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Circular Regression

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This Demonstration considers an application of circular regression. Starting with a scatter plot of experimental data, we try to determine the center and radius of the circle that best fit the observations.

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The first application of least squares minimizes the objective function with center at and radius :

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Since this represents the averaged distance of the observed points from the optimal circumference, it is referred to as a geometric fit.

The second objective function is referred to as an algebraic fit:

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In the latter case, an expedient redefinition of the parameters reduces the problem to a linear regression.

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Contributed by: Lorenzo Roi (June 13)
Open content licensed under CC BY-NC-SA

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Reference

[1] N. Chernov, Circular and Linear Regression: Fitting Circles and Lines by Least Squares, Boca Raton: Taylor & Francis, 2010.

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