Number of clusters in $k$-means clustering

Question

Say I have n data points and wanted to create k clusters where k > n. Does it means that K-means will create clusters with no member since the number of data points is less?

Answer 1

$k$-means clustering starts with $k$ cluster centers and iteratively partitions the data set into the points nearest each cluster, then recomputes the cluster center, and does it again. Generally one chooses the initial $k$ centers from points the $n$ data set where of course $k<n$.

I suppose you could start with $k$ "virtual centers" and $n<k$ data points, leading to a cluster with zero members, but this is pathological, and would never be done in a realistic situation.

(You're confusing matters by using "$m$" in $k$-means clustering. The whole point of naming it $k$ is that there are... well... $k$ means.)