HR: 0800h
AN: NG11A-0177    [Abstracts]
TI: Physically correct kernel learning for geophysics
AU: * Kuzma, H A
EM: hkuzma@berkeley.edu
AF: University of California, Berkeley, P.O. Box 987, Truckee, CA 96160,
AU: Martinez, J F
EM: jlfm@uniovi.es
AF: Universidad de Oviedo, C/ Calvvo Sotelo SIN, Oviedo, 33007, Spain
AU: Rector, J W
EM: jwrector@lbl.gov
AF: University of California, Berkeley, P.O. Box 987, Truckee, CA 96160,
AB: In this poster, we use the term Kernel Learning to encompass a class of computer learning algorithms in which the output of the algorithm is a linear combination of an input compared to a set of known inputsi. The comparison is done using a kernel function. Kriging, which is often used for spatial interpolation, is the most well-known kernel learning method in the earth sciences. Support Vector Machines (SVMs) and radial basis functions are also kernel algorithms. If the kernel is chosen to be a symmetric positive semi-definite function, then it can be interpreted as a transformation of the inputs into a feature space. The assumption of linearity in the model implies linearity between inputs and outputs once the inputs have been transformed into feature space. In many geophysical situations, the relationship between an earth model and data measured at specific locations can be expressed as the inner product of the model with a Green's function (which might possibly depend on the model parameters). If it is possible to use this knowledge to construct a feature space, then it should be possible to construct a kernel which transforms inputs into the same, or a closely related feature space. In this poster, we train SVMs to approximate forward and inverse relationships between earth models and synthetic geophysical data and study their performance as a function of the ability of a kernel to generate a physically appropriate feature space.
DE: 0555 Neural networks, fuzzy logic, machine learning
DE: 3260 Inverse theory
DE: 3299 General or miscellaneous
DE: 4499 General or miscellaneous
DE: 9810 New fields (not classifiable under other headings)
SC: Nonlinear Geophysics [NG]
MN: 2007 Fall Meeting