  Understanding human behavior fundamentally relies on accurate 3D human pose
estimation. Graph Convolutional Networks (GCNs) have recently shown promising
advancements, delivering state-of-the-art performance with rather lightweight
architectures. In the context of graph-structured data, leveraging the
eigenvectors of the graph Laplacian matrix for positional encoding is
effective. Yet, the approach does not specify how to handle scenarios where
edges in the input graph are missing. To this end, we propose a novel
positional encoding technique, PerturbPE, that extracts consistent and regular
components from the eigenbasis. Our method involves applying multiple
perturbations and taking their average to extract the consistent and regular
component from the eigenbasis. PerturbPE leverages the Rayleigh-Schrodinger
Perturbation Theorem (RSPT) for calculating the perturbed eigenvectors.
Employing this labeling technique enhances the robustness and generalizability
of the model. Our results support our theoretical findings, e.g. our
experimental analysis observed a performance enhancement of up to $12\%$ on the
Human3.6M dataset in instances where occlusion resulted in the absence of one
edge. Furthermore, our novel approach significantly enhances performance in
scenarios where two edges are missing, setting a new benchmark for
state-of-the-art.
