dm.cs.tu-dortmund.de/en/mlbits/cluster-kmeans-limitations/
Limitations of k-Means Clustering – Lecture Notes
{|S|}{|S|-1}\left\lVert \smash {\mu _S-x}\mathstrut \right\rVert ^2 = \tfrac {1}{2} 4^2 - \tfrac {4}{3} 3^2 = 8 - 12 = -4 \end{align*}\]
➜ The standard \(k\) -means algorithm can get stuck in sub-optimal [...] standard \(k\) -means algorithm can be arbitrarily poor:
Consider the one-dimensional data set, with \(k=3\) :
Given \(x\lt{}z\lt{}y\) , the optimum solution would cluster {a,b}, but with bad starting conditions [...] Clustering
\(k\) -means can not handle clusters with different radius well.
Toy mouse data set:
Best \(3\) -means:
Best \(5\) -means:
➜ could we estimate mean and radius?
➜ model the data with multivariate …
