18 research outputs found
Kymatio: Scattering Transforms in Python
The wavelet scattering transform is an invariant signal representation
suitable for many signal processing and machine learning applications. We
present the Kymatio software package, an easy-to-use, high-performance Python
implementation of the scattering transform in 1D, 2D, and 3D that is compatible
with modern deep learning frameworks. All transforms may be executed on a GPU
(in addition to CPU), offering a considerable speed up over CPU
implementations. The package also has a small memory footprint, resulting
inefficient memory usage. The source code, documentation, and examples are
available undera BSD license at https://www.kymat.io
Deep Network Classification by Scattering and Homotopy Dictionary Learning
We introduce a sparse scattering deep convolutional neural network, which
provides a simple model to analyze properties of deep representation learning
for classification. Learning a single dictionary matrix with a classifier
yields a higher classification accuracy than AlexNet over the ImageNet 2012
dataset. The network first applies a scattering transform that linearizes
variabilities due to geometric transformations such as translations and small
deformations. A sparse dictionary coding reduces intra-class
variability while preserving class separation through projections over unions
of linear spaces. It is implemented in a deep convolutional network with a
homotopy algorithm having an exponential convergence. A convergence proof is
given in a general framework that includes ALISTA. Classification results are
analyzed on ImageNet
Riesz feature representation: scale equivariant scattering network for classification tasks
Scattering networks yield powerful and robust hierarchical image descriptors
which do not require lengthy training and which work well with very few
training data. However, they rely on sampling the scale dimension. Hence, they
become sensitive to scale variations and are unable to generalize to unseen
scales. In this work, we define an alternative feature representation based on
the Riesz transform. We detail and analyze the mathematical foundations behind
this representation. In particular, it inherits scale equivariance from the
Riesz transform and completely avoids sampling of the scale dimension.
Additionally, the number of features in the representation is reduced by a
factor four compared to scattering networks. Nevertheless, our representation
performs comparably well for texture classification with an interesting
addition: scale equivariance. Our method yields superior performance when
dealing with scales outside of those covered by the training dataset. The
usefulness of the equivariance property is demonstrated on the digit
classification task, where accuracy remains stable even for scales four times
larger than the one chosen for training. As a second example, we consider
classification of textures