Perturbation analysis for circles, spheres, and generalized hyperspheres fitted to data by geometric total least-squares |
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Authors: | Yves Nievergelt |
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Institution: | Department of Mathematics, Eastern Washington University, 216 Kingston Hall, Cheney, Washington 99004-2418 |
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Abstract: | A continuous extension of the objective function to a projective space guarantees that for each data set there exists at least one hyperplane or hypersphere minimizing the average squared distance to the data. For data sufficiently close to a hypersphere, as the collinearity of the data increases, so does the sensitivity of the fitted hypersphere to perturbations of the data. |
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Keywords: | Fitting geometric circles spheres total least-squares |
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