Kessler et al. (2010b) to mimic those of the Dark Energy Survey, our methods
achieve (cross-validated) 95% Type Ia purity and 87% Type Ia efficiency on the
spectroscopic sample, but only 50% Type Ia purity and 50% efficiency on the
photometric sample due to their spectroscopic follow-up strategy. To improve
the performance on the photometric sample, we search for better spectroscopic
follow-up procedures by studying the sensitivity of our machine learned
supernova classification on the specific strategy used to obtain training sets.
With a fixed amount of spectroscopic follow-up time, we find that deeper
magnitude-limited spectroscopic surveys are better for producing training sets.
For supernova Ia (II-P) typing, we obtain a 44% (1%) increase in purity to 72%
(87%) and 30% (162%) increase in efficiency to 65% (84%) of the sample using a
25th (24.5th) magnitude-limited survey instead of the shallower spectroscopic
sample used in the original simulations. When redshift information is
available, we incorporate it into our analysis using a novel method of altering
the diffusion map representation of the supernovae. Incorporating host
redshifts leads to a 5% improvement in Type Ia purity and 13% improvement in
Type Ia efficiency.Comment: 16 pages, 11 figures, accepted for publication in MNRA