Agglomerative Clustering (average linkage) and Pearson Correlation

Does having a positive or negative correlation between features being clustered affect the agglomerative clustering result?

I have three columns in my dataset, and I'm trying to figure out if I should cluster on all three features or use only a subset.

The Pearson correlation coefficients are:

X & Z --> -0.07, p=0.14
X & Y --> -0.08, p=0.08
Z & Y --> 0.68, p<0.001


The Variance Inflation Factor is:

variables   VIF
Y           2.816716
X           3.552227
Z           6.232414


Should I choose X and Y because p-value > 0.05: The correlation is not statistically significant? Just looking at the Variance Inflation Factor and Pearson Correlation analysis enough to determine which features should be chosen for clustering?

• Welcome to DataScienceSE. I'm confused, are you clustering the features or the instances? Assuming it's the standard case of clustering instances, I don't think correlation between features matters much and I would keep all 3 features. Jul 17 at 23:49
• @Erwan When Keeping all 3, I found that the clustering output is greatly influenced by column Z. In an attempt to investigate why that happened, I calculated the Pearson correlation and VIF and found that the VIF for Z was very high. So I'm wondering if that could be the reason?
– Hoda
Jul 18 at 15:35
• But why is it a problem that the clustering output is influenced by Z? I'm not particularly expert with clustering but my thinking would be to keep all the relevant features unless there is a strong reason not to. I'm not aware that it's recommended to avoid correlated features in general. Jul 18 at 20:06