COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules
COMPLEX embeds multiparameter persistence modules with a closed-form two-sided distortion bound and strong Orbit scores.
COMPLEX is a closed-form, training-free embedding of multiparameter persistence modules that slices each module along a near-diagonal net and embeds slice barcodes with the PLACE/PALACE landmark map. Under a checkable coherence condition, reported for every audited Orbit5k pair, it supplies a lower gauge and, with the usual upper bound, a two-sided distortion bound. Using only a cross-validated SVM head, it reaches 91.95% on Orbit5k and 92.98% on Orbit100k. An RBF-SVM scores 91% where 1-NN scores 78%, and one fixed configuration beats GRIL on four molecular benchmarks.
- Slices modules and embeds barcodes using certified PLACE/PALACE landmark maps.
- Reports 91.95% on Orbit5k and 92.98% on Orbit100k with an SVM.
- RBF-SVM reaches 91% while one-nearest-neighbor reaches 78% on the same features.
- Exceeds GRIL on four shared molecular benchmarks with one fixed configuration.
From the original article
1 min read at arxiv.orgEvery multiparameter persistence vectorization we know of carries a one-sided Lipschitz upper bound and nothing below it: without a lower gauge there is no sense in which the features are faithful, and no per-prediction guarantee can be built on them. This paper supplies the missing side.
By Sushovan Majhi · arxiv.org
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