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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?

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  • $\begingroup$ 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. $\endgroup$
    – Erwan
    Jul 17 at 23:49
  • $\begingroup$ @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? $\endgroup$
    – Hoda
    Jul 18 at 15:35
  • $\begingroup$ 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. $\endgroup$
    – Erwan
    Jul 18 at 20:06

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