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Found 5 papers, 3 papers with code
On-Manifold Projected Gradient Descent
We use these tools to obtain adversarial examples that reside on a class manifold, yet fool a classifier.
ActUp: Analyzing and Consolidating tSNE and UMAP
tSNE and UMAP are popular dimensionality reduction algorithms due to their speed and interpretable low-dimensional embeddings.
GiDR-DUN; Gradient Dimensionality Reduction -- Differences and Unification
In this work, we show that this is indeed possible by combining the two approaches into a single method.
Applications of topological graph theory to $2$-manifold learning
The algorithm developed gives a meaningful description of the embedding as a piecewise linear structure, which is obtained from combinatorial data by projecting points in the point cloud into estimates of tangent planes.
Numerical Analysis
Consistent Manifold Representation for Topological Data Analysis
Finally, we conjecture that CkNN is topologically consistent, meaning that the homology of the Vietoris-Rips complex (implied by the graph Laplacian) converges to the homology of the underlying manifold (implied by the Laplace-de Rham operators) in the limit of large data.
Classical Analysis and ODEs
