PCA(Principal Component Analysis)

[Jerry]

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Referenced by 주성분 분석(PCA)이란? (tistory.com)

Conserve dispersion.

The projection to the hyperplane of a low dimension comes to cut down on the dimension. Then what hyperplane choice looks better? 

Let's look at the example like the above, When to have a simple 2 dimensional dataset, the 3 axis takes a place as our hyperplane candidate. Here we can take a look at that a way to pick up the solid line is the conservation of a dispersion to the maximum and the c2 dotted line selection is a way to make a decrease in the dispersion. 

It can be thought of that selecting an axis enable to make  dispersion conservation into the maximum rather than a projection to the other direction is a least loss of information. and a large dispersion make a distinction on the difference between data where it is due to that we can make a our model into much better direction.    

Therefore, detecting an axis that the dispersion comes to the maximum in the PCA , and after the orthogonal to this first axis, the second axis conserving the remaining dispersion to the maximum searches out. 

There is no option to pick-up in the 2 dimension example. However, in case of the multi- dimensional dataset, an axis orthogonal to several directions will be found out.

In this way, a unit vector defining the i-th axis is called the i-th principal component. In the upper example, the first PC is c1 and the second is c2.