Loss function

Triplet Loss:

$x_i^a$xia​是anchor, $x_i^p$xip​是positive , $x_i^n$xin​是negtive
$\sum_i^N[||f(x_i^a)-f(x_i^p)||^2 - || f(x_i^a)-f(x_i^n)||^2 + \alpha]_{+}$∑iN​[∣∣f(xia​)−f(xip​)∣∣2−∣∣f(xia​)−f(xin​)∣∣2+α]+​

Center Loss

在cross-entry loss的基础之上，增加同一类的均值loss.

$L=L_S+\lambda L_C = -\sum_{i=1}^m log \frac{e^{W_{y_i}^T x_i + b_{y_i}}}{\sum_{j=1}^n e^{W_{y_j}^T x_i + b_{y_j}}} + \frac{\lambda}{2}\sum_{i=1}^m ||x_i-c_{y_i}||^2_2$L=LS​+λLC​=−∑i=1m​log∑j=1n​eWyj​T​xi​+byj​​eWyi​T​xi​+byi​​​+2λ​∑i=1m​∣∣xi​−cyi​​∣∣22​

A-softmax Loss

Large Angle Margin
$L_{ang}=\frac{1}{N}\sum_{i=1}-log(\frac{e^{||x_i||cos(m \theta_{y_i},i)}}{e^{||x_i||cos(m \theta_{y_i},i)} + \sum_{j \neq y_i}e^{||x_i||cos(\theta_{y_i},i)}})$Lang​=N1​∑i=1​−log(e∣∣xi​∣∣cos(mθyi​​,i)+∑j​=yi​​e∣∣xi​∣∣cos(θyi​​,i)e∣∣xi​∣∣cos(mθyi​​,i)​)