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Metric Embedding.pdf

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Preview of Metric Embedding
🔗 Source: tcs.nju.edu.cn
📊 Size: 5.91 MB
📄 Pages: 56 pages
⬇️ Downloads: 149

Summary

Dimension Reduction involves mapping points from a high-dimensional space to a lower-dimensional space with minimal distortion. The Johnson-Lindenstrauss Theorem states that for any set of n points in ℝd, there exists a mapping ϕ to ℝk with k = O(ϵ−2 log n) such that ∀x, y: (1 −ϵ)∥x −y∥2 ≤ ∥ϕ(x) −ϕ(y)∥2 ≤ (1 + ϵ)∥x −y∥2, allowing embedding in O(log n) dimension with constant distortion.

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Description

Dimension Reduction involves mapping points from a high-dimensional space to a lower-dimensional space with minimal distortion.

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  • File Format: PDF
  • File Size: 5.91 MB
  • Pages: 56
  • Language: EN
  • Total Downloads: 149
  • Last Updated: 2 days ago

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This PDF document about Metric Embedding provides comprehensive information and guidance. Whether you're a beginner or advanced user, this resource offers valuable insights into Metric Embedding.

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