Abstract: Since the existing inverse-matrix-free extreme learning machine (IF-ELM) only works well in batched way, this paper extends it into its inverse-matrix-free online sequential version called the inverse-matrix-free online sequential extreme learning machine (IOS-ELM). When the proposed algorithm increases the training samples, the Sherman Morrison Woodbury formula is used to update the model, and the newly added hidden layer output weights are directly calculated to avoid the iterative calculation of output weight of analysed training samples. The detailed derivations of the proposed machine IOS-ELM are accordingly given. The experimental results on different types and sizes of datasets show that IOS-ELM indeed is very suitable for the datasets which are gradually generated in an online way, in the sense of both fast training and promising performance.

Key words: inverse-matrix-free, extreme learning machine, online sequential learning, neural networks

摘要： 无逆矩阵极限学习机只能以批量学习方式进行训练，将其拓展为无逆矩阵在线学习版本，提出了无逆矩阵在线序列极限学习机算法（IOS-ELM）。所提算法增加训练样本时，利用Sherman Morrison Woodbury公式对新增样本数据后的模型进行更新，直接计算出新增隐含层输出权重，避免对已经分析过的训练样本的输出权重进行重复计算。给出了所提IOS-ELM算法的详细推导过程。在不同类型和大小的数据集上的实验结果表明，所提IOS-ELM算法非常适合在线方式逐步生成的数据集，在快速学习和性能方面都有很好的表现。

关键词: 无逆矩阵, 极限学习机, 在线序列学习, 神经网络