dm.cs.tu-dortmund.de/mlbits/cluster-kmeans-initialization/
Initialization of k-means – Lecture Notes
as initial cluster centers proportional to \(\left\lVert x-y\right\rVert ^2\) .
\[\begin{alignat*}{3} \text{{\textcolor[RGB]{100,150,0}{1.}}}& \; \text{First center:}\qquad & p(c_1=x) & = \tfrac {\sum [...] \propto \left\lVert \smash {x - c_1}\mathstrut \right\rVert ^2 \\ \text{{\textcolor[RGB]{100,150,0}{3.-k.}}}& \; \text{Remaining centers:}\qquad & p(c_i=x) & = \tfrac {\min _{j=1,\ldots ,i-1} \left\lVert …