diff --git a/markdown/week2.md b/markdown/week2.md index 15d4e301..62950a95 100644 --- a/markdown/week2.md +++ b/markdown/week2.md @@ -238,7 +238,7 @@ $\theta ={{\left( {X^{T}}X \right)}^{-1}}{X^{T}}y$ 的推导过程: $J\left( \theta \right)=\frac{1}{2m}\sum\limits_{i=1}^{m}{{{\left( {h_{\theta}}\left( {x^{(i)}} \right)-{y^{(i)}} \right)}^{2}}}$ 其中:${h_{\theta}}\left( x \right)={\theta^{T}}X={\theta_{0}}{x_{0}}+{\theta_{1}}{x_{1}}+{\theta_{2}}{x_{2}}+...+{\theta_{n}}{x_{n}}$ -将向量表达形式转为矩阵表达形式,则有$J(\theta )=\frac{1}{2}{{\left( X\theta -y\right)}^{2}}$ ,其中$X$为$m$行$n$列的矩阵($m$为样本个数,$n$为特征个数),$\theta$为$n$行1列的矩阵,$y$为$m$行1列的矩阵,对$J(\theta )$进行如下变换 +将向量表达形式转为矩阵表达形式,则有$J(\theta )=\frac{1}{2}{{\left( X\theta -y\right)}^{2}}$ (此处平方不表示矩阵幂运算),其中$X$为$m$行$n+1$列的矩阵($m$为样本个数,$n$为特征个数),$\theta$为$n+1$行1列的矩阵,$y$为$m$行1列的矩阵,对$J(\theta )$进行如下变换 $J(\theta )=\frac{1}{2}{{\left( X\theta -y\right)}^{T}}\left( X\theta -y \right)$