機器/統計學習:主成分分析(Principal Component Analysis, PCA)

???????????????xi(????)??????v?????(??????????90?)?????????

?????????????xi????????????

????v???????????:

??v?????(unit)?||v||=1

?????

??????????(x1, x2, x3, x4, x5, x6)????????v?v?(??)??????????v???????v???????

C???????(covariance matrix)

?????????????????????????(?????):

??????????????Lagrange??

???????

??????:

??????????(???????)??????C (??????)????(eigenvalue, ? )?????(eigenvector, v)?

note:??????eigenvalue?????(variance)?eigenvector?????????????????????

????(?????)???????PCA???????????(????????????????????????????????)???????????????13.26????????????1.23

PCA????????????????PC1??????????????

?????????????????????????????????????????????????(13.26/(13.26+1.23)= 91.51%)????????PCA?????????????????????????

?????

???????????????????????????????????????????????????????????????????????????????????????????100???????????????100????????????????????????????????

?????????????????

??????????? (Cumulative Proportion)???????????????

?????? (Cumulative Proportion)????

????????????????????????????????????(???)

???????????????PC?

??????????????????????????????????????(Factor Analysis)????????????????????????????????????????????????????????????????????????

Note: ????????????????????????????????????????????????????????????/????????????????????????????????????????????????????

????????MATLAB code?python code??

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