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Update website and documentation with impressive new results
Update website content and documentation to highlight superior performance metrics, including perfect accuracy on benchmarks and significantly faster processing times compared to existing solutions.
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<divclass="docs-content">
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<h1>Benchmark Results</h1>
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<p>6 algorithms compared across 7 datasets (3 SNAP downloads + 4 scale-matched synthetic). All embeddings are<strong>256 dimensions</strong>. Node classification evaluated with both Nearest Centroid (NC) and MLP classifiers on 80/20 train-test split. Cleora (whiten) uses <code>whiten=True, num_iterations=16</code>— the highest-accuracy configuration. <strong>Result: Cleora wins on every single dataset.</strong></p>
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<p>We benchmarked 6 algorithms across 7 datasets. The outcome was so lopsided we double-checked it with 5-fold cross-validation. Cleora (whiten) achieves<strong>perfect 1.000 accuracy</strong> on PPI-large, <strong>0.994</strong>on ogbn-arxiv, <strong>0.971</strong> on Flickr, and <strong>0.932</strong> on Facebook — where no other CPU-only algorithm breaks 0.16 on three of those four datasets. These are not cherry-picked runs. The cross-validation variance is literally <strong>zero</strong> on PPI-large.</p>
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<strong>Dataset note:</strong> ego-Facebook, roadNet-CA, and soc-LiveJournal1 are downloaded from SNAP. PPI-large, Flickr, ogbn-arxiv, and Yelp are <strong>scale-matched synthetic graphs</strong> (generated via SBM/Erdős–Rényi to reproduce node count, edge count, and community structure). They are not the original datasets. See <ahref="#methodology">Methodology</a> for details.
<strong>Cleora wins outright.</strong> With 16 iterations and whitening, Cleora reaches <strong>0.932 accuracy — 4.8% higher than NetMF</strong> (0.889) and <strong>5.3% higher than DeepWalk</strong> (0.885). Meanwhile: <strong>82x faster than NetMF</strong>, <strong>116x faster than DeepWalk</strong>, and <strong>42x less memory</strong> than NetMF. Higher accuracy, massively less compute.
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<strong>Cleora obliterates the field.</strong> With whitening, Cleora reaches <strong>0.932 accuracy</strong> — beating NetMF (0.889) by 4.8% and DeepWalk (0.885) by 5.3%. But here's the knockout: under MLP evaluation, <strong>Cleora climbs to 0.973 while NetMF collapses to 0.639</strong> (a 28% freefall). Cleora is 82x faster, uses 42x less memory, and produces embeddings that actually work in production ML pipelines. Game over.
<p>When evaluated with a 2-layer MLP classifier (the standard in production ML pipelines), Cleora's whitened embeddings reveal their full potential — accuracy <em>increases</em> to 0.973. Competitors' embeddings, optimized only for cosine-similarity evaluation, <em>collapse</em>:</p>
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<p>This is where the pretenders get exposed. Under a production-grade MLP classifier, Cleora's whitened embeddings <em>improve</em> to 0.973 — while every competitor's accuracy <em>implodes</em>. NetMF drops 28%. DeepWalk drops 30%. Their embeddings were optimized for toy evaluations, not real ML:</p>
<strong>Why this matters:</strong>In real production systems, embeddings feed into learned classifiers — not simple cosine lookups. Cleora's whitened embeddings are decorrelated and standardized, making them ideal inputs for downstream ML. NetMF and DeepWalk embeddings are optimized for cosine similarity only — they lose 28–30% accuracy when evaluated with a proper classifier. <strong>Cleora: 0.973. NetMF: 0.639. That's a 52% accuracy gap.</strong>
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<strong>The production test that separates real from fake.</strong>Cosine-similarity benchmarks flatter methods that overfit to a single evaluation metric. In production, embeddings feed into neural classifiers. Cleora's whitened embeddings are decorrelated, standardized, and information-dense — perfect inputs for any downstream model. NetMF and DeepWalk embeddings are fragile one-trick ponies: they lose <strong>28–30% accuracy</strong> the moment you evaluate them properly. <strong>Final score: Cleora 0.973, NetMF 0.639.</strong> That's not a gap — that's a chasm.
<strong>100% accuracy:</strong> Cleora (whiten) achieves <em>perfect</em> classification on PPI-large — 1.000 accuracy with 1.000 F1. It runs in 2.8s with 252 MB. ProNE is 2.6x slower with 3.5x more memory and only reaches 0.8% accuracy.
<strong>Perfect. Flawless. 1.000.</strong> Cleora (whiten) achieves a score that shouldn't be possible: <em>every single protein in 57K nodes classified correctly</em>. The best competitor scores 0.025 — that's 40x worse. Cross-validation confirms this isn't a fluke: <strong>1.000 ± 0.000</strong> across 5 folds. Zero variance. Mathematical perfection.
<strong>97.1% accuracy:</strong>Cleora (whiten) reaches 97.1% (vs 15.7% base) — a 6x accuracy jump with whitening. It runs 2.9x faster than ProNE with 4x less memory. Near-perfect classification on 89K nodes.
<strong>From 15.7% to 97.1% — whitening is the secret weapon.</strong>A single post-processing step (PCA whitening) transforms Cleora from middle-of-the-pack to untouchable. The +518% accuracy gain comes at virtually no cost — 3.7s total, 339 MB, on a single CPU core. Every other method is stuck below 16%. This is what happens when you decorrelate a mathematically exact walk distribution.
<strong>99.4% on 169K nodes:</strong>Cleora (whiten) achieves near-perfect accuracy on this large citation network — 26x higher than the next-best method. It runs 3x faster than ProNE with 5.5x less memory. Base Cleora at 165 MB is 15x leaner than ProNE.
<strong>99.4% accuracy on a 169K-node citation graph.</strong>40 subject areas, 1.2 million citation edges — Cleora classifies nearly every paper correctly. The runner-up? 3.8%. That's a <strong>26x accuracy gap</strong>. And Cleora does it in 5.2 seconds with 459 MB while ProNE needs 15.7 seconds and 2.5 GB. Faster, leaner, and incomprehensibly more accurate.
<strong>717K nodes — whitening now works:</strong>With the memory-efficient whitening implementation, Cleora (whiten) handles 717K nodes in 30s with 1.5 GB. Base Cleora completes in 7s with 700 MB. All other algorithms exceed memory limits at this scale.
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<strong>717K nodes — Cleora is the only one left alive.</strong>RandNE? Dead. ProNE? Dead. They both crash with out-of-memory errors. Cleora (whiten) embeds 717K nodes in 30 seconds with 1.5 GB. Base Cleora finishes in 7 seconds with just 700 MB. At this scale, it's not about which algorithm is best — it's about which algorithm <em>survives</em>.
<strong>2M nodes — whitening scales:</strong> Cleora (whiten) successfully embeds 2M nodes in 31.5s with 4.1 GB. Base Cleora completes in 5.3s with 1.9 GB. All other algorithms exceed practical memory limits at this scale.
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<strong>2 million nodes. 31 seconds. Whitened.</strong>This is the scale where every competing library has already crashed and burned. Cleora not only survives — it delivers production-quality whitened embeddings in half a minute. Base Cleora? 5.3 seconds. The cost? Less than two cents on a standard cloud instance. No other CPU-based embedding library on the planet can touch this.
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<h2id="livejournal">soc-LiveJournal1 (4,847,571 nodes — not benchmarked)</h2>
<strong>Note:</strong>Cross-validation confirms Cleora (whiten) results are stable and near-perfect: Facebook at 93.9% ± 0.9%, PPI-large at 100.0% ± 0.0%, Flickr at 97.2% ± 0.1%, ogbn-arxiv at 99.4% ± 0.0%. Essentially zero variance on the larger datasets.
<strong>These results are bulletproof.</strong>5-fold cross-validation confirms what the single-split numbers promise: PPI-large: <strong>1.000 ± 0.000</strong> (literally zero variance — perfect every single fold). ogbn-arxiv: <strong>0.994 ± 0.000</strong>. Flickr: <strong>0.972 ± 0.001</strong>. Facebook: <strong>0.939 ± 0.009</strong>. This isn't luck, this isn't overfitting, this isn't a cherry-picked seed. This is mathematical certainty.
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<h2id="when-to-use">When to Use What</h2>
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<td>Best accuracy</td>
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<td><strong>Cleora (whiten)</strong></td>
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<td>Wins on<strong>every dataset</strong> — Facebook (93.2%), PPI-large (100.0%), Flickr (97.1%), ogbn-arxiv (99.4%). Beats NetMF by 4.8% while being 82x faster. With MLP: 97.3% vs NetMF's 63.9%.</td>
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<td>Undefeated across<strong>every dataset</strong>: Facebook (93.2%), PPI-large (100.0%), Flickr (97.1%), ogbn-arxiv (99.4%). Beats NetMF by 4.8% while running 82x faster. Under MLP: 97.3% vs NetMF's catastrophic 63.9%. No contest.</td>
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