Curvature Augmented Manifold Embedding and Studying

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arXiv:2403.14813v1 Announce Kind: new
Summary: A brand new dimensional discount (DR) and information visualization methodology, Curvature-Augmented Manifold Embedding and Studying (CAMEL), is proposed. The important thing novel contribution is to formulate the DR downside as a mechanistic/physics mannequin, the place the power discipline amongst nodes (information factors) is used to seek out an n-dimensional manifold illustration of the information units. In contrast with many current attractive-repulsive force-based strategies, one distinctive contribution of the proposed methodology is to incorporate a non-pairwise power. A brand new power discipline mannequin is launched and mentioned, impressed by the multi-body potential in lattice-particle physics and Riemann curvature in topology. A curvature-augmented power is included in CAMEL. Following this, CAMEL formulation for unsupervised studying, supervised studying, semi-supervised studying/metric studying, and inverse studying are offered. Subsequent, CAMEL is utilized to many benchmark datasets by evaluating current fashions, equivalent to tSNE, UMAP, TRIMAP, and PacMap. Each visible comparability and metrics-based analysis are carried out. 14 open literature and self-proposed metrics are employed for a complete comparability. Conclusions and future work are steered primarily based on the present investigation. Associated code and demonstration can be found on https://github.com/ymlasu/CAMEL for readers to breed the outcomes and different functions.



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