针对极端学习机(ELM)不能用于多层前向神经网络学习的问题,通过揭示单层前向神经网络(SLFN)的ELM与岭回归以及中心化的岭回归之间的关系,提出了SLFN的最小学习机。通过证明核化的中心化岭回归与核化的PCA之间的关系,提出以无限可微的核函数为激励函数的多层前向神经网络(MLFN)的最小学习机LLM.SLFN/MLFN的最小学习机能够保持ELM的上述优势。
In this paper,the link among extreme learning machine(ELM) for single-layer feedforward neural network(SLFN)and ridge regression and centered ridge regression is theoretically revealed,and accordingly,least learning machine(LLM) is proposed for SLFN.By using iteratively kernelized PCAs + centered ridge regression,LLM for multi-layer feedforward neural network with kernel activation functions is theoretically developed with keeping the same advantage of ELM and LLM for SLFN.