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I know that feature scaling is always a requirement for clustering algorithms. Currently I am implementing hierarchal clustering on this dataset, I will use only the annual income and the spending rate features. Now I am confused of whether to use feature scaling here, this is because both features approximately have the same scale, where the scale for annual income is [15-137] and the scale for spending rate is [1-100]. The two features have approximately same scale so do I still need to feature scale them ?

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If you scale all features to the same range, this makes all features equally important in the distance measure (assuming an ordinary Minkowski distance like Euclidean or Manhatten).

This does, however, in general not improve clustering, because, for clustering, greater weight should be given to features with greater discriminatory power. Obtaining good weights requires a labelled training set, though, and thus might not be feasible in your situation.

In your special case, however, both features seem to be of the same unit, and the ordinary Minkowski distance seems to make sense. I would thus leave them as is and not scale them.

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  • $\begingroup$ Thank you very much. I still have one question regarding your answer, you are saying that I don't need to scale them because they have the same unit, so this means that if we have two features with the same unit ( weight for example) but the first is the weight of human and the second is the weight of a car ( and for sure they will have different ranges) then I don't need to scale them ? Or you mean by the same unit , same scale, that's why I don't need to scale the features in my case ? $\endgroup$
    – AAA
    Commented Nov 29, 2022 at 12:48
  • $\begingroup$ No, you cannot compare the weight of a car with the weight of a human because their range is very different (not even overlapping). But maybe I misunderstood your variables: I thought that both are an amount of money (in whatever unit), and that the money must come in before it is spent, so the money spent is close to the income (except for very high incomes). $\endgroup$
    – cdalitz
    Commented Nov 29, 2022 at 12:58
  • $\begingroup$ Thanks a lot. You have understood correctly my variables. I was just asking a general question. So the idea here is that when we have features of the same scale, then we don't need to feature scale them as non of them will be the dominant when calculating the Euclidean distance for example. $\endgroup$
    – AAA
    Commented Nov 29, 2022 at 13:02

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