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We show that the recently proposed variant of the Support Vector machine (SVM) algorithm, known as v-SVM, can be interpreted as a maximal separation between subsets of the convex hulls of the data, which we call soft convex hulls. The soft convex hulls are controlled by choice of the parameter v. If the intersection of the convex hulls is empty, the… (More)

We give necessary and sufficient conditions for uniqueness of the support vector solution for the problems of pattern recognition and regression estimation, for a general class of cost functions. We show that if the solution is not unique, all support vectors are necessarily at bound, and we give some simple examples of non-unique solutions. We note that… (More)

The EPOXI Discovery Mission of Opportunity reused the Deep Impact flyby spacecraft to obtain spatially and temporally resolved visible photometric and moderate resolution near-infrared (NIR) spectroscopic observations of Earth. These remote observations provide a rigorous validation of whole-disk Earth model simulations used to better understand remotely… (More)

Kernel methods have attracted wide interest in the machine learning community over the last few years. Their appeal lies in their performance as algorithms and in their rich mathematical context and tractability. In this work 1 , we address the question of when a kernel algorithm has a unique solution, using support vector machines for classification and… (More)

- Rangasayi N Halthore, David Crisp, Stephen E Schwartz, G P Anderson, A Berk, J H Mather
- 2005

[1] Computation of components of shortwave (SW) or solar irradiance in the surface-atmospheric system forms the basis of intercomparison between 16 radiative transfer models of varying spectral resolution ranging from line-by-line models to broadband and general circulation models. In order of increasing complexity the components are: direct solar… (More)

The principal goal of the NASA Terrestrial Planet Finder (TPF) and European Space Agency's Darwin mission concepts is to directly detect and characterize extrasolar terrestrial (Earthsized) planets. This first generation of instruments is expected to provide disk-averaged spectra with modest spectral resolution and signal-to-noise. Here we use a spatially… (More)

- David Crisp, Stephen B Fels, M D Schwarzkopf
- 2007

The CO 2 15-/ • m band provides an important source of thermal opacity in the atmospheres of Venus, Earth, and Mars. Efficient and accurate methods for finding the transmission in this band are therefore needed before complete, self-consistent physical models of these atmospheres can be developed. In this paper we describe a hierarchy of such methods. The… (More)