Table 2 Work flow of LR

Step 1. Constructing a prediction function

 \( {h}_{\theta }(x)=g\left({\theta}^Tx\right)=\frac{1}{1+{e}^{-{\theta}^Tx}} \)

 θis regression variable, x is independent variable

Step 2. Construction loss function

 \( J\left(\theta \right)=-\frac{1}{m}\sum \limits_{i=1}^m\left[{y}_i\log {h}_{\theta}\left({x}_i\right)+\left(1-{y}_i\right)\log \left(1-{h}_{\theta}\left({x}_i\right)\right)\right] \)

 y is true similarity, m is the number of sample

Step 3. Newton method for getting the minimum J(θ)

 \( \theta \leftarrow \theta -\frac{l^{\hbox{'}}\left(\theta \right)}{l^{\hbox{'}\hbox{'}}\left(\theta \right)} \)

 l(θ) is maximum likelihood function