Feauture selection for clustering regarding zero-correlated feature I want to cluster a 5 feature data-set. Firstly to explore the data I did a correlation matrix to see if some features where highly correlated so I could reduce them. Then I saw a feature that have close to zero correlation against all the other features. This got me wondering if I should exclude this parameter since it acts as a kind of "noise" relatively to all the other features. What's your opinion?
Lack of correlation with other features is not a reason to omit a feature. On the contrary, it is usually a reason to keep the feature because it may provide unique information. Typically, highly correlated features provide redundant information and feature reduction techniques (e.g., Principal Components Analysis) are used to remove the redundancy.

While it is possible that the uncorrelated feature is noise, you should not make that assumption. It could be that the uncorrelated feature is the only one containing information and the other 4 features are all correlated noise.