Deep Haar Scattering Networks
This work addresses the challenge of unsupervised learning in deep networks for researchers in machine learning, offering a novel mathematical model with applications in image classification on graphs.
The paper tackles the problem of unsupervised deep network learning by introducing an orthogonal Haar scattering transform, which uses a hierarchy of additions, subtractions, and absolute values over pairs of coefficients, and applies it to classification on image databases with known or unknown graph connectivity, achieving results that demonstrate its effectiveness.
An orthogonal Haar scattering transform is a deep network, computed with a hierarchy of additions, subtractions and absolute values, over pairs of coefficients. It provides a simple mathematical model for unsupervised deep network learning. It implements non-linear contractions, which are optimized for classification, with an unsupervised pair matching algorithm, of polynomial complexity. A structured Haar scattering over graph data computes permutation invariant representations of groups of connected points in the graph. If the graph connectivity is unknown, unsupervised Haar pair learning can provide a consistent estimation of connected dyadic groups of points. Classification results are given on image data bases, defined on regular grids or graphs, with a connectivity which may be known or unknown.