Deep Network Classification by Scattering and Homotopy Dictionary\n Learning

Abstract

We introduce a sparse scattering deep convolutional neural network, which\nprovides a simple model to analyze properties of deep representation learning\nfor classification. Learning a single dictionary matrix with a classifier\nyields a higher classification accuracy than AlexNet over the ImageNet 2012\ndataset. The network first applies a scattering transform that linearizes\nvariabilities due to geometric transformations such as translations and small\ndeformations. A sparse $\\ell^1$ dictionary coding reduces intra-class\nvariability while preserving class separation through projections over unions\nof linear spaces. It is implemented in a deep convolutional network with a\nhomotopy algorithm having an exponential convergence. A convergence proof is\ngiven in a general framework that includes ALISTA. Classification results are\nanalyzed on ImageNet.\n