Wasserstein distance based semi-supervised manifold learning and application to GNSS multi-path detection

TL;DR

This work tackles the challenge of training high-performing GNSS multi-path detectors with scarce labeled data by marrying graph-based semi-supervised learning with a Wasserstein-distance–driven similarity metric. The method propagates labels through a neural network by weighting pairwise prediction differences with Wasserstein-based affinities between image samples, computed channel-wise for GNSS I/Q data. Extensive experiments across varying signal-to-noise conditions show that, for suitable hyperparameters, semi-supervised learning can significantly improve classification accuracy over fully supervised training. The approach demonstrates a scalable, data-frugal framework for real-world GNSS interference detection using optimal transport as the key similarity measure.

Abstract

The main objective of this study is to propose an optimal transport based semi-supervised approach to learn from scarce labelled image data using deep convolutional networks. The principle lies in implicit graph-based transductive semi-supervised learning where the similarity metric between image samples is the Wasserstein distance. This metric is used in the label propagation mechanism during learning. We apply and demonstrate the effectiveness of the method on a GNSS real life application. More specifically, we address the problem of multi-path interference detection. Experiments are conducted under various signal conditions. The results show that for specific choices of hyperparameters controlling the amount of semi-supervision and the level of sensitivity to the metric, the classification accuracy can be significantly improved over the fully supervised training method.

Figures (3)

• Figure 1: Examples of pairs of $I$ and $Q$ images from the data generator.
• Figure 2: Architecture of the used in this work LeNail2019.
• Figure 3: Median maximum accuracy for the fully supervised reference cases.