  In the last few years, large improvements in image clustering have been
driven by the recent advances in deep learning. However, due to the
architectural complexity of deep neural networks, there is no mathematical
theory that explains the success of deep clustering techniques. In this work we
introduce Projected-Scattering Spectral Clustering (PSSC), a state-of-the-art,
stable, and fast algorithm for image clustering, which is also mathematically
interpretable. PSSC includes a novel method to exploit the geometric structure
of the scattering transform of small images. This method is inspired by the
observation that, in the scattering transform domain, the subspaces formed by
the eigenvectors corresponding to the few largest eigenvalues of the data
matrices of individual classes are nearly shared among different classes.
Therefore, projecting out those shared subspaces reduces the intra-class
variability, substantially increasing the clustering performance. We call this
method Projection onto Orthogonal Complement (POC). Our experiments demonstrate
that PSSC obtains the best results among all shallow clustering algorithms.
Moreover, it achieves comparable clustering performance to that of recent
state-of-the-art clustering techniques, while reducing the execution time by
more than one order of magnitude. In the spirit of reproducible research, we
publish a high quality code repository along with the paper.
