I know this topic of scaling and normalizing variables for PCA has been posted on a lot, 1, 2, 3. However, I am performing PCA on coordinate data that is measured all on the same scale, i.e. (x,y) data. Would I have to standardize or normalize this data to account for the variance? Or is that not neccassary since the variables are measured on the same scale.
I tested an instnace within my data and found that when I do not scale or normalize the data, I explain 73.8% of the variance in the x direction and 26.1% of the variacne in the y direction. When I scale the data, 88.6% in the x and 11.4% in the y. Normalizing the data doesn't effect the results when there is no scaling because the coordiante data is the range from [0,100], which can be scaled to [0,1].
To be specific, I am performing PCA on coordinate data of individual players to find their area. So I have all the xy data of each player in a set. Before I run PCA on each player I would scale the entire dataset. Then I filtered to get the player, applied PCA, extracted the standard deviation, then used the elipsodial area equation to find the area.