Many algorithms, such as k-means clustering (see Chapter 8), rely on the Euclidean distance function between vectors  and Show that the distance function can be kernelized, that is, can be written in...

Many algorithms, such as k-means clustering (see Chapter 8), rely on the Euclidean distance function between vectors
 and

Show that the distance function can be kernelized, that is, can be written in terms of inner products between vectors
 and
. This shows that analysis algorithms based on distance metrics can also use kernel functions.