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"a general search can be machine learning" I don't get this sentence: Machine learning is about building a mathematical model of sample data, known as "training data".

If you want to talk about machine learning and search you should probably talk about learning to rank (https://en.m.wikipedia.org/wiki/Learning_to_rank)

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I'd argue that you're too restrictive in your definition. e.g. unsupervised clustering has no sample training data.

The usual definition (due to Mitchell) is that machine learning is a system s.t. its performance on a given task improves by past experience.

Actually, any unsupervised method, including clustering, still has training data. The only difference is it doesn't have a target y variable in the training set to minimize the error metric, hence the name unsupervised.

But the definition you mention is right. Yet, any dataset that you use to fit your model will be your training set, even if you don't have a train test split or the like, because you used it to train your model over.

K-means has no "training data" per se.

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