# Negative correlation in incremental learning

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## Abstract

Negative Correlation Learning (NCL) has been successfully applied to construct neural network ensembles. It encourages the neural networks that compose the ensemble to be different from each other and, at the same time, accurate. The difference among the neural networks that compose an ensemble is a desirable feature to perform incremental learning, for some of the neural networks can be able to adapt faster and better to new data than the others. So, NCL is a potentially powerful approach to incremental learning. With this in mind, this paper presents an analysis of NCL, aiming at determining its weak and strong points to incremental learning. The analysis shows that it is possible to use NCL to overcome catastrophic forgetting, an important problem related to incremental learning. However, when catastrophic forgetting is very low, no advantage of using more than one neural network of the ensemble to learn new data is taken and the test error is high. When all the neural networks are used to learn new data, some of them can indeed adapt better than the others, but a higher catastrophic forgetting is obtained. In this way, it is important to find a trade-off between overcoming catastrophic forgetting and using an entire ensemble to learn new data. The NCL results are comparable with other approaches which were specifically designed to incremental learning. Thus, the study presented in this work reveals encouraging results with negative correlation in incremental learning, showing that NCL is a promising approach to incremental learning.

## Keywords

Neural network ensembles Incremental learning Negative correlation learning Multi-layer perceptrons Self-generating neural tree Self-organising neural grove Classification## Abbreviations

- NCL
Negative correlation learning

- SGNT
Self-generating neural tree

- SGNN
Self-generating neural network

- ESGNN
Ensemble of self-generating neural networks

- SONG
Self-organising neural grove

- MLP
Multi-layer perceptron

- SOM
Self-organising map

- EFuNN
Evolving fuzzy neural network

- AdaBoost
Adaptive boosting

- ART
Adaptive resonance theory

- GL
Generalization loss

## Notes

### Acknowledgements

The first author would like to thank the United Kingdom Government and the School of Computer Science of the University of Birmingham for the financial support in the form of an Overseas Research Students Award (ORSAS) and a School Research Scholarship. The authors are grateful to the guest editor, Professor Bogdan Gabrys, and anonymous referees for their valuable comments, which have helped to improve the quality of this paper.

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