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Part.12_Logistic_Regression(ML_Andrew.Ng.)

Last updated Aug 19, 2021 Edit Source

# Logistic Regression

2021-08-19

Tags: #LogisticRegression #MachineLearning #Classification

# Logistic Function

Logistic Function

# Hypothesis Representation

# Decision Boundary

假如我们采用这样的分类方法: hθ(x)0.5y=1hθ(x)<0.5y=0\begin{aligned} &h_{\theta}(x) \geq 0.5 \rightarrow y=1 \\ &h_{\theta}(x)<0.5 \rightarrow y=0 \end{aligned}

那么分类结果最终由h(x)h(x)的值决定: θTx0y=1θTx<0y=0\begin{aligned} θ^Tx≥0⇒y=1\\ θ^Tx<0⇒y=0 \end{aligned}

一个例子: 图中划分数据集的线便是这个h(x)h(x), Decision Boundary, 在曲线上面的点h(x)0h(x)\geq 0, 分类结果为1, 在曲线下面的点h(x)<0h(x)< 0, 分类结果为0.

注意Decision Boundary是h(x)h(x)的性质, 即使上图不画数据点, Boundary依然存在.

# Nonlinearity

就像线性回归可以推广为多项式回归一样, Logistic 回归也可以有非线性的决策边界: