### Abstract

We consider the problem of Gaussian mixture clustering in the high-dimensional limit where the data consists of $m$ points in $n$ dimensions, $n,m\rightarrow\infty$ and $\alpha=m/n$ stays finite. Using exact but non-rigorous methods from statistical physics, we determine the critical value of $\alpha$ and the distance between the clusters at which it becomes information-theoretically possible to reconstruct the membership into clusters better than chance. We also determine the accuracy achievable by the Bayes-optimal estimation algorithm. In particular, we find that when the number of clusters is sufficiently large, $r>4+2\sqrt{\alpha}$, there is a gap between the threshold for information-theoretically optimal performance and the threshold at which known algorithms succeed.

Publication

Proc. 54th Annual Allerton Conference on Communication, Control, and Computing (2016)

###### CyberValley Research Group Leader

My research focuses on understanding, optimizing and predicting relations between the microscopic and macroscopic properties of complex large-scale interacting systems.