Clustering based on features of varied importance Suppose I have a dataset that includes the following features {HairColor, EyeColor, EducationLevel, Income}. I would like to perform clustering to separate the dataset into smaller datasets that you would expect to behave similarly.  The difficulty that arises is that it is clear that EducationLevel and Income are much more important than HairColor and EyeColor but I do not know how to measure that importance for the sake of clustering.
In the example below, I would want it to be clear that Row 1 is more similar to Row 3, than to Row 2.




ID
EyeColor
HairColor
EducationLevel
Income




1
1
1
1
1


2
1
1
2
2


3
2
2
1
1
If education level and income are more important than other features, you can multiply those features by a factor (greater than 1). That will allow the  clustering algo to focus more on those features than the rest.
For larger datasets, with features where the differences are not so obvious, you will need to rely on your judgement based on the end objective of the clustering. If you have a target variable in mind, you want to choose or boost those features that are highly correlated with the target