Just one example from recent practice, to automatically collect a number of texts (pdfs) into a set of groups for easier subsequent processing (summarization). Without K-Means you'd have a pretty hard time figuring out for each subsequent document which group you want to add it to or whether or not you need to make a new group. With K-Means given a fairly simple 'distance' function all of the grouping is automatic. In fact, once you have K-Means coded up the distance function is the problem to solve. If you can't meaningfully define a distance then you probably won't be able to use it.

This is probably the biggest (only?) advantage of k-means in real problems: it's easy to put new data points into existing clusters. You can do this with mean-shift clustering as well.

It's not obvious how to do this with HDBSCAN or hierarchical clustering. Maybe you'd have to draw some kind of boundary around each cluster after fixing the parameters.

You mean to update the clusters incrementally as new data arrives?

Do you have an example of the groups ( = output) and what you are using as variables for input ?

Eg. Wouldn't KNN be easier if you want to classify new groups later on? I'm probably missing something, but defining the groups upfront seems more labor intensive ( note: novice in this area )

Not tp but I’ve tried using k-means for similar task and and LDA and found LDA to be better. Particularly if your documents have mixture of topics

Well, you don't so much define the groups up front as that you define the number of groups up front, the distance function is what will eventually result in the mapping of inputs to groups if you use the groups (for instance: sample texts in those groups) as a part of the scoring system.

Depending on the task but using K- means implies you have have idea of the clusters you might have ( unsupervised learning). KNN assumes the groups already exist.

Interesting did you try any other techniques like HDBSCAN? I've found HDBSCAN to produce more meaningful clusters for a similar workflow.