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I am working on a clustering project where we have collected protein data from over 100 patients samples. This data is normalized and log transformed. The goal is to cluster samples based upon their similarities, I am using hierarchal clustering and trying out combinations of distance metrics and clustering algorithms. (We haven't made a decision on distance method or clustering algorithms) My question is related to the centering and scaling, Is it absolutely necessary to both scale and center the data?, even in scenarios where all the data is coming from the same platform and with same units of measurement.

Appreciate your input on this one.

Thanks

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My question is related to the centering and scaling, Is it absolutely necessary to both scale and center the data?, even in scenarios where all the data is coming from the same platform and with same units of measurement.

It depends on the type of data you have. For some types of well defined data, there may be no need to scale and center. A good example is geolocation data (longitudes and latitudes). If you were seeking to cluster towns, you wouldn't need to scale and center their locations.

For data that is of different physical measurements or units, its probably a good idea to scale and center. For example, when clustering vehicles, the data may contain attributes such as number of wheels, number of doors, miles per gallon, horsepower etc. In this case it may be a better idea to scale and center since you are unsure of the relationship between each attribute.

The intuition behind that is that since many clustering algorithms require some definition of distance, if you do not scale and center your data, you may give attributes which have larger magnitudes more importance.

In the context of your problem, I would scale and center the data if it contains attributes like patient height, weight, age etc.

This answer on a similar question has more.

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  • $\begingroup$ Thank you very much for your response. In my case we measured ~600 protein levels in 100 patients. My aim is to cluster patients based upon their protein level similarities. The physical measurement/units for all proteins is the same and hence scaling wouldn't be essential. We normalized all the proteins, so does it make sense to still center the data? $\endgroup$
    – Mdhale
    Commented Aug 18, 2017 at 15:49
  • $\begingroup$ What procedure did you use to normalize your protein data? Depending on what you did, you could have already centered the data. Also, just because the units are the same does not mean scaling is no longer necessary. $\endgroup$
    – lostlostlostlostlost
    Commented Aug 19, 2017 at 5:42
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If your variables are of incomparable units then you should standardize variables by scaling. K-clustering is 'isotropic' in all directions, meaning that the clusters tend to be more or less round. By not scaling, you're essentially putting a weight on certain variables.

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