solution

# solution - Link between LDA and OLS Jean-Philippe Vert June...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Link between LDA and OLS Jean-Philippe Vert June 9, 2011 This is the solution to exercise 4.2 of [1] which shows a link between linear discriminant analysis (LDA) and ordinary least squares (OLS) in the binary case. We have features x ∈ R p and a two-class response, with class sizes N 1 , N 2 . The training patterns are denoted x 1 , . . . , x N ∈ R p , stored in the n × p matrix X . We encode the class of each training point in the real number y i =- N/N 1 for patterns x i in class 1, and y i = N/N 2 for patterns x i in class 2. (a) From equation (4.11) in [1] we know that, in the binary case, the LDA rule classifies a pattern x to class 2 if x > ˆ Σ- 1 (ˆ μ 2- ˆ μ 1 ) > 1 2 ˆ μ > 2 ˆ Σ- 1 ˆ μ 2- 1 2 ˆ μ > 1 ˆ Σ- 1 ˆ μ 1 + log N 1 N- log N 2 N , (1) and class 1 otherwise. (b) Let us introduce a few more notations. Let U i ∈ R n be the class indicator vector of class i , and U = U 1 + U 2 be the vector with all entries equal to 1. When we encode class 1 (resp. class 2) by the real number a 1 =- N/N 1 (resp. a 2 = N/N 2), the vector of labels becomes Y = a 1 U 1 + a 2 U 2 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

solution - Link between LDA and OLS Jean-Philippe Vert June...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online