A Spectral Decomposition Framework for Multiscale Nonlinear Dimensionality Reduction
Dimensionality reduction (DR) involves two longstanding trade-offs. First, preserving local neighborhoods can come at the cost of global structure. Neighbor embedding methods such as t-SNE and UMAP prioritize local similarity preservation but do not explicitly constrain global organization, whereas standard spectral methods such as Laplacian Eigenmaps capture smooth, coarse-scale graph structure but offer limited flexibility to depict finer local structure. Second, the flexibility of nonlinear DR methods often comes at the cost of analytical transparency. Many methods do not explicitly reveal how high-dimensional structure produces patterns in the embedding. We introduce SDMP (Spectral De...
| Authors | Zeyang Huang, Angelos Chatzimparmpas, Thomas Höllt et al. |
|---|---|
| Primary category | cs.LG |
| Published | 2 April 2026 |
| Last updated at source | 15 September 2026 |
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