  Irregular features disrupt the desired classification. In this paper, we
consider aggressively modifying scales of features in the original space
according to the label information to form well-separated clusters in
low-dimensional space. The proposed method exploits spectral clustering to
derive scaling factors that are used to modify the features. Specifically, we
reformulate the Laplacian eigenproblem of the spectral clustering as an
eigenproblem of a linear matrix pencil whose eigenvector has the scaling
factors. Numerical experiments show that the proposed method outperforms
well-established supervised dimensionality reduction methods for toy problems
with more samples than features and real-world problems with more features than
samples.
