Phase Transitions for High Dimensional Clustering and Related Problems

Jiashun Jin, Zheng Tracy Ke, Wanjie Wang

Consider a two-class clustering problem where we observe $X_i={\ell }_i\mu +Z_i$, $Z_i\stackrel{iid}{\sim }N(0,I_p)$, $1\le i\le n$. The feature vector $\mu \in R^p$ is unknown bu…