# k-means clustered data: how to label newly incoming data

I have a data set with labels that were produced by a $$k$$-means clustering algorithm. Now there is some data (with the same data structure) from another source and I wonder what is the most sensible way to label this new, yet unseen data? I was thinking about either

• calculating the distance to the prior $$k$$-means centroids and label the data to the the nearest centroids accordingly
• run a new algorithm (e.g. SVM) on the new data using the old data as the training set

Unfortunately, I couldn't find anything about this particular problem. There are only a few questions about the general use of $$k$$-means as a classification model:

• Can $$k$$-means clustering do classification?
• How to segment new data with existing $$k$$-means model?