พูดคุย:Machine Learning at U of C

แยก page เป็น week ๆ เหอะ (เดี๋ยวตามอ่านทุกอาทิตย์) -- Jung 16:22, 4 เมษายน 2007 (ICT)

question about OLS

In OLS section, you say

Assume WLOG that ${\mathcal {W}}=span\{v_{1},\ldots ,v_{m}\}$ and ${\mathcal {W}}^{\bot }=ker\mathbf {X} ^{T}\mathbf {X} =span\{v_{m+1},\ldots ,v_{d}\}$.

but what is $m$?? -- Jung 01:25, 9 เมษายน 2007 (ICT)

• Jung -- m is the number of nonzero eigenvalues. ${\mathcal {W}}$ is a subspace spanned by eigenvectors corresponding to nonzero eigenvalues. Recall that if all eigenvalues are positive, then the linear-map has no nullspace (and thus invertible). Basically, I splited the whole space to the invertible part (spanned eigenvectors corresponding to positive lambdas) and noninvertible part (spanned by the rest eigenvectors). --Ed 13:36, 9 เมษายน 2007 (ICT)

Thanks. I was confusing because I thought $m$ might be the geometric multiplicity of $\mathbf {X} ^{T}\mathbf {X}$. -- Jung 01:50, 10 เมษายน 2007 (ICT)