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

Abstract

A recent paper (Neural Networks, 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 the pointwise error in approximation using least squares optimization based on this kernel, in particular, how the error 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 investigating the use of different pre-processing measures, kernels, and manifold dimension. Specifically, it is shown that the Gaussian kernel introduced in the above mentioned paper leads to a near-competitive performance to deep neural networks, and offers significant improvements in speed and memory requirements. Similarly, a kernel based on treating the feature space as a submanifold of the Grassman manifold outperforms conventional hand-crafted features. To demonstrate the fact that our methods are agnostic to the domain knowledge, we examine the classification problem in a simple video data set.

Local approximation of operators

“…It can then be shown (see [24,Theorem 6.1]) for a recent proof) using the localization properties of the kernels Φ Ξ1,n proved in [23] that with n = c 2 n 1 for a suitable constant c 2 , the system of equations…”