Algorithm 1: Auto-encoder training algorithm.

Input: Sets of data to train $x_1,x_2\dots x_n$ Output: encoder $f_{\varphi }$, decoder $g_{\theta }$   $\varphi ,\theta \leftarrow$ Initialize network parameters repeat   Compute mean squared error   $L_{(\varphi ,\theta ;x_i)}={\sum }_i\left|\right|x_i-g_{\theta }\left(f_{\varphi }\left(x_i\right)\right){\left|\right|}^2$   $\varphi ,\theta \leftarrow$ Update parameters by SGD until convergence of parameters ($\varphi ,\theta$)