Gaussian Random Projection

Status: outline — expand with notation and a small NumPy demo.

Goals¶

• Project (\mathbb{R}^n \to \mathbb{R}^m) with a random Gaussian matrix

• Scaling so expected lengths are preserved

• Compare with other random maps (e.g. sparse / Achlioptas-style)

Outline¶

1. Projection matrix (R \in \mathbb{R}^{m \times n}) with i.i.d. Gaussian entries

2. Typical length preservation after projection

3. Simple experiment: pairwise distances before/after

4. Link to the Johnson–Lindenstrauss lemma

Sources¶

• Random-Projection.ipynb in this folder

• Blum–Hopcroft–Kannan, random projections sections