PCA explained variance and clustering Social scientist here with little background in stats. I have a question regarding a PCA I've carried out on my data. I have 17 variables catching different properties of neighbourhoods (geometrical and topological). The correlation matrix shows little correlation among them; as I understand, that's okay because it means my variables are actually catching different features of the individuals (300 neighbourhoods).
I ran PCA using FactoMineR, I generated the factor map, and then cut the dendrogram using HCPC. The dendrogram comes out with a line that cuts the it at 5, which, I asume is the optimal number of clusters.
Here's my questions:
1) The factor map indicates that my two first principal components explain 48% of the variance in the data. I've read that this might be due to that the correlation among variables is not very significant. Is this really important? My goal is mostly to group the individuals by type and claim that there's x types of neighbourhoods in my city.
2) The dendrogram seems to indicate 5 as an optimal number of clusters but when I cut it at 8 it seems closer to what I'm looking for. Would it be statistically wrong if I decided to go for 8 and omit the grouping of 5? I know that 8 sounds arbitrary and that I maybe should have gone with a simple k-means clustering but I tried that and it didn't work. The groups k-means generated didn't make any sense. 
Any help greatly appreciated.
JF


 A: If the first two components would explain almost 100%, then this would essentially say that most of your attributes are meaningless. So no, you do not want this value to be too high.
At the same time, if you would need all 17 components, you will likely already see the curse of dimensionality where similarity becomes hard to decide.
A: 1) The factor map indicates that my two first principal components explain 48% of the variance in the data. I've read that this might be due to that the correlation among variables...
PCA does only make sense when correlation exist.
It is a variance maximizing orthogonal projection. I.e. no correlation no fun.
2) The dendrogram seems to indicate 5 as an optimal number of clusters but when I cut it at 8 it seems closer to what I'm looking for. Would it be statistically wrong if I decided to go for 8 and omit the grouping of 5...
The dendogram is created with a distance matrix (and the distance measure is up to you). If it makes practical sense to go for 8 and you can explain those 8 in a meaningful way, then go for it.
What do you try to analyze?
There might be better ways to achieve dimensionality reduction.
