clustification: train/predict on approximated manifold instead of original space

[sreichl]

• high dimensional UMAP/densMAP embedding (pro: non-linear; con: requires parameters)
• PCA (pro: no parameters; con: linear)
• Laplacian / spectral space (pro: more topologic; con: requires parameters and more steps)
  • VS: i.e. build your c-knn/densmap network, take the laplacian, then take the eigenvectors of the laplacian to represent the intrinsic topology/geometry of the manifold
  • VS: As I understand the 0 eigenvalued (first) eigenvectors give you anyway the connected components and then the next low frequency eigenvectors can start to give you more geometry.