Upper bound estimations of misclassification rate in the heteroscedastic clustering model with sub‐Gaussian noises

Abstract

Clustering is an important tool in statistics, machine learning and applied mathematics. This paper considers the clustering model , where the noise matrix consists of independent sub‐Gaussian entries and the variance may vary across different coordinates. Our aim is to estimate the error between the label vector and its defined estimator . We provide upper bound estimations for the misclassification rate in the sense of expectation and probability, respectively. Finally, some simulations have been carried out to support our theoretical results and illustrate the advantage of our proposed estimator.