# Efficient hinging hyperplanes neural network and its application in nonlinear system identification

## TL;DR

This paper introduces the efficient hinging hyperplanes (EHH) neural network, a fast trainable, interpretable model based on convex optimization, applied successfully to nonlinear system identification with promising accuracy and speed.

## Contribution

The paper proposes the EHH neural network, a novel, interpretable model with a two-stage construction process and demonstrates its effectiveness in nonlinear system identification.

## Key findings

- Fast training via convex optimization
- Good interpretability through ANOVA decomposition
- Effective nonlinear system identification with high accuracy

## Abstract

In this paper, the efficient hinging hyperplanes (EHH) neural network is proposed based on the model of hinging hyperplanes (HH). The EHH neural network is a distributed representation, the training of which involves solving several convex optimization problems and is fast. It is proved that for every EHH neural network, there is an equivalent adaptive hinging hyperplanes (AHH) tree, which was also proposed based on the model of HH and find good applications in system identification. The construction of the EHH neural network includes 2 stages. First the initial structure of the EHH neural network is randomly determined and the Lasso regression is used to choose the appropriate network. To alleviate the impact of randomness, secondly, the stacking strategy is employed to formulate a more general network structure. Different from other neural networks, the EHH neural network has interpretability ability, which can be easily obtained through its ANOVA decomposition (or interaction matrix). The interpretability can then be used as a suggestion for input variable selection. The EHH neural network is applied in nonlinear system identification, the simulation results show that the regression vector selected is reasonable and the identification speed is fast, while at the same time, the simulation accuracy is satisfactory.