# Random Projections and Natural Sparsity in Time-Series Classification: A Theoretical Analysis

arXiv: https://arxiv.org/abs/2502.17061 · HTML: https://mlsanity.com/paper/2502.17061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 38 references that are in the map.
- First posted on arXiv 24 Feb 2025.

## Builds on (most cited first, 9 of 9)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Deep learning for time series classification: a review](https://mlsanity.com/paper/1809.04356/) (2018)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification](https://mlsanity.com/paper/2012.08791/) (2020)
- [Bake off redux: a review and experimental evaluation of recent time series classification algorithms](https://mlsanity.com/paper/2304.13029/) (2023)
- [MultiRocket: Multiple pooling operators and transformations for fast and effective time series classification](https://mlsanity.com/paper/2102.00457/) (2021)
- [HYDRA: Competing convolutional kernels for fast and accurate time series classification](https://mlsanity.com/paper/2203.13652/) (2022)
- [Time Series Clustering With Random Convolutional Kernels](https://mlsanity.com/paper/2305.10457/) (2023)
- [An Experimental Evaluation of Nearest Neighbour Time Series Classification](https://mlsanity.com/paper/1406.4757/) (2014)

## Abstract (arXiv)

Time-series classification is essential across diverse domains, including medical diagnosis, industrial monitoring, financial forecasting, and human activity recognition. The Rocket algorithm has emerged as a simple yet powerful method, achieving state-of-the-art performance through random convolutional kernels applied to time-series data, followed by non-linear transformation. Its architecture approximates a one-hidden-layer convolutional neural network while eliminating parameter training, ensuring computational efficiency. Despite its empirical success, fundamental questions about its theoretical foundations remain unexplored. We bridge theory and practice by formalizing Rocket's random convolutional filters within the compressed sensing framework, proving that random projections preserve discriminative patterns in time-series data. This analysis reveals relationships between kernel parameters and input signal characteristics, enabling more principled approaches to algorithm configuration. Moreover, we demonstrate that its non-linearity, based on the proportion of positive values after convolutions, expresses the inherent sparsity of time-series data. Our theoretical investigation also proves that Rocket satisfies two critical conditions: translation invariance and noise robustness. These findings enhance interpretability and provide guidance for parameter optimization in extreme cases, advancing both theoretical understanding and practical application of time-series classification.