# Plotting decision boundary of Logistic Regression (liblinear)

I have liblinear model file for a classifier learned using logistic regression. In the file, they say, the weight vector and intercept term. But when I simply plot it as $$w^Tx + b$$ on the original data, it does not seems like the proper decision boundary. But in case of SVM, plotting

$$w^Tx+b$$ seems to be the correct way. Is there any difference in case of Logistic Regression with liblinear ?

Logistic regression does not have decision boundaries. It is a method to estimate probabilities of events/class membership. Decisions are made in a separate step once you know the estimated risk along with utilities/costs/loss function, which is the way optimum decisions are made.

• but if i am not mistaken, it is among the linear classifiers, and the probability of class membership is decided based on $$\frac{1}{1+exp(-f(x))}$$ where $$f(x) = w^Tx+b$$, which is a linear decision boundary. – Shew Dec 4 '14 at 16:57
• That would be true if "decision" were part of logistic regression. It is not. – Frank Harrell Dec 4 '14 at 16:58
• what do you mean by "decision" being part of logistic regression ?. In normal settings (without any thresholding), the decision is similar to the case of SVMs, right ?. +ve, $$if p(x) \geq 0.5$$ (similar to $$f(x) >= 0$$ – Shew Dec 4 '14 at 17:03
• I said that "decision" is not part of logistic regression. The construct you wrote which uses a highly arbitrary 0.5 risk threshold is not part of logistic regression. Logistic regression is a direct probability estimator. – Frank Harrell Dec 4 '14 at 17:10
• Ok. In that case, what is the $$w$$ and $$b$$ in the logistic model file ?. What is the plane $$w^T+x$$ corresponds to ? – Shew Dec 4 '14 at 20:06