MDS简介

MDS是一个统计技术集合,用于可视化地描述距离集合中的相似性和差异性.对于经典的MDS的处理过程包括:输入一个包含数据集中任意两个数据点之间距离的距离矩阵,返回一个坐标集合,这个集合可以近似反应每对数据点之间的距离.

之所以说是近似反应,是因为在二维空间中很可能不存在被一组距离分开的点集. 例如: 3个彼此之间距离都是1的点,是一个等边三角形的顶点.因此,不可能另外一个点到这个三角形的三个顶点的距离都是1.

MDS简单应用

构建距离矩阵

library('foreign')

library('ggplot2')

# 构建不用样本对p1-6的评价矩阵1 0 -1表示

set.seed(851982) # To make sure results are consistent

ex.matrix

row.names(ex.matrix)

colnames(ex.matrix)

数据如下

P1 P2 P3 P4 P5 P6

A 0 -1 0 -1 0 0

B -1 0 1 1 1 0

C 0 0 0 1 -1 1

D 1 0 1 -1 0 0

构建相似性矩阵

这里用A*t(A)表示不同样本间的相似性

ex.mult

ex.mult

数据如下

A B C D

A 2 -1 -1 1

B -1 4 0 -1

C -1 0 3 -1

D 1 -1 -1 3

计算欧氏距离

ex.dist

ex.dist

数据如下

A B C

B 6.244998

C 5.477226 5.000000

D 2.236068 6.782330 6.082763

MDS进行可视化

# Visualize clusters

ex.mds

plot(ex.mds, type = 'n')

text(ex.mds, c('A', 'B', 'C', 'D'))

结果:

A B C

B 6.244998

C 5.477226 5.000000

D 2.236068 6.782330 6.082763

书中投票分类例子

dataclean

收集数据文件名

library('foreign')

library('ggplot2')

data.dir

data.files

data.files

#[1] "sen101kh.dta" "sen102kh.dta"

#[3] "sen103kh.dta" "sen104kh.dta"

#[5] "sen105kh.dta" "sen106kh.dta"

#[7] "sen107kh.dta" "sen108kh_7.dta"

#[9] "sen109kh.dta" "sen110kh_2008.dta"

#[11] "sen111kh.dta"

foreign包读取dta数据

rollcall.data

function(f)

{

read.dta(file.path(data.dir, f), convert.factors = FALSE)

})

# Ninth code snippet

dim(rollcall.data[[1]])

#[1] 103 647

head(rollcall.data[[1]])

#cong id state dist lstate party eh1 eh2 name V1 V2 V3 ... V638

#1 101 99908 99 0 USA 200 0 0 BUSH 1 1 1 ... 1

#2 101 14659 41 0 ALABAMA 100 0 1 SHELBY, RIC 1 1 1 ... 6

#3 101 14705 41 0 ALABAMA 100 0 1 HEFLIN, HOW 1 1 1 ... 6

#4 101 12109 81 0 ALASKA 200 0 1 STEVENS, TH 1 1 1 ... 1

#5 101 14907 81 0 ALASKA 200 0 1 MURKOWSKI, 1 1 1 ... 6

#6 101 14502 61 0 ARIZONA 100 0 1 DECONCINI, 1 1 1 ... 6

按照document清洗数据

rollcall.simplified

{

no.pres

for(i in 10:ncol(no.pres))

{

no.pres[,i] 6, 0, no.pres[,i])

no.pres[,i] 0 & no.pres[,i] < 4, 1, no.pres[,i])

no.pres[,i] 1, -1, no.pres[,i])

}

return(as.matrix(no.pres[,10:ncol(no.pres)]))

}

rollcall.simple

计算mDS(important part)

# and calculate the Euclidan distance between each Senator.

rollcall.dist

构建MDS数据矩阵

congresses

for(i in 1:length(rollcall.mds))

{

names(rollcall.mds[[i]])

congress

congress.names

function(n) strsplit(n, "[, ]")[[1]][1])# [, ]正则表达式 有逗号或空格就拆分字符串

rollcall.mds[[i]]

name = congress.names,

party = as.factor(congress$party),

congress = congresses[i])

}

head(rollcall.mds[[1]])

mds图形化

base.110

scale_size(range = c(2,2), guide = 'none') +

scale_alpha(guide = 'none') +

theme_bw() + #bw背景

theme(axis.ticks = element_blank(), axis.text.x = element_blank(), axis.text.y = element_blank(), panel.grid.major = element_blank()) +

ggtitle("Roll Call Vote MDS Clustering for 110th U.S. Senate") +

xlab("") +# 无横纵坐标名

ylab("") +

scale_shape(name = "Party", breaks = c("100", "200", "328"), #按照不同的Party画不同shape的points labels = c("Dem.", "Rep.", "Ind."), solid = FALSE) +# 标签

scale_color_manual(name = "Party", values = c("100" = "black", "200" = "dimgray", "328"="grey"), breaks = c("100", "200", "328"), labels = c("Dem.", "Rep.", "Ind."))

print(base.110 + geom_text(aes(color = party, alpha = 0.75, label = cong.110$name,#在x,y处画名字 size = 2)))

按不同届的国会记录画多图

# Fourteenth code snippet

# Create a single visualization of MDS for all Congresses on a grid

all.mds

all.plot

geom_point(aes(shape = party, alpha = 0.75, size = 2)) +

scale_size(range = c(2, 2), guide = 'none') +

scale_alpha(guide = 'none') +

theme_bw() +

theme(axis.ticks = element_blank(), axis.text.x = element_blank(), axis.text.y = element_blank(), panel.grid.major = element_blank()) +

ggtitle("Roll Call Vote MDS Clustering for U.S. Senate (101st - 111th Congress)") +

xlab("") +

ylab("") +

scale_shape(name = "Party", breaks = c("100", "200", "328"), labels = c("Dem.", "Rep.", "Ind."), solid = FALSE) +

facet_wrap(~ congress)

print(all.plot)