Research Article

Broad Echo State Network with Reservoir Pruning for Nonstationary Time Series Prediction

Algorithm 1

BPESN with pruning optimization.
Input: mappingNum, enhanceNum, mapFunction, enhanceFunction, thresholdRMSE, thresholdPrunNum, N, K
    mappingNum ← number of neurons in mapping layer
    enhanceNum ← number of neurons in mapping layer
    mapFunction ← mapping layer activation function
    enhanceFunction ← enhanced layer activation function
    thresholdRMSE ← threshold of RMSE in incremental learning
    thresholdPrunNum ← threshold of the number of pruning
           N ← number of neurons in reservoir pool in ESN
           K ← logarithms of neurons pruning the reservoir pool
Output: network prediction output after each pruning optimization
Algorithm:
(1)    for i in mappingNum:
(2)      for j in enhanceNum:
(3)          enter data into the mapping layer and initialize it and get the matrix ;
(4)          initialize the ESN of the reinforced layer, collect the calculation result matrix H;
(5)          each ESN is pruned and optimized, and the RMSE after optimization is calculated and record the number of pruning C;
(6)          if RMSE < thresholdRMSE or C < thresholdPrunNum:
(7)             Add unpruned ESN units into the reinforced layer for further pruning;
(8)          else:
(9)             Calculation of the same mapping layer different enhancement layer ESN pruning optimized performance index;
(10)    end
(11)end
(12)the optimized parameters and predicted output are calculated.