12. ...
MDS
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13. ...
MDS
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14. ...
MDS
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15. ...
MDS
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16. ...
MDS
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17. ...
MDS
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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
@yokkuns (R Tokyo.R#09 )
R II 4 2010/09/19 20 / 40
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
@yokkuns (R Tokyo.R#09 )
R II 4 2010/09/19 21 / 40
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
@yokkuns (R Tokyo.R#09 )
R II 4 2010/09/19 23 / 40
24. d2j = ||xi ||2 + ||x j ||2 − 2bi j
i
d2 = ||xi ||2
i
d2j = d2 + d2 − 2bi j
i i j
@yokkuns (R Tokyo.R#09 )
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25. bi j
1 2
bi j = (d + d2 − d2j )
2 i j i
@yokkuns (R Tokyo.R#09 )
R II 4 2010/09/19 25 / 40
26. MDS
MDS
cmdscale(d, k = 2, ei g = F ALSE)
d : dist
k :
eig :
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27. 21
(eur.cmd< −cmdscale(eurodist))
plot(eur.cmd,type=”n”)
text(eur.cmd,rownames(eur.cmd ))
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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, ...)
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