How can I perform a classification with a custom function?

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I plotted two data sets on a two-dimensional space. Imagine a scatterplot with points that can either be 'x' or 'o'.
I want to compute and draw a decision function, which is given except for one parameter b, simplified: y = ln(b * exp(-6x+7) -b)/10 The decision function with the ideal b should divide the scatterplot into 'x' and 'o' points and minimize the error.
As my function is neither linear nor quadratic I would like to know how I can use my custom ln function.

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Sannsch
Sannsch 2013-8-28
Thank you for the tip. I decided to have another look at the constraints and to express them as a minimax problem. Once I have the optimal b I have the resulting function and can just draw it.

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Image Analyst
Image Analyst 2013-8-28
How about using SVM?

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