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Principal Component Analysis

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Title: Principal Component Analysis


1
Principal Component Analysis
2
????
????(weighted sum) ????(linear combination)
?
?????? (?? ???)(????) (?? ???)(????)
????(intellectual ability)
?????? (? ???)(?) (??? ???)(???)
?
?????(weight vector)
3
????? ???? ??
Dimension reduction
ex)
??, ??
????
4
?????? ????
?? ??????
?? ??????
?? ??????? ??(principal component candidate)
? ???? ?? ? ??? ????? ???? ???
5
????? ???? ??
????? ?????? ??? ????(??? ??)
??? ?????? ???? ??(?? ???)? ???? ?????? ?? ??
? ?? 20? ??? ?? ??? ??
6
??
??
??
??
??
1
2
3
??
0
2
4
? ???(data point)??? ??? ??? ??? ??.
7
?????
?????(principal component analysis PCA)? p?? ???
??? ??? ?? ?1????? ?p????? p?? ???(????) ? ?
???? ?????? ?? ????? ? ? ??.
?1???(first principal component) ???
?? ? ????(weighted sum) ?2???(second principal
component) (?1???? ????? ??) ??? ? ???
? ???? ?3???( third principal component)
(?1??? ? ?2???? ????? ??) ??? ? ??? ?
????
????? ?????(principal component score)??
??. ????? ?? ???? ?? ????.
8
?? ????? ?1???, ?2???, ? ?3???? ???? ???? ???
??? ??? ?????.
9
?????? ??-??? ??
10
X1,X2,X3? 3?? ?????
lt?? 4.3gt
11
3D Scatter Plot, Pairwise Scatter Plot
12
PCA_EXAMPLE??? SigmaPlot?? ??? ??
lt?? 4.4gt
PCA_Example.JNB ??
13
PCA_EXAMPLE??? SAS? ??? ??
lt?? 4.5gt
Pairwise scatter plot(PCA_EXAMPLE).txt ?? ??
14
?????
15
?1???
16
lt?? 4.6gt
17
Z1? ???? ??? ??? ????? ?? ??
lt?? 4.7gt
18
?2???
19
?3???
20
Z1, Z2, Z3? ???
21
???? ????
22
(No Transcript)
23
R? ???/????
24
??????
? ???? ???? ?
1 0.7 0.7 1
data example(typecorr) input _type_ _name_
x1 x2 cards corr x1 1 . corr x2 0.7
1 run proc princomp dataexample run
25
proc princomp dataPCA_EXAMPLE run
26
proc factor n3 run
27
??????
SAS? ??? ??????
?????(PCA_EXAMPLE)proc iml.txt ??
?????(PCA_EXAMPLE)proc factor.txt ??
28
???? ??
29
?????(GSP_RAW) ??
30
(No Transcript)
31
GSP_RAW??? ??????
32
???????(GSP_SHARE)??
33
GSP_RAW? ????
34
(No Transcript)
35
?????(gsp_share)proc princomp.txt
36
GSP_SHARE? ????
37
(No Transcript)
38
??? ???
39
GSP_SHARE.JNB
40
????? ???
41
GSP_SHARE.JNB
42
?????? ????
????(dimension reduction)
???? ????(pattern recognition)
43
Cavalli-Sforza? ??
lt?? 4.1gt, lt?? 4.2gt p.85
44
(No Transcript)
45
??????
46
???????
47
???? ????
48
?????? ??
49
(No Transcript)
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