?????????????xi????????????
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-1.png)
????v???????????:
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-2.png)
??v?????(unit)?||v||=1
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-3.png)
?????
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-4.png)
??????????(x1, x2, x3, x4, x5, x6)????????v?v?(??)??????????v???????v???????
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-5.png)
C???????(covariance matrix)
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-6.png)
?????????????????????????(?????):
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-7.png)
??????????????Lagrange??
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-8.png)
???????
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-9.png)
??????:
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-10.png)
??????????(???????)??????C (??????)????(eigenvalue, ? )?????(eigenvector, v)?
note:??????eigenvalue?????(variance)?eigenvector?????????????????????
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-11.png)
????(?????)???????PCA???????????(????????????????????????????????)???????????????13.26????????????1.23
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-12.png)
PCA????????????????PC1??????????????
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-13.png)
?????????????????????????????????????????????????(13.26/(13.26+1.23)= 91.51%)????????PCA?????????????????????????
?????
???????????????????????????????????????????????????????????????????????????????????????????100???????????????100????????????????????????????????
?????????????????
??????????? (Cumulative Proportion)???????????????
?????? (Cumulative Proportion)????
????????????????????????????????????(???)
???????????????PC?
![](https://stayfreemagazine.org/wp-content/uploads/2021/08/e6a99fe599a8-e7b5b1e8a888e5adb8e7bf92e4b8bbe68890e58886e58886e69e90principal-component-analysis-pca-14.png)
??????????????????????????????????????(Factor Analysis)????????????????????????????????????????????????????????????????????????
Note: ????????????????????????????????????????????????????????????/????????????????????????????????????????????????????
????????MATLAB code?python code??