We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a $K$-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the $K$-means clustering method achieves such sharp threshold for exact recovery without assuming the symmetry of cluster centers.

翻译：我们决定了集束中心分离的信息理论截断值,以便精确回收聚类标签,其集聚点标签模式为$-元成分高斯混合模型,其集聚体尺寸相同。 此外,我们表明,半无限期地制定方案(SDP ), 放松以K$为单位的集聚法,在不假定集聚点中心对称的情况下,实现了精确回收的临界值如此尖锐。