Abstract:

To solve the problem that multi-class extreme learning machine (ELM) lacks the ability of probabilistic output, a multi-class probabilistic ELM (MPELM) algorithm is presented based on the combination of sigmoid posterior probability mapping and Lagrange pairwise coupling. Firstly, after separating the multi-class problem into the type of two-class problem by pairwise coupling, each two-class ELM output is transformed to the probabilistic output by sigmoid function. Then, the multi-class probabilistic computing expression is deduced based on the Lagrange multiplier method, which is utilized to fuse all two-class probabilistic outputs. Finally, the probabilistic results of predicted samples belonging to different classes are obtained. The proposed MPELM is applied to remaining useful life (RUL) prognosis. The experiment results show that, compared with multi-class probabilistic support vector machine (MPSVM), though time consuming of the proposed MPELM is higher than MPSVM, less optimized parameter is required while higher forecasting accuracy is achieved by MPELM. The predicting accuracy of the proposed MPELM is similar to MPELM based on the Hastie pairwise coupling (Hastie-MPELM) algorithm. But test time consuming of the proposed MPELM is less than Hastie-MPELM.