Table 2 The algorithm of a stacked auto-encoder

Input: train pictures after integral projection: X, train labels: L

Output: weight matrices: \( {\left\{\overset{\wedge }{W_1^h}\right\}}_{h=1}^{H+1} \) , biases: \( {\left\{\overset{\wedge }{W_0^h}\right\}}_{h=1}^{H+1} \)/*H: number of hidden layers*/

Step 1: the training of hidden layers:

① Initialization: Y₀ = X

② Greedy layer-wise training (h ∈ {1, …, H})

- Acquire the parameters \( \left\{{W}_1^h,{W}_0^h\right\} \) for the h-th hidden layer

- \( {Y}_h=f\left({W}_1^h{Y}_{h-1}+{W}_0^h\right) \)

Step 2: fine-tuning the whole network:

① Initialization:\( {\left\{\overset{\wedge }{W_1^h}={W}_1^h,\overset{\wedge }{W_0^h}={W}_0^h\right\}}_{h=1}^H,\left\{{\overset{\wedge }{W}}_1^{H+1},{\overset{\wedge }{W}}_0^{H+1}\right\} \)=random

② Back-propagation with a gradient-descent theory