# Reservoir computing approaches for representation and classification of multivariate time series

arXiv: https://arxiv.org/abs/1803.07870 · HTML: https://mlsanity.com/paper/1803.07870/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2018.

## Built on by (most cited first, 30 of 38)

- [Scalable Spatiotemporal Graph Neural Networks](https://mlsanity.com/paper/2209.06520/) (2022)
- [Self-Supervised Time Series Representation Learning via Cross Reconstruction Transformer](https://mlsanity.com/paper/2205.09928/) (2022)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [TodyNet: Temporal Dynamic Graph Neural Network for Multivariate Time Series Classification](https://mlsanity.com/paper/2304.05078/) (2023)
- [Direct data-driven forecast of local turbulent heat flux in Rayleigh-B'enard convection](https://mlsanity.com/paper/2202.13129/) (2022)
- [Leading or Following? Dyadic Robot Imitative Interaction Using the Active Inference Framework](https://mlsanity.com/paper/2103.02137/) (2021)
- [Latent Processes Identification From Multi-View Time Series](https://mlsanity.com/paper/2305.08164/) (2023)
- [PRformer: Pyramidal Recurrent Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2408.10483/) (2024)
- [ResCP: Reservoir Conformal Prediction for Time Series Forecasting](https://mlsanity.com/paper/2510.05060/) (2025)
- [Cluster-based Input Weight Initialization for Echo State Networks](https://mlsanity.com/paper/2103.04710/) (2021)
- [Stochastic Reservoir Computers](https://mlsanity.com/paper/2405.12382/) (2024)
- [Structure is information: structural identifiability mappings for machine learning with partially observed dynamical systems](https://mlsanity.com/paper/2502.04131/) (2025)
- [Clustering Method for Time-Series Images Using Quantum-Inspired Computing Technology](https://mlsanity.com/paper/2305.16656/) (2023)
- [Time-Series Forecasting and Sequence Learning Using Memristor-based Reservoir System](https://mlsanity.com/paper/2405.13347/) (2024)
- [Optimal input representation in neural systems at the edge of chaos](https://mlsanity.com/paper/2107.05709/) (2021)
- [Resource-efficient Medical Image Analysis with Self-adapting Forward-Forward Networks](https://mlsanity.com/paper/2406.14038/) (2024)
- [Interpreting Temporal Graph Neural Networks with Koopman Theory](https://mlsanity.com/paper/2410.13469/) (2024)
- [From Neurons to Computation: Biological Reservoir Computing for Pattern Recognition](https://mlsanity.com/paper/2505.03510/) (2025)
- [Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics](https://mlsanity.com/paper/2507.06050/) (2025)
- [Sensitivity-Guided Framework for Pruned and Quantized Reservoir Computing Accelerators](https://mlsanity.com/paper/2603.08737/) (2026)
- [Deep Neural Networks for Approximating Stream Reasoning with C-SPARQL](https://mlsanity.com/paper/2106.08452/) (2021)
- [Caformer: Rethinking Time Series Analysis from Causal Perspective](https://mlsanity.com/paper/2403.08572/) (2024)
- [k-Graph: A Graph Embedding for Interpretable Time Series Clustering](https://mlsanity.com/paper/2502.13049/) (2025)
- [FlowMixer: A Depth-Agnostic Neural Architecture for Interpretable Spatiotemporal Forecasting](https://mlsanity.com/paper/2505.16786/) (2025)
- [From Neural Activity to Computation: Biological Reservoirs for Pattern Recognition in Digit Classification](https://mlsanity.com/paper/2510.05637/) (2025)
- [A Weak Penalty Neural ODE for Learning Chaotic Dynamics from Noisy Time Series](https://mlsanity.com/paper/2511.06609/) (2025)
- [Neuro-Inspired Visual Pattern Recognition via Biological Reservoir Computing](https://mlsanity.com/paper/2602.05737/) (2026)
- [Reservoir observer enhanced with residual calibration and attention mechanism](https://mlsanity.com/paper/2604.08592/) (2026)
- [Direct Spatial Implementation of Sparse Matrix Multipliers for Reservoir Computing](https://mlsanity.com/paper/2101.08884/) (2021)
- [Faster than LASER -- Towards Stream Reasoning with Deep Neural Networks](https://mlsanity.com/paper/2106.08457/) (2021)

## Abstract (arXiv)

Classification of multivariate time series (MTS) has been tackled with a large variety of methodologies and applied to a wide range of scenarios. Reservoir Computing (RC) provides efficient tools to generate a vectorial, fixed-size representation of the MTS that can be further processed by standard classifiers. Despite their unrivaled training speed, MTS classifiers based on a standard RC architecture fail to achieve the same accuracy of fully trainable neural networks. In this paper we introduce the reservoir model space, an unsupervised approach based on RC to learn vectorial representations of MTS. Each MTS is encoded within the parameters of a linear model trained to predict a low-dimensional embedding of the reservoir dynamics. Compared to other RC methods, our model space yields better representations and attains comparable computational performance, thanks to an intermediate dimensionality reduction procedure. As a second contribution we propose a modular RC framework for MTS classification, with an associated open-source Python library. The framework provides different modules to seamlessly implement advanced RC architectures. The architectures are compared to other MTS classifiers, including deep learning models and time series kernels. Results obtained on benchmark and real-world MTS datasets show that RC classifiers are dramatically faster and, when implemented using our proposed representation, also achieve superior classification accuracy.