I have always been a bit confused about logistic regression modeling. If I speak to a statistician, they refer to the modeling efforts in terms of the logit link function. However, if I speak with a machine learning expert, they refer to logistic regression as simply implementing a hyperplane (similar to SVM). What is the relationship between the logistic function and the separating hyperplane?
The picture below will probably answer your question.
A logistic regression model with 2 features creates a wave based on the logit link function.
Applying the decision rule (for example above 50%) transforms the wave to a separating hyperplane like that, but not similar to, one found in SVM. This is illustrated in the picture below. Note that this separating hyperplane is in feature space.
These pictures come from http://blog.data-miners.com/2014/03/lines-and-circles-and-logistic.html You can find an expose on om the subject.