I am experimenting with Kmeans clustering. My data (vectors) was in 300 dimensions which I am converting into 2D and 3D using PCA. Now, to find the optimal number of clusters, I used the Silhouette score. However, for 2D the best Silhouette score is showing for 3 clusters (silhouette score = 0.45), and for 3D it is showing 9 clusters (silhouette score = 0.3861).
I want to know whether it is normal? If yes, what is the reason for this? What should I choose 2D or 3D?
Also, the reason for experimenting with 2D and 3D is because I wanted to plot the 3D graph using seaborn.