1. R
II 4
.
@yokkuns
.
R Tokyo.R#09
2010/09/19
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2. R
II 4
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3. AGENDA
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4. AGENDA
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5. ID : yokkuns
:
: Web
http://twitter.com/yokkuns
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6. - 1
R Tokyo.R
http://groups.google.co.jp/group/r-study-tokyo
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7. - 2
http://groups.google.co.jp/group/grinning-math
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8. -
PRML
2010.09.11 RPML 13.3 13.3.3
9 R R II
2010.09.19
Tokyo.R#09 4
7
2010.09.25 +WEB
Tokyo.Webmining#7
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9. -
PRML
2010.09.11 RPML 13.3 13.3.3
9 R R II
2010.09.19
Tokyo.R#09 4
7
2010.09.25 +WEB
Tokyo.Webmining#7
@yokkuns (R Tokyo.R#09 )
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10. AGENDA
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11. MDS: multi-dimensional scaling
2 3
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12. ...
MDS
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13. ...
MDS
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14. ...
MDS
@yokkuns (R Tokyo.R#09 )
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15. ...
MDS
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16. ...
MDS
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17. ...
MDS
@yokkuns (R Tokyo.R#09 )
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18. ...
MDS
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19. D n×n = [di j ]
i j di j
di j = ||Xi − X j ||
di j ≥ 0
di j = d ji
di j + d jk ≥ dik
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20. ∑
p ∑
p
edi j = (xik − x jk )2 cdi j = |xik − x jk |
k=1 k=1
∑
p
mdi j = |xik − x jk | q
q
k=1
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21. ∑p
(xik − xi )(x jk − x j )
k=1
ri j = √∑
p ∑n
(xik − xi )2 k=1
(x jk − x j )2
k=1
∑p
xik x jk
k=1
psi j = √∑
p ∑n
x2 k=1
x2
k=1 ik jk
rdi j = 1 − ri j pdi j = 1 − psi j
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22. AGENDA
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23. 2
d2j = ||xi − x j ||2 = (xi − x j )T (xi − x j )
i
= ||xi ||2 + ||x j ||2 − 2xT x j
i
2
bi j = xT x j = xi1 x j1 + xi2 x j2 + · · · + xi p x j p
i
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24. d2j = ||xi ||2 + ||x j ||2 − 2bi j
i
d2 = ||xi ||2
i
d2j = d2 + d2 − 2bi j
i i j
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25. bi j
1 2
bi j = (d + d2 − d2j )
2 i j i
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26. MDS
MDS
cmdscale(d, k = 2, ei g = F ALSE)
d : dist
k :
eig :
@yokkuns (R Tokyo.R#09 )
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27. 21
(eur.cmd< −cmdscale(eurodist))
plot(eur.cmd,type=”n”)
text(eur.cmd,rownames(eur.cmd ))
@yokkuns (R Tokyo.R#09 )
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28. iris
iris.dist< −dist(iris[,-5])
iris.cmd< −cmdscale(iris.dist)
plot(iris.cmd,type=”n”)
iris.lab< −factor(c(rep(”S”,50),rep(”C”,50),rep(”V”,50)))
text(iris.cmd,labels=iris.lab,col=unclass(iris.lab))
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29. AGENDA
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30. ∑∑ ˆ − di j )2
i j ( di j
STRESS1 = ∑∑ 2
di j
STRESS1 %
0.200 20.0%
0.100 10.0%
0.050 5.0%
0.025 2.5%
0.000 0%
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31. MDS
MASS
isoM DS(d, y = cmdscale(d, k), k = 2, maxit = 50, t race = TRUE, t ol =
1e − 3, p = 2)
MASS
sammon(d, y = cmdscale(d, k), k = 2, niter = 100, t race = TRUE, ma gic =
0.2, t ol = 1e − 4)
vegan
met aM DS(comm, dist ance = ”bray”, k = 2, t rymax = 20, aut ot rans f orm =
TRUE, noshare = 0.1, wascores = TRUE, expand = TRUE, t race = 1, plot =
FALSE, previous.best, old.wa = FALSE, ...)
@yokkuns (R Tokyo.R#09 )
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32. install.packages(”mlbench”)
library(mlbench)
install.packages(”e1071”)
set.seed(100)
p< −mlbench.corners(n=160)
lab=as.numeric(p$classes)
x.dist< −dist(p$x)
library(MASS)
par(mar=c(4.5,4.5,1,1), mfrow=c(2,2))
plot(cmdscale(x.dist),pch=lab,col=lab)
plot(sammon(x.dist)$points,pch=lab,col=lab)
plot(isoMDS(x.dist)$points,pch=lab,col=lab)
install.packages(”vegan”)
library(vegan)
x.dist2< −as.matrix(x.dist)
plot(metaMDS(x.dist2)$point,pch=lab,col=lab)
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33. @yokkuns (R Tokyo.R#09 )
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34. AGENDA
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35. cmdscale
isoMDS
sammon
metaMDS
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36. AGENDA
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37. R Tokyo.R#10
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38. AGENDA
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39. @yokkuns (R Tokyo.R#09 )
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