如何在R中的线性判别分析图上绘制分类边界 [英] How to plot classification borders on an Linear Discrimination Analysis plot in R
问题描述
我使用线性判别分析(LDA)来研究一组变量在3组之间的区别程度.然后，我使用 plot.lda()函数将数据绘制在两个线性判别式上(x轴为LD1，y轴为LD2).我现在想将LDA的分类边界添加到绘图中.我在允许此功能的函数中看不到参数. partimat()函数允许可视化LD分类边界，但是在这种情况下，变量用作x和y轴，而不是线性判别式.任何有关如何向 plot.lda 添加分类边界的建议，将不胜感激.下面是一些示例代码:
I have used a linear discriminant analysis (LDA) to investigate how well a set of variables discriminates between 3 groups. I then used the plot.lda() function to plot my data on the two linear discriminants (LD1 on the x-axis and LD2 on the y-axis). I would now like to add the classification borders from the LDA to the plot. I cannot see a argument in the function that allows this. The partimat() function allows visualisation of the LD classification borders, but variables are used as the x and y axes in this case, rather than the linear discriminants. Any advice on how to add classification borders to plot.lda would be greatly appreciated. Below is some example code:
library(MASS)
# LDA
t.lda = lda(Group ~ Var1 + Var2, data=mydata,
na.action="na.omit", CV=TRUE)
# Scatter plot using the two discriminant dimensions
plot(t.lda,
panel = function(x, y, ...) { points(x, y, ...) },
col = c(4,2,3)[factor(mydata$Group)],
pch = c(17,19,15)[factor(mydata$Group)],
ylim=c(-3,3), xlim=c(-5,5))
下面是一些示例数据(3组，2个变量):
Below is some example data (3 groups, 2 variables):
> dput(mydata)
structure(list(Group = c("a", "a", "a", "a", "a", "a", "a", "a",
"b", "b", "b", "b", "b", "b", "b", "b", "c", "c", "c", "c", "c",
"c", "c", "c"), Var1 = c(7.5, 6.9, 6.5, 7.3, 8.1, 8, 7.4, 7.8,
8.3, 8.7, 8.9, 9.3, 8.5, 9.6, 9.8, 9.7, 11.2, 10.9, 11.5, 12,
11, 11.6, 11.7, 11.3), Var2 = c(-6.5, -6.2, -6.7, -6.9, -7.1,
-8, -6.5, -6.3, -9.3, -9.5, -9.6, -9.1, -8.9, -8.7, -9.9, -10,
-6.7, -6.4, -6.8, -6.1, -7.1, -8, -6.9, -6.6)), .Names = c("Group",
"Var1", "Var2"), class = "data.frame", row.names = c(NA, -24L
))
> head(mydata)
Group Var1 Var2
1 a 7.5 -6.5
2 a 6.9 -6.2
3 a 6.5 -6.7
4 a 7.3 -6.9
5 a 8.1 -7.1
6 a 8.0 -8.0
从Roman的答案开始，我尝试更改代码以在线性判别标度(这是我要实现的目标)而不是原始变量的标度上绘制分类边界.但是，边界不在应有的位置.对于我在这里做错的任何建议，将不胜感激:
Following on from Roman's answer, I tried to alter the code to plot the classification border on the linear discriminant scale (this is what I am trying to achieve), rather than on the scale of the original variables. However, the border does not sit where it should. Any advice on what I am doing wrong here would be much appreciated:
#create new data
np = 300
nd.x = seq(from = min(mydata$Var1), to = max(mydata$Var1), length.out = np)
nd.y = seq(from = min(mydata$Var2), to = max(mydata$Var2), length.out = np)
nd = expand.grid(Var1 = nd.x, Var2 = nd.y)
#run lda and predict using new data
new.lda = lda(Group ~ Var1 + Var2, data=mydata)
prd = as.numeric(predict(new.lda, newdata = nd)$class)
#create LD sequences from min - max values
p = predict(new.lda, newdata= nd)
p.x = seq(from = min(p$x[,1]), to = max(p$x[,1]), length.out = np) #LD1 scores
p.y = seq(from = min(p$x[,2]), to = max(p$x[,2]), length.out = np) #LD2 scores
#create original plot
quartz()
plot(t.lda, panel = function(x, y, ...) { points(x, y, ...) },
col = c(4,2,3)[factor(mydata$Group)],
pch = c(17,19,15)[factor(mydata$Group)],
ylim=c(-3,3), xlim=c(-5,5))
#add classification border on scale of linear discriminants (NOTE: this step currently doesn't work)
contour(x = p.x, y = p.y, z = matrix(prd, nrow = np, ncol = np),
levels = c(1, 2, 3), add = TRUE, drawlabels = FALSE)
推荐答案
I adapted my code to follow the example found here.
require(MASS)
# generate data
set.seed(357)
Ng <- 100 # number of cases per group
group.a.x <- rnorm(n = Ng, mean = 2, sd = 3)
group.a.y <- rnorm(n = Ng, mean = 2, sd = 3)
group.b.x <- rnorm(n = Ng, mean = 11, sd = 3)
group.b.y <- rnorm(n = Ng, mean = 11, sd = 3)
group.a <- data.frame(x = group.a.x, y = group.a.y, group = "A")
group.b <- data.frame(x = group.b.x, y = group.b.y, group = "B")
my.xy <- rbind(group.a, group.b)
# construct the model
mdl <- lda(group ~ x + y, data = my.xy)
# draw discrimination line
np <- 300
nd.x <- seq(from = min(my.xy$x), to = max(my.xy$x), length.out = np)
nd.y <- seq(from = min(my.xy$y), to = max(my.xy$y), length.out = np)
nd <- expand.grid(x = nd.x, y = nd.y)
prd <- as.numeric(predict(mdl, newdata = nd)$class)
plot(my.xy[, 1:2], col = my.xy$group)
points(mdl$means, pch = "+", cex = 3, col = c("black", "red"))
contour(x = nd.x, y = nd.y, z = matrix(prd, nrow = np, ncol = np),
levels = c(1, 2), add = TRUE, drawlabels = FALSE)
编辑
如果我尝试
library(MASS)
mydata <- structure(list(Group = c("a", "a", "a", "a", "a", "a", "a", "a",
"b", "b", "b", "b", "b", "b", "b", "b", "c", "c", "c", "c", "c",
"c", "c", "c"), Var1 = c(7.5, 6.9, 6.5, 7.3, 8.1, 8, 7.4, 7.8,
8.3, 8.7, 8.9, 9.3, 8.5, 9.6, 9.8, 9.7, 11.2, 10.9, 11.5, 12,
11, 11.6, 11.7, 11.3), Var2 = c(-6.5, -6.2, -6.7, -6.9, -7.1,
-8, -6.5, -6.3, -9.3, -9.5, -9.6, -9.1, -8.9, -8.7, -9.9, -10,
-6.7, -6.4, -6.8, -6.1, -7.1, -8, -6.9, -6.6)), .Names = c("Group",
"Var1", "Var2"), class = "data.frame", row.names = c(NA, -24L
))
np <- 300
nd.x = seq(from = min(mydata$Var1), to = max(mydata$Var1), length.out = np)
nd.y = seq(from = min(mydata$Var2), to = max(mydata$Var2), length.out = np)
nd = expand.grid(Var1 = nd.x, Var2 = nd.y)
#run lda and predict using new data
new.lda = lda(Group ~ Var1 + Var2, data=mydata)
prd = as.numeric(predict(new.lda, newdata = nd)$class)
#create LD sequences from min - max values
p = predict(new.lda, newdata= nd)
p.x = seq(from = min(p$x[,1]), to = max(p$x[,1]), length.out = np) #LD1 scores
p.y = seq(from = min(p$x[,2]), to = max(p$x[,2]), length.out = np) #LD2 scores
# notice I don't use t.lda for first variable
plot(new.lda, panel = function(x, y, ...) { points(x, y, ...) },
col = c(4,2,3)[factor(mydata$Group)],
pch = c(17,19,15)[factor(mydata$Group)],
ylim=c(-3,3), xlim=c(-5,5))
contour(x = p.x, y = p.y, z = matrix(prd, nrow = np, ncol = np),
levels = c(1, 2, 3), add = TRUE, drawlabels = FALSE)
我知道
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