为什么逻辑回归是线性分类器？【转载】

转自：https://stats.stackexchange.com/questions/93569/why-is-logistic-regression-a-linear-classifier

1.提问

Since we are using the logistic function to transform a linear combination of the input into a non-linear output, how can logistic regression be considered a linear classifier?

Linear regression is just like a neural network without the hidden layer, so why are neural networks considered non-linear classifiers and logistic regression is linear?

2.回答

因为逻辑回归的函数中，μ可以写为x的线性函数。而神经网络不能写为自变量x的线性函数。

并且关于决策边界:

=0.5是一个决策边界，sigmoid函数值>0.5是被预测为正类（假设阈值设置为0.5），<0.5被预测为负类。

那么此时关于x的函数即是Θ*x=0.<-决策边界。