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My goal is to find out where a user would cut a curve. During training, whenever a point on a curve is chosen by the user to be a cutting point, we record some features and use the label '+1' to indicate these features correspond to a cutting point. In order to reduce the training efforts, we would like to avoid recording the points where the user would not cut.

In other words, our training data only consists of inputs labeled with '+1'. I would like to know if there's any SVM-related technique which can handle this case. Finally, we would like the learning machine to tell us whether a point is a cutting point or not.

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What's wrong with making a SVM regression predicting position of the cutting point? – mbq♦ Oct 27 '12 at 22:12
@mbq, can you be more specific? The input to the learning machine is a feature vector, and the output is the (x,y,z) coordinates of the cutting point, is this what you mean? – user11869 Oct 28 '12 at 1:38
What are you trying to predict, the $(x,y,z)$? Then you have a regression problem, not classification. The label is not $+1$, it is $(x,y,z)$. – Douglas Zare Oct 28 '12 at 5:04
As Douglas said. Plus, if this is a curve $(x,y,z)$ translates to one number -- distance to one of the ends. – mbq♦ Oct 28 '12 at 9:07
Construct the +0 points using some sort of sampling? Perhaps random sampling of the curve? – curious_cat Mar 1 at 8:15

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Well, the way I see it, you've got an one-class SVM problem or more broadly a open-set classification problem.

It's implemented in scikit-learn [1] [2]. Maybe taking a look on the formulation here of the Open Set Classification problem and the related machine would help.

[1] http://scikit-learn.org/stable/modules/svm.html#svm-outlier-detection

[2] http://scikit-learn.org/stable/auto_examples/svm/plot_oneclass.html#example-svm-plot-oneclass-py

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