A Global Geometric Framework for Nonlinear Dimensionality Reduction¶
Tenenbaum, J. B., Silva, V. d., & Langford, J. C. (2000). A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science, 290(5500), 2319-2323.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Dimension
- Modern nonlinear methods — Isomap
This sourceIsomap nonlinear manifold-learning method preserving geodesic distances along the data manifold.
- Modern nonlinear methods — Isomap
- Dimensionality Reduction
- The central insight is that real-world data in many high-dimensional spaces actually lies on or near a low-dimensional manifold: thousands of gene-expression measurements per tissue sample often reflect tens of latent biological programs; millions of image pixels reflect dozens of visual features; hundreds of survey items reflect a small set of latent constructs
This sourceIsomap; supports marker 062 (real data lies on/near a low-dimensional manifold). Companion LLE paper: Roweis & Saul, Science 290 (2000): 2323–2326.
- The central insight is that real-world data in many high-dimensional spaces actually lies on or near a low-dimensional manifold: thousands of gene-expression measurements per tissue sample often reflect tens of latent biological programs; millions of image pixels reflect dozens of visual features; hundreds of survey items reflect a small set of latent constructs
- Manifold
- The manifold hypothesis transfers the same framing to high-dimensional data analysis, justifying nonlinear dimensionality reduction as the recovery of the data's intrinsic geometry and letting methods like Isomap and diffusion maps port differential-geometric tools directly.
This sourceThe Isomap method recovers the intrinsic low-dimensional geometry of data lying on a nonlinear manifold, independent of the ambient embedding.
- The manifold hypothesis transfers the same framing to high-dimensional data analysis, justifying nonlinear dimensionality reduction as the recovery of the data's intrinsic geometry and letting methods like Isomap and diffusion maps port differential-geometric tools directly.
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