Research map / Graph learning / Graph algorithms and clustering
Tight and fast generalization error bound of graph embedding in metric space
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Evaluate graph-embedding hypotheses as functions of the finite set of pairwise representation distances | Graph embedding in metric spaces · Couple-label pair data | excess-risk bound dependence on space radius | Helped |
| Localize the hypothesis class around the optimal representations | Proposed graph-embedding bound · Couple-label pair data | fastest excess-risk convergence rate: O(1/\sqrt{\NData}) -> O(1/\NData) | Helped |
| Use the proposed bound instead of the existing hyperbolic-space bound | Hyperbolic graph embedding on a complete balanced 5-ary tree of height 4 · Tree graph; \DistanceExponent=1 | sufficient training data size: 7.30 \times 10^{72} -> 1.19 \times 10^{9} | Helped |
| Use the proposed bound instead of the existing hyperbolic-space bound | Hyperbolic graph embedding on a complete balanced 5-ary tree of height 4 · Tree graph; \DistanceExponent=2 | sufficient training data size: 7.43 \times 10^{12} | Helped |
| Use a hyperbolic ball rather than a Euclidean ball | Graph embedding of a tree · Tree graph | embedding approximation error | Helped |
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