The brief structure leading to the milestone of PCA is as below:
Happy Holiday, friends.
After undestanding the definition of mean value, variance and covariance,
I would like to share how to combine linear transformation with what we've learned.
Here, there are two linear transformations: shift and scale.
Assume the original dataset and its mean value is as follows:
income_data = [23000, 50000, 40000]
E[income_data] = (23000+50000+40000)/3 = 37666.67
Because of the national holiday, the government decides to add 1000 dollars to every citizen.
income_shift_data = [24000, 51000, 41000]
E[income_shift_data] = (24000+51000+41000)/3
= 38666.67 = 37666.67 + 1000 = E[income_data] + 1000
By observing the change of the value, we got a relationship between the orginal dataset and the shifted dataset, that is, E[income_shift_data] = E[income_data] + 1000.
Having the formular be more general, it as follows:
E[D+a] = E[D] + a, where a is the number of shifted value.
And let's see how linear transformation of scale works tomorrow!
Have a good day.