Yousef Saad Department Of Computer Science And Engineering

The problem of Dimension Reduction
➤ Given d ≪ m find a mapping
Φ : x ∈ R m −→ y ∈ R d
➤ Mapping may be explicit [typically linear], e.g.:
➤ Or implicit (nonlinear)
Practically:
y = V T x
Given: X ∈ R m×n .
Want: a low-dimensional representation
Y ∈ R d×n of X
CSE Colloquium 11/09/09 p. 22