dm.cs.tu-dortmund.de/mlbits/cluster-kmeans-intro/
k-means Clustering – Lecture Notes
by} \quad \quad \mu _{C,d} = \tfrac {1}{|C|} \sum \nolimits _{x_i\in C} x_{i,d}\]
Assigning every point \(x_i\) to its least-squares closest cluster \(C\) usually 1 reduces \(\textup{SSQ}\) , too.
Note: [...] \nolimits _x |x-\mu |^2 + N |\mu |^2\) , i.e., \(\operatorname {Var}(X) = \frac1N \sum \nolimits _x |x-\mu |^2 = |\mu |^2-\frac1N \sum \nolimits _x x^2 = E[X]^2 - E[X^2]\) .
Note: avoid \(E[X]^2 - E[X^2]\) [...] all input data is normalized to have \(\lVert x\rVert=1\)
at each iteration, the new centers are normalized to \(\mu_C^\prime:=\lVert\mu_C\rVert=1\)
the normalized mean \(\mu_C^\prime\) minimizes the average …
