In extreme learning machine (ELM), a large number of hidden nodes are required due to the randomly generated hidden layer. To improve network compactness, the ELM with smoothed ℓ₀ regularizer (ELM-SL0 for short) is studied in this paper. Firstly, the ℓ₀ regularization penalty term is introduced into the conventional error function, such that the unimportant output weights are gradually forced to zeros. Secondly, the batch gradient method and the smoothed ℓ₀ regularizer are combined for training and pruning ELM. Furthermore, both the weak convergence and strong convergence of ELM-SL0 are investigated. Compared with other existing ELMs, the proposed algorithm obtains better performance in terms of estimation accuracy and network sparsity.

在极限学习机（ELM）中，由于随机生成的隐藏层，因此需要大量的隐藏节点。为了提高网络紧凑，具有平滑的ELM ℓ ₀正则化（ELM-SL0的简称）中进行了研究。首先，ℓ ₀正则化惩罚项被引入到传统的误差函数，使得不重要输出权重被逐渐被迫零。其次，批次梯度法和平滑ℓ ₀正则化器结合在一起用于培训和修剪ELM。此外，还研究了ELM-SL0的弱收敛性和强收敛性。与其他现有的ELM相比，该算法在估计精度和网络稀疏性方面都具有更好的性能。