How can I perform a classification with a custom function?

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 a start I read this: http://www.mathworks.co.uk/products/statistics/examples.html?file=/products/demos/shipping/stats/classdemo.html

As my function is neither linear nor quadratic I would like to know how I can use my custom ln function.

Answer 1

[Sannsch]

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.

Answer 2

[Image Analyst]

How about using SVM?

See diagram on: http://en.wikipedia.org/wiki/Support_vector_machine