in this video we will discuss wavelets
scattering transform and how it can be
used as an automatic robust feature
extractor for classification we will
cover the working of the wavelet
scattering technique for signals but the
same technique can also be applied to
images wavelet scattering is best
understood in the context of deep
convolutional networks or deep cnn's
which some of you may already be
familiar with at a high level deep
convolutional networks filter the data
apply some non-linearity and pool or
average the output these steps are
repeated to form the layers there are a
few challenges with deep cnn's first
these models typically require large
data sets and significant computing
resources for training and evaluation
second typically you must choose many
settings for your networks which do not
independently affect performance lastly
it can be difficult to understand and
interpret the features that are
extracted now that you have this
background let us see how wavelet
scattering addresses these challenges
the motivation behind using wavelet
scattering networks is to start with a
set of known filters since the filters
in fully trained networks often resemble
wavelet like filters the main difference
here is that the filter weights are
learnt in the case of convolutional
neural networks while the filter weights
are fixed in the case of wave light
scattering networks now let's dive into
the details of the network an input
signal is first average using wavelet
low-pass filters this is the layer 0
scattering features with the averaging
operation you lose high-frequency detail
in the signal the details lost in the
first step are captured at the
subsequent layer by performing a
continuous wavelet transform of the
signal to yield a set of Skellig Ramco
efficient
it's a nonlinear operator in this case a
modulus is applied on the scaler gram
coefficients and then the output is
filtered with the wavelet low-pass
filter
yielding a set of layer 1 scattering
coefficients the same process is
repeated to obtain the layer to
scattering coefficients meaning the
output of the scalar gram coefficients
in the previous layer becomes the input
to the operations in the next layer then
we apply the same modulus operator and
filter the output with the wavelet low
pass function to yield the layer 2
scattering coefficients you can have
more than three layers in the scattering
Network but in practice the energy
dissipates with every iteration so three
layers are enough for most applications
the coefficients are typically
downsampled to reduce the computational
complexity of the network these
coefficients are collectively referred
to as the scattering features you can
also visualize and interpret these
features a wavelet scattering network is
referred to as a deep network because it
performs three main tasks that make a
deep network convolution non-linearity
and pooling in this case convolution is
performed by wavelets the modulus
operator serves as the non-linearity and
filtering with wavelet low-pass filters
is analogous to pooling this way you can
use the features obtained from the
wavelet scattering networks and build
models that can classify your data for
more information and examples please
refer to the documentation section of
wavelet toolbox