Embedding Visuals — Fast Graph Embeddings

Visuals

UMAP Embedding Projections

Each plot shows 64-dimensional embeddings reduced to 2D via UMAP. Points are colored by ground-truth class labels. Tight, well-separated clusters indicate that the embedding captures the graph's community structure.

Cora 2,708 nodes · 7 classes · Citation Network

Cleora 86.1%

NetMF 83.9%

DeepWalk 83.5%

HOPE 82.1%

ProNE 17.9%

RandNE 24.7%

Cleora shows the tightest, most distinct clusters — 7 classes cleanly separated. NetMF and DeepWalk also show structure but with more overlap. ProNE and RandNE produce noisy, unstructured projections.

CiteSeer 3,312 nodes · 6 classes · Citation Network

Cleora 82.4%

NetMF 81.0%

HOPE 72.4%

ProNE 21.1%

RandNE 20.2%

Cleora separates 6 subject areas into clear, compact groups. NetMF is close behind but with more inter-class mixing. HOPE captures some structure. ProNE and RandNE show little meaningful separation.

Facebook 4,039 nodes · Louvain Communities · Social Network

Cleora 99.0%

NetMF 95.7%

ProNE 68.5%

RandNE 63.2%

Facebook ego-network communities detected via Louvain. Cleora and NetMF both capture the community structure well, with Cleora achieving the tightest separation. ProNE and RandNE show less organized projections.

PubMed 19,717 nodes · 3 classes · Citation Network

Only 3 algorithms complete on PubMed — HOPE, NetMF, GraRep, DeepWalk, and Node2Vec fail (timeout or OOM).

Cleora 87.9%

ProNE 33.9%

RandNE 35.1%

At 19.7K nodes, most algorithms crash. Cleora cleanly separates all 3 diabetes paper categories with distinct, well-formed clusters. ProNE and RandNE produce uniform noise — the difference is dramatic.

PPI 3,890 nodes · 50 classes · Protein Interaction

Only 3 algorithms complete on PPI — HOPE, NetMF, GraRep, DeepWalk, and Node2Vec fail (timeout or OOM).

Cleora 100%

ProNE 2.3%

RandNE 7.3%

PPI has 50 protein function classes. Cleora achieves perfect classification accuracy and its UMAP shows rich, multi-cluster structure. ProNE and RandNE produce near-random noise with no discernible class separation.

Methodology

All embeddings use 64 dimensions, reduced to 2D via UMAP (n_neighbors=15, min_dist=0.1, random_state=42)
Cleora uses num_iterations=40, propagation='left', normalization='l2', whiten=True
Points are colored by ground-truth labels (Cora/CiteSeer/PubMed/PPI) or Louvain communities (Facebook)
Accuracy numbers from the full benchmark suite (separate 128-dim runs, 3-run average)