Yousef Saad Department Of Computer Science And Engineering

Linear Dimensionality Reduction
Given: a data set X = [x1, x2, . . . , xn], and d the dimension
of the desired reduced space Y = [y1, y2, . . . , yn].
Want: A linear transformation from X to Y
d
m
v T
m
X
Y
n
x
y
n
i
i
d
X ∈ R m×n
V ∈ R m×d
Y = V ⊤ X
→ Y ∈
R d×n
➤ m-dimens. objects (xi) ‘flattened’ to d-dimens. space (yi)
Constraint: The yi’s must satisfy certain properties
➤ Optimization problem
CSE Colloquium 11/09/09 p. 23