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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Online Sequential Extreme Learning Machine With Kernels
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Online Sequential Extreme Learning Machine With Kernels

机译：带内核的在线顺序极限学习机

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摘要

The extreme learning machine (ELM) was recently proposed as a unifying framework for different families of learning algorithms. The classical ELM model consists of a linear combination of a fixed number of nonlinear expansions of the input vector. Learning in ELM is hence equivalent to finding the optimal weights that minimize the error on a dataset. The update works in batch mode, either with explicit feature mappings or with implicit mappings defined by kernels. Although an online version has been proposed for the former, no work has been done up to this point for the latter, and whether an efficient learning algorithm for online kernel-based ELM exists remains an open problem. By explicating some connections between nonlinear adaptive filtering and ELM theory, in this brief, we present an algorithm for this task. In particular, we propose a straightforward extension of the well-known kernel recursive least-squares, belonging to the kernel adaptive filtering (KAF) family, to the ELM framework. We call the resulting algorithm the kernel online sequential ELM (KOS-ELM). Moreover, we consider two different criteria used in the KAF field to obtain sparse filters and extend them to our context. We show that KOS-ELM, with their integration, can result in a highly efficient algorithm, both in terms of obtained generalization error and training time. Empirical evaluations demonstrate interesting results on some benchmarking datasets.
机译：极限学习机（ELM）最近被提议为不同学习算法系列的统一框架。经典的ELM模型由固定数量的输入矢量非线性扩展的线性组合组成。因此，在ELM中学习等同于找到使数据集上的错误最小化的最佳权重。此更新以批处理模式工作，可使用显式功能映射或内核定义的隐式映射。尽管已经针对前者提出了在线版本，但对于后者而言，到目前为止尚未完成任何工作，并且是否存在针对基于内核的在线ELM的有效学习算法仍然是一个未解决的问题。通过简要介绍非线性自适应滤波与ELM理论之间的一些联系，在此简要介绍中，我们提出了用于此任务的算法。特别是，我们提出了将属于内核自适应过滤（KAF）系列的众所周知的内核递归最小二乘法直接扩展到ELM框架。我们称结果算法为内核在线顺序ELM（KOS-ELM）。此外，我们考虑在KAF领域中使用两种不同的准则来获得稀疏滤波器并将其扩展到我们的上下文中。我们证明，在获得的泛化误差和训练时间方面，KOS-ELM及其集成可导致高效算法。实证评估显示了一些基准数据集上有趣的结果。

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