I have a set of user queries from a search engine that I want to cluster. The only clustering algorithm I have come across so far is the K-means clustering algorithm, which requires defining the number of clusters up front. But in this case, I do not know how many clusters exist in the data. Is there any clustering algorithm that performs clustering without predefining the number of clusters?
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There are several techniques that allow you to cluster unsupervised data. K-means is probably the most famous one. But as you have already seen, most k-means algorithms require the number of clusters to be specified in advance.
Nevertheless, at least two kinds of algorithms might suit your needs:
By the way, there is a similar question in StackOverflow.