Abstract

The spectral clustering algorithm is used as a binary clustering method by applying the principal component analysis. Homoscedasticity of two clusters is commonly supposed in existing studies, but this restrictive assumption is often unrealistic in practice. Therefore, we consider the allometric extension model, that is, the directions of the first eigenvectors of two covariance matrices and the direction of the difference of two mean vectors coincide. A non-asymptotic bound of the error probability is provided for the spectral clustering.