Show that as the stiffness ß goes to infinity, the soft K-means algorithm becomes identical to the original hard K-means algorithm,

Show that as the stiffness ß goes to infinity, the soft K-means algorithm becomes identical to the original hard K-means algorithm, except for the way in which means with no assigned points behave. Describe what those means do instead of sitting still.
This is an exercise from the following book (Exercise 20.2, page 289):http://www.inference.org.uk/itprnn/book.pdfI would appreciate it if you could response as soon as possible.

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