My set of data points can roughly be broken up into 2 sets with different means. In each set, the points are close to each other (geometrically). Moreover, the variance is the same across both sets of data points.
What is the best way to run PCA on such a dataset? Ideally, I do not want to have to split the dataset. The tricky part is standardizing the data before performing PCA, and in this case, given that I have 2 sets of data centered around 2 different means, there isn't an obvious good way to do that.
Should I perhaps use one mean for standardizing one set and another for the other set, then merge them, and finally perform PCA?
My goal is to use PCA as a low-pass filter: to use the main PCs to eliminate noise from the original data.