document: Fast nonlinear regression via eigenimages applied to galactic morphology Astronomy increasingly faces the issue of massive , unwieldly data sets . The Sloan Digital Sky Survey ( SDSS ) ( 11 ) has so far generated tens of millions of images of distant galaxies , of which only a tiny fraction have been morphologically classified . Morphological classification in this context is achieved by fitting a parametric model of galaxy shape to a galaxy image . This is a nonlinear regression problem , whose challenges are threefold , 1 ) blurring of the image caused by atmosphere and mirror imperfections , 2 ) large numbers of local minima , and 3 ) massive data sets . Our strategy is to use the eigenimages of the parametric model to form a new feature space , and then to map both target image and the model parameters into this feature space . In this low-dimensional space we search for the best image-to-parameter match . To search the space , we sample it by creating a database of many random parameter vectors ( prototypes ) and mapping them into the feature space . The search problem then becomes one of finding the best prototype match , so the fitting process a nearest-neighbor search . In addition to the savings realized by decomposing the original space into an eigenspace , we can use the fact that the model is a linear sum of functions to reduce the prototypes further : the only prototypes stored are the components of the model function . A modified form of nearest neighbor is used to search among them . Additional complications arise in the form of missing data and heteroscedasticity , both of which are addressed with weighted linear regression . Compared to existing techniques , speed-ups ach-ieved are between 2 and 3 orders of magnitude . This should enable the analysis of the entire SDSS dataset .
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