# Comparison of echo state network output layer classification methods on noisy data

## TL;DR

This paper compares three output layer training methods for echo state networks on noisy data, highlighting their effectiveness in different noise conditions for classification tasks.

## Contribution

It introduces a comparative analysis of linear, sparse, and low-rank approximation methods for echo state network output layers on noisy datasets.

## Key findings

- Regularized least squares excel on low-noise data.
- Low-rank approximations improve accuracy with high noise.
- Sparse weights offer a trade-off between complexity and performance.

## Abstract

Echo state networks are a recently developed type of recurrent neural network where the internal layer is fixed with random weights, and only the output layer is trained on specific data. Echo state networks are increasingly being used to process spatiotemporal data in real-world settings, including speech recognition, event detection, and robot control. A strength of echo state networks is the simple method used to train the output layer - typically a collection of linear readout weights found using a least squares approach. Although straightforward to train and having a low computational cost to use, this method may not yield acceptable accuracy performance on noisy data. This study compares the performance of three echo state network output layer methods to perform classification on noisy data: using trained linear weights, using sparse trained linear weights, and using trained low-rank approximations of reservoir states. The methods are investigated experimentally on both synthetic and natural datasets. The experiments suggest that using regularized least squares to train linear output weights is superior on data with low noise, but using the low-rank approximations may significantly improve accuracy on datasets contaminated with higher noise levels.