In this paper we explore tying together the ideas from Scattering Transforms and Convolutional Neural Networks (CNN) for Image Analysis by proposing a learnable ScatterNet. Previous attempts at tying them together in hybrid networks have tended to keep the two parts separate, with the ScatterNet forming a fixed front end and a CNN forming a learned backend. We instead look at adding learning between scattering orders, as well as adding learned layers before the ScatterNet. We do this by breaking down the scattering orders into single convolutional-like layers we call ‘locally invariant’ layers, and adding a learned mixing term to this layer. Our experiments show that these locally invariant layers can improve accuracy when added to either a CNN or a ScatterNet. We also discover some surprising results in that the ScatterNet may be best positioned after one or more layers of learning rather than at the front of a neural network.
The potential benefits of applying machine learning methods to-omics data are becoming increasingly apparent, especially in clinical settings. However, the unique characteristics of these data are not always well suited to machine learning techniques. These data are often generated across different technologies in different labs, and frequently with high dimensionality. In this paper we present a framework for combining-omics data sets, and for handling high dimensional data, making-omics research more accessible to machine learning applications. We demonstrate the success of this framework through integration and analysis of multi-analyte data for a set of 3,533 breast cancers. We then use this data-set to predict breast cancer patient survival for individuals at risk of an impending event, with higher accuracy and lower variance than methods trained on individual data-sets. We hope that our pipelines for data-set generation and transformation will open up-omics data to machine learning researchers. We have made these freely available for noncommercial use at www.ccg.ai.
This paper examines the possibility of, and the possible advantages to learning the filters of convolutional neural networks (CNNs) for image analysis in the wavelet domain. We are stimulated by both Mallat’s scattering transform and the idea of filtering in the Fourier domain. It is important to explore new spaces in which to learn, as these may provide inherent advantages that are not available in the pixel space. However, the scattering transform is limited by its inability to learn in between scattering orders, and any Fourier domain filtering is limited by the large number of filter parameters needed to get localized filters. Instead we consider filtering in the wavelet domain with learnable filters. The wavelet space allows us to have local, smooth filters with far fewer parameters, and learnability can give us flexibility. We present a novel layer which takes CNN activations into the wavelet space, learns parameters and returns to the pixel space. This allows it to be easily dropped in to any neural network without affecting the structure. As part of this work, we show how to pass gradients through a multirate system and give preliminary results.
Scattering Transforms (or ScatterNets) introduced by Mallat are a promising start into creating a well-defined feature extractor to use for pattern recognition and image classification tasks. They are of particular interest due to their architectural similarity to Convolutional Neural Networks (CNNs), while requiring no parameter learning and still performing very well (particularly in constrained classification tasks). In this paper we visualize what the deeper layers of a ScatterNet are sensitive to using a ‘DeScatterNet’.