Consider a standard centered Gaussian vector $(X_1,...,X_n)$ with an approximate block structure, i.e. there is $q$ and a partition of $\{1,...,n\}$ in $q$ classes such that if $i,j$ are in the same class, then the covariance/correlation matrix $\Gamma$ satisfies $\Gamma_{i,j}>1-\varepsilon$ for some $\varepsilon>0$, and if they are not $\Gamma_{i,j}<1-\delta$ for some $\delta>0$.
This of cours makes sense only if $\varepsilon$ is small and $\delta$ is not.
Now apply a standard $k$-means algorithm to this sample to recover the (unknown) classes, has the classification error been quantified in some way? I figured there would be scientific works addressing this question.
