# A manifold learning approach for gesture recognition from micro-Doppler radar measurements

arXiv: https://arxiv.org/abs/2110.01670 · HTML: https://mlsanity.com/paper/2110.01670/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 52 references that are in the map.
- First posted on arXiv 4 Oct 2021.

## Builds on (most cited first, 12 of 12)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Overfitting or perfect fitting? Risk bounds for classification and regression rules that interpolate](https://mlsanity.com/paper/1806.05161/) (2018)
- [Measuring the tendency of CNNs to Learn Surface Statistical Regularities](https://mlsanity.com/paper/1711.11561/) (2017)
- [Deep ReLU network approximation of functions on a manifold](https://mlsanity.com/paper/1908.00695/) (2019)
- [Theory of Deep Learning III: explaining the non-overfitting puzzle](https://mlsanity.com/paper/1801.00173/) (2017)
- [Deep nets for local manifold learning](https://mlsanity.com/paper/1607.07110/) (2016)
- [Kernel based analysis of massive data](https://mlsanity.com/paper/2003.13226/) (2020)
- [Theory IIIb: Generalization in Deep Networks](https://mlsanity.com/paper/1806.11379/) (2018)
- [An analysis of training and generalization errors in shallow and deep networks](https://mlsanity.com/paper/1802.06266/) (2018)
- [DNN Transfer Learning from Diversified Micro-Doppler for Motion Classification](https://mlsanity.com/paper/1811.08361/) (2018)
- [Automatic Arm Motion Recognition Based on Radar Micro-Doppler Signature Envelopes](https://mlsanity.com/paper/1910.11176/) (2019)
- [Micro-Doppler Based Human-Robot Classification Using Ensemble and Deep Learning Approaches](https://mlsanity.com/paper/1711.09177/) (2017)

## Built on by (most cited first, 2 of 2)

- [Local approximation of operators](https://mlsanity.com/paper/2202.06392/) (2022)
- [Learning on manifolds without manifold learning](https://mlsanity.com/paper/2402.12687/) (2024)

## Abstract (arXiv)

A recent paper (Neural Networks, bf 132 (2020), 253-268) introduces a straightforward and simple kernel based approximation for manifold learning that does not require the knowledge of anything about the manifold, except for its dimension. In this paper, we examine how the pointwise error in approximation using least squares optimization based on similarly localized kernels depends upon the data characteristics and deteriorates as one goes away from the training data. The theory is presented with an abstract localized kernel, which can utilize any prior knowledge about the data being located on an unknown sub-manifold of a known manifold. We demonstrate the performance of our approach using a publicly available micro-Doppler data set, and investigate the use of different preprocessing measures, kernels, and manifold dimensions. Specifically, it is shown that the localized kernel introduced in the above mentioned paper when used with PCA components leads to a near-competitive performance to deep neural networks, and offers significant improvements in training speed and memory requirements. To demonstrate the fact that our methods are agnostic to the domain knowledge, we examine the classification problem in a simple video data set.