forked from szcf-weiya/ESL-CN
-
Notifications
You must be signed in to change notification settings - Fork 0
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
illustrate the results of szcf-weiya#144
- Loading branch information
1 parent
90523bc
commit acf8fdf
Showing
1 changed file
with
66 additions
and
0 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,66 @@ | ||
library(MASS) | ||
X = rbind(iris3[,,1], iris3[,,2], iris3[,,3]) | ||
Y = cbind(rep(c(1, 0, 0), rep(50, 3)), | ||
rep(c(0, 1, 0), rep(50, 3)), | ||
rep(c(0, 0, 1), rep(50, 3))) | ||
labels = rep(c("s","c","v"), rep(50,3)) | ||
|
||
lda.xfit = lda(labels ~ X) | ||
lm.fit = lm(Y ~ X) | ||
Yhat = lm.fit$fitted.values | ||
lda.yfit = lda(labels ~ Yhat) | ||
|
||
coef(lm.fit) %*% coef(lda.yfit) | ||
# LD1 LD2 | ||
# (Intercept) -3.9697359 5.74257900 | ||
# XSepal L. -0.8293776 -0.02410215 | ||
# XSepal W. -1.5344731 -2.16452123 | ||
# XPetal L. 2.2012117 0.93192121 | ||
# XPetal W. 2.8104603 -2.83918785 | ||
|
||
coef(lda.xfit) | ||
# LD1 LD2 | ||
# XSepal L. -0.8293776 0.02410215 | ||
# XSepal W. -1.5344731 2.16452123 | ||
# XPetal L. 2.2012117 -0.93192121 | ||
# XPetal W. 2.8104603 2.83918785 | ||
|
||
# ############################## | ||
# calculate from scratch | ||
# ############################## | ||
|
||
M = t(Y) %*% X | ||
W = cov(X) | ||
eW = eigen(W) | ||
W2 = eW$vectors %*% diag(1/sqrt(eW$values)) %*% t(eW$vectors) | ||
Mstar = M %*% W2 | ||
Bstar = cov(Mstar) | ||
#Vstar = svd(Mstar)$v # only centered, the svd would correspond to the eigenvector | ||
#Vstar = svd(scale(Mstar, scale = FALSE))$v | ||
Vstar = eigen(Bstar)$vectors | ||
V = W2 %*% Vstar | ||
|
||
M.Yhat = t(Y) %*% Yhat | ||
W.Yhat = cov(Yhat) | ||
eW.Yhat = eigen(W.Yhat) | ||
W2.Yhat = eW.Yhat$vectors %*% diag(1/sqrt(eW.Yhat$values)) %*% t(eW.Yhat$vectors) | ||
Mstar.Yhat = M.Yhat %*% W2.Yhat | ||
Bstar.Yhat = cov(Mstar.Yhat) | ||
# or Vstar.Yhat = svd(scale(Mstar.Yhat, scale = FALSE))$v | ||
Vstar.Yhat = eigen(Bstar.Yhat)$vectors | ||
V.Yhat = W2.Yhat %*% Vstar.Yhat | ||
|
||
coef(lm.fit) %*% V.Yhat | ||
# [,1] [,2] [,3] | ||
# (Intercept) 33.0576048 -8.7664831 5.845502e+08 | ||
# XSepal L. 0.1449341 0.0214029 6.631017e-07 | ||
# XSepal W. 0.2681498 1.9221120 -3.725290e-07 | ||
# XPetal L. -0.3846627 -0.8275534 -1.010485e-07 | ||
# XPetal W. -0.4911291 2.5212213 -5.960464e-08 | ||
|
||
V | ||
# [,1] [,2] [,3] [,4] | ||
# [1,] -0.1449341 -0.0214029 2.9164752 1.336939 | ||
# [2,] -0.2681498 -1.9221120 -1.2263996 -2.405814 | ||
# [3,] 0.3846627 0.8275534 -1.2073719 -2.782287 | ||
# [4,] 0.4911291 -2.5212213 -0.1306168 4.591166 |