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I am looking to apply k-means clustering on two features of remote sensing data. The first layer is the Normalized Difference Vegetation Index (NDVI), which is expressed on a scale between 0-1. The second layer is the land surface temperature, with units of Kelvin (implying a non-standard range unlike NDVI).

I would like to apply k-means separately for each layer, and while I understand it is best to try and combine such information, I have a non-related reason why they can be treated separately.

Therefore, I would like to apply k-means for both NDVI and temperature separately. However, when I looked into pre-processing steps needed for k-means, there are some that suggest that normalizing variables to a common range can help reduce the influence of one feature over another. In this context, however, it would seem that normalization is most relevant when two feature layers are being combined together (in this case 0-1 for NDVI and min/max for temperature).

Onto my question: would normalization be needed if k-means clustering are to applied separately to each layer?

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If you apply k-means to each feature separately, then no, no need to normalize them.

The advice is when you apply the same k-means model on a set of features. In this instance, as k-means works on distances, you should have isometric distances in all directions, hence the normalization.

In your case, you are not applying the same k-means, but different ones.

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