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Higher-order extreme learning machine
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AI
DOI：10.1016/j.cogsys.2026.101474.png)
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Abstract
En 中文
The training process of feed-forward neural networks is a slow and computationally intensive procedure mainly due to the iterative nature of most algorithms. A solution to this problem was the creation of the extreme learning machine (ELM) algorithm for single-layer neural networks (SLNNs). This method uses a very fast approach where the hidden-layer weights and thresholds are randomized, and the output layer's weights are analytically calculated using the Moore-Penrose pseudo-inverse. Although it provides good generalization performance, it is restricted in traditional neuron types where each neuron's input is multiplied by its corresponding weight. On the other hand, most ELM variants have focused on algorithmic enhancements such as robustness or parameter tuning, without considering the integration of higher-order or multi-cube neurons into the hidden and output layers while preserving ELM's single-pass training speed. This paper introduces six ELM architectures for single-layer neural networks (SLNNs) that replace low-order units with higher-order (sigma-pi) and multi-cube variants (the latter enable controllable expressivity without exponential weight growth). The advantage of higher-order units lies in their ability to utilize more weights than traditional neurons, thereby overcoming the linear separability limitation of low-order units. The experimental results indicated that higher-order SLNN variants demonstrated better generalization performance compared to SLNNs trained with the traditional ELM and online sequential ELM (OS-ELM) algorithms. This observation experimentally verified across 15 classification datasets and eight regression datasets.
Keywords:
Artificial neural network
Extreme learning machine
Feed forward neural network
Higher-order neuron
Multi-cube neuron
Sigma-pi neuron