Background: I have a set of 321 observations of 18 correlated variables, so I do PCA to extract a low dimensional set of features from this high dimensional data set. I select 9 of 18 components(the number of components that explains 80% of total variance) After determining the number of clusters with NbClust, apply k-means clustering to do the classification. I am using the PCA for dimensionality reduction in order to reduce the complexity of my problem, given an interpretation to all the components. My Question: Why are the clusters differenziated only in PC1-other Component plane (example PC1-PC2 plane, PC1-PC3 plane,etc...)? How can i solve this problem?
It might be helpful to look at a plot of the %variance explained vs Component number. If PC1 explains a lot more of the variance than any other component, it may be necessary for clustering of your data.
Also, PC1 may contain the important information that is differentiating your groups. PCA is looking at variance in general, so higher components are possibly capturing smaller deviations (such as those within a group).