What's the common way to utilize distance functions for clustering?

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What's the common way to utilize distance functions for clustering?

Like does one set some thresholds for the distances and do grouping based on that?

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I worked on K-means clustering,

you dont need any thresholds for clustering the data, your algorithm with club your data into appropriate buckets, for each input data , your bucket entries will change, only one thing you need to do : define $k$, i.e number of buckets , usually, $k = n^\frac{1}{2}, n=$ number of data set.