This experiment extends Batched K-means by smoothing feature vectors over graph neighborhoods before clustering.

Smoothing combines each node feature with features from nearby nodes over $H$ hops:

\[\boldsymbol{x}_i^{(h)} = \alpha \boldsymbol{x}_i^{(h - 1)} + (1 - \alpha) \left( \sum_{j \in \mathcal{N}_i} \boldsymbol{x}_j^{(h - 1)} \right), \qquad h=1, \dots, H\]

where $\alpha$ controls how strongly the original feature is preserved and $\mathcal{N}_i$ is the neighborhood of node $i$.

Method Visual Overview

The graph is built and sampled as in the Graph Autoencoder.

Results

Results below use $H=3$ hops. More hops increase smoothing; fewer hops preserve more local variability.

Lyngen

Nordnes

Svalbard