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I'm new to sklearn and want to interpret classification results. I'm confused that what the differences between decision surface and decision boundary are? I saw two examples showing the differences of classifiers:

1) http://scikit-learn.org/stable/auto_examples/svm/plot_iris.html#example-svm-plot-iris-py

2) http://scikit-learn.org/stable/auto_examples/classification/plot_classifier_comparison.html

Both are used to show the difference of classifiers. But the first one used predict and the second one used predict_proba or decision function. So I'm confused.

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The decision surface or boundary is the same. For example in classifications if you have 2 classes of which you want to predict and these 2 classes are represented by three dimensions (N=3) e.g. length, width, height. The decision boundary is a hyperplane of size N-1. The logic here is that to separate N dimensions, you need an object of size N-1 dimensions.

Both of your examples show decision boundaries/surfaces

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