Algorithm 1 Training process of an autoencoder.

Input: Dataset $A=\left\{a^i\right\},a^i\in {\mathbb{R}}^{KN}$, the number of hidden units $n_h$ and the number of the iterations T, initialize the matrices and biases randomly. Output: The optimization outcomes. 1:for$i=1$ to T do 2:   Perform forward propagation to compute $r\left(a^i\right)$. 3:   Compute output error by $h\left(a^i\right)-r\left(a^i\right)$. 4:   Perform backward propagation to compute $\mathsf{\Delta }\psi$ and $\mathsf{\Delta }{\psi }^{\prime }$. 5:   Update $\psi$ by $\psi =\psi +\mathsf{\Delta }\psi$ and ${\psi }^{\prime }={\psi }^{\prime }+\mathsf{\Delta }{\psi }^{\prime }$. 6:end for