I have a dataset which contains 10000 examples. Each example has 100 dimensions. These dimensions have the same scale.
It seems that it is appropriate to make the number of clusters equal to 3.
I actually do not see any clue from the 2-D plot that the dataset can be separated into 3 clusters... It seems that all examples huddle together.
I feel that the clustering is kind of "rigid" in the 2D space.
So my questions are:
1) I trust the result of the elbow plot moreat this moment. So how does PCA help people to understand whether the dataset can be separable?
2) If PCA shows that a dataset cannot be separated well in 2D space, does it mean that the data still can be well separated in the original high dimension space?
============ EDIT: I Have also tried Multidimensional scaling (MDS).
It seems that it does not look much better than PCA... Three clusters are not very "natural".
========== EDIT 1/26:
@ttnphns @Anony-Mousse @usεr11852 Thanks for your comments. You guy are right. I just find that there are a lot of all-zero vectors in my dataset. Since they are meaningless in my application. So now I removed them, reduce dimensions by PCA, and plot it again.
I think It looks more reasonable now.