  The spectral clustering algorithm is often used as a binary clustering method
for unclassified data by applying the principal component analysis. To study
theoretical properties of the algorithm, the assumption of conditional
homoscedasticity is often supposed in existing studies. However, this
assumption is restrictive and often unrealistic in practice. Therefore, in this
paper, 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, and we provide a non-asymptotic bound
of the error probability of the spectral clustering algorithm for the
allometric extension model. As a byproduct of the result, we obtain the
consistency of the clustering method in high-dimensional settings.
