modwtLayer
Description
A MODWT layer computes the maximal overlap discrete wavelet transform (MODWT) and MODWT multiresolution analysis (MRA) of the input. Use of this layer requires Deep Learning Toolbox™.
Creation
Description
creates a MODWT layer. By
default, the layer computes the MODWTMRA to level 5 using the Daubechies least-asymmetric
wavelet with four vanishing moments (layer
= modwtLayer'sym4'
).
The input to modwtLayer
must be a real-valued dlarray
(Deep Learning Toolbox) object in
"CBT"
format. The size of the time dimension of the tensor input must
be greater than or equal to 2Level, where Level is the
transform level of the MODWT. modwtLayer
formats the output as
"SCBT"
. For more information, see Layer Output Format.
Note
The object initializes the weights internally for use as wavelet filters in the MODWT. It is not recommended to initialize the weights directly.
creates a MODWT layer with properties
specified by name-value arguments. For example, layer
= modwtLayer(Name=Value
)layer =
modwtLayer(Wavelet="haar")
creates a MODWT layer that uses the Haar wavelet.
You can specify the wavelet and the level of decomposition, among others.
Properties
MODWT
Wavelet
— Orthogonal wavelet
"sym4"
(default) | character vector | string scalar
This property is read-only.
Name of an orthogonal wavelet used in the MODWT, specified as a character vector or a string scalar.
Orthogonal wavelets are designated as type 1 wavelets in the wavelet manager.
Valid built-in orthogonal wavelet families begin with 'haar'
,
'dbN'
,
'fkN'
,
'coifN'
,
'blN'
,
'hanSR.LP'
,
'symN'
, 'vaid'
, or
'beyl'
. Use waveinfo
with the wavelet family
short name to see supported values for any numeric suffixes and how to interpret those
values. For example, waveinfo("han")
.
For a wavelet specified by wname, the associated lowpass and
highpass filters Lo
and Hi
, respectively, are
[~,~,Lo,Hi] = wfilters(wname)
.
Data Types: char
| string
LowpassFilter
— Lowpass (scaling) filter
[]
(default) | even-length real-valued vector
This property is read-only.
Lowpass (scaling) filter, specified as an even-length real-valued vector.
LowpassFilter
and HighpassFilter
must have
equal length and correspond to the lowpass and highpass filters associated with an
orthogonal wavelet. You can use isorthwfb
to determine
orthogonality.
[~,~,Lo,Hi] = wfilters("db2");
[tf,checks] = isorthwfb(Lo,Hi);
[]
and modwtLayer
uses
Wavelet
to determine the filters used in MODWT.
You cannot specify both a wavelet name and a wavelet filter pair.
Example: layer =
modwtLayer('LowpassFilter',Lo,'HighpassFilter',Hi)
Data Types: single
| double
HighpassFilter
— Highpass (wavelet) filter
[]
(default) | even-length real-valued vector
This property is read-only.
Highpass (wavelet) filter, specified as an even-length real-valued vector.
LowpassFilter
and HighpassFilter
must have
equal length and correspond to the lowpass and highpass filters associated with an
orthogonal wavelet. You can use isorthwfb
to determine orthogonality.
If unspecified, both filters default to []
and
modwtLayer
uses Wavelet
to determine the
filters used in MODWT.
You cannot specify both a wavelet name and a wavelet filter pair.
Data Types: single
| double
Level
— Transform level
5
(default) | positive integer
This property is read-only.
Transform level to compute the MODWT, specified as a positive integer less than or
equal to floor(log2(N))
, where
N is the size of the layer input in the time dimension.
Data Types: single
| double
Boundary
— Boundary condition
"periodic"
(default) | "reflection"
This property is read-only.
Boundary condition to use in the computation of the MODWT, specified as one of these:
"periodic"
— The signal is extended periodically along the time dimension. The number of wavelet coefficients equals the size of the signal in the time dimension."reflection"
— The signal is reflected symmetrically along the time dimension at the terminal end before computing the MODWT. The number of wavelet coefficients returned is twice the length of the input signal.
SelectedLevels
— Selected levels
1:Level
(default) | vector
Level
This property is read-only.
Selected levels for modwtLayer
to output, specified as a vector
of positive integers less than or equal to Level
.
Data Types: single
| double
IncludeLowpass
— Include lowpass coefficients
true
or 1
(default) | false
or 0
This property is read-only.
Include lowpass coefficients, specified as a numeric or logical
1
(true
) or 0
(false
). If specified as true
, the MODWT layer
includes the Level
th level lowpass (scaling) coefficients in the
MODWT, or Level
th level smooth in the MODWTMRA.
Data Types: logical
AggregateLevels
— Aggregate selected levels
false
or 0
(default) | true
or 1
This property is read-only.
Aggregate selected levels, specified as a numeric or logical 1
(true
) or 0
(false
). If
specified as true
, the MODWT layer aggregates the selected levels
and lowpass level (if IncludeLowpass
is true
)
of each input channel by summation. If AggregateLevels
is
true
, the size of the output in the spatial dimension is
1
. For more information, Compare modwtLayer Output with modwt and modwtmra Outputs.
Data Types: logical
Algorithm
— Algorithm
"MODWTMRA"
(default) | "MODWT"
This property is read-only.
Algorithm modwtLayer
uses to compute the output, specified as
one of these:
"MODWTMRA"
— Compute the maximal overlap discrete wavelet transform based multiresolution analysis."MODWT"
— Compute the wavelet coefficients of the maximal overlap discrete wavelet transform.
For more information, see Comparing MODWT and MODWTMRA.
Layer
WeightLearnRateFactor
— Multiplier for weight learning rate
0
(default) | nonnegative scalar
Multiplier for weight learning rate, specified as a nonnegative scalar. If not
specified, this property defaults to zero, resulting in weights that do not update
with training. You can also set this property using the setLearnRateFactor
(Deep Learning Toolbox) function.
The learnable parameter 'Weights'
in
modwtLayer
is a two-row matrix of the current filter pair. The
first row is the lowpass filter and the second row is the highpass filter. By default,
the weights are the lowpass and highpass filters associated with the default wavelet
and do not update.
Data Types: single
| double
Name
— Layer name
""
(default) | character vector | string scalar
Layer name, specified as a character vector or string scalar.
For Layer
array input, the trainnet
(Deep Learning Toolbox) and
dlnetwork
(Deep Learning Toolbox) functions automatically assign
names to layers with the name ""
.
The modwtLayer
object stores this property as a character vector.
Data Types: char
| string
NumInputs
— Number of inputs
1
(default)
This property is read-only.
Number of inputs to the layer, returned as 1
. This layer accepts a
single input only.
Data Types: double
InputNames
— Input names
{'in'}
(default)
This property is read-only.
Input names, returned as {'in'}
. This layer accepts a single input
only.
Data Types: cell
NumOutputs
— Number of outputs
1
(default)
This property is read-only.
Number of outputs from the layer, returned as 1
. This layer has a
single output only.
Data Types: double
OutputNames
— Output names
{'out'}
(default)
This property is read-only.
Output names, returned as {'out'}
. This layer has a single output
only.
Data Types: cell
Examples
Use modwtLayer
in Deep Learning Network
Create a MODWT layer to compute the multiresolution analysis for the input signal. Use a coiflet wavelet with order 5. Set the transform level to 8. Only keep the details at levels 3, 5, and 7, and the approximation.
layer = modwtLayer(Wavelet="coif5",Level=8, ... SelectedLevels=[3,5,7],Name="MODWT");
Create a dlnetwork
object containing a sequence input layer, a MODWT layer, and an LSTM layer. For a level-8 decomposition, set the minimum sequence length to 2^8 samples. To work with an LSTM layer, a flatten layer is also needed before the LSTM layer to collapse the spatial dimension into the channel dimension.
mLength=2^8; sqLayer = sequenceInputLayer(1,Name="input",MinLength=mLength); layers = [sqLayer layer flattenLayer lstmLayer(10,Name="LSTM") ]; dlnet = dlnetwork(layers);
Run a batch of 10 random single-channel signals through the dlnetwork
object. Inspect the size and dimensions of the output. The flatten layer has collapsed the spatial dimension.
dataout = dlnet.forward(dlarray(randn(1,10,2000,'single'),'CBT')); size(dataout)
ans = 1×3
10 10 2000
dims(dataout)
ans = 'CBT'
Compare modwtLayer
Output with modwt
and modwtmra
Outputs
Load the Espiga3 electroencephalogram (EEG) dataset. The data consists of 23 channels of EEG sampled at 200 Hz. There are 995 samples in each channel. Save the multisignal as a dlarray
, specifying the dimensions in order. dlarray
permutes the array dimensions to the "CBT"
shape expected by a deep learning network.
load Espiga3 [N,nch] = size(Espiga3); x = dlarray(Espiga3,"TCB");
Use modwt
and modwtmra
to obtain the MODWT and MRA of the multisignal down to level 6. By default, modwt
and modwtmra
use the sym4
wavelet.
lev = 6; wt = modwt(Espiga3,lev); mra = modwtmra(wt);
Compare with modwt
Create a MODWT layer that can be used with the data. Set the transform level to 6. Specify the layer to use MODWT to compute the output. By default, the layer uses the sym4
wavelet.
mlayer = modwtLayer(Level=lev,Algorithm="MODWT");
Create a two-layer dlnetwork
object containing a sequence input layer and the MODWT layer you just created. Treat each channel as a feature. For a level-6 decomposition, set the minimum sequence length to 2^6.
mLength = mlayer.Level; sqInput = sequenceInputLayer(nch,MinLength=2^mLength); layers = [sqInput mlayer]; dlnet = dlnetwork(layers);
Run the EEG data through the forward
method of the network.
dataout = forward(dlnet,x);
The modwt
and modwtmra
functions return the MODWT and MRA of a multichannel signal as a 3-D array. The first, second, and third dimensions of the array correspond to the wavelet decomposition level, signal length, and channel, respectively. Convert the network output to a numeric array. Permute the dimensions of the network output to match the function output. Compare the network output with the modwt
output.
q = extractdata(dataout); q = permute(q,[1 4 2 3]); max(abs(q(:)-wt(:)))
ans = 8.4402e-05
Choose a MODWT result from modwtLayer
. Compare with the corresponding channel in the EEG data. Plot each level of the modwtLayer
output. Different levels contain information about the signal in different frequency ranges. The levels are not time aligned with the original signal because the layer uses the MODWT algorithm.
channel = 10; t = 100:400; subplot(lev+2,1,1) plot(t,Espiga3(t,channel)) ylabel("Original EEG") for k=2:lev+1 subplot(lev+2,1,k) plot(t,q(k-1,t,channel)) ylabel(["Level ",k-1," of MODWT"]) end subplot(lev+2,1,lev+2) plot(t,q(lev+1,t,channel)) ylabel(["Scaling","Coefficients","of MODWT"]) set(gcf,Position=[0 0 500 700])
Compare with modwtmra
Create a second network similar to the first network, except this time specify that modwtLayer
use the MODWTMRA algorithm and aggregate the fourth, fifth, and sixth levels. Do not include the lowpass level in the aggregation.
sLevels = [4 5 6]; mlayer = modwtLayer(Level=lev, ... SelectedLevels=sLevels, ... IncludeLowpass=0, ... AggregateLevels=1); layers = [sqInput mlayer]; dlnet2 = dlnetwork(layers);
Run the EEG data through the forward
method of the network. Convert the network output to a numeric array. Permute the dimensions as done previously.
dataout = forward(dlnet2,x); q = extractdata(dataout); q = permute(q,[1 4 3 2]);
Aggregate the fourth, fifth, and sixth levels of the MRA. Compare with the network output.
mraAggregate = sum(mra(sLevels,:,:)); max(abs(q(:)-mraAggregate(:)))
ans = 2.1036e-04
Inspect a MODWTMRA result from the layer. Compare with the corresponding channel in the EEG data. By choosing only the fourth, fifth, and six levels, and not including the lowpass component, the layer removes several high and low frequency components from the signal. The transformed signal is smoother than the original signal and the low frequency components are removed so that the offset is closer to 0. The output is time aligned with the original signal because the layer uses the default MODWTMRA algorithm. Depending on your goal, preserving time alignment can be useful.
channel = 10; t = 100:400; figure hold on plot(t, Espiga3(t,channel)) plot(t,q(1,t,1,channel)) hold off legend(["Original EEG", "Layer Output"], ... Location="northwest")
More About
Layer Output Format
modwtLayer
formats the output as
"SCBT"
, a sequence of 1-D images where the image height corresponds to
the level of the wavelet transform, the second dimension corresponds to the channel, the
third dimension corresponds to the batch, and the fourth dimension corresponds to time. The
kth row, where k ≤ Level
, contains the kth level detail of the
signal. The (
th row contains the
Level
+1)Level
th level smooth of the signal.
You can feed the output of
modwtLayer
unchanged to a 1-D convolutional layer when you want to convolve along the level ("S"
) dimension. For more information, seeconvolution1dLayer
(Deep Learning Toolbox).To feed the output of
modwtLayer
to a 1-D convolutional layer when you want to convolve along the time ("T"
) dimension, you must place a flatten layer after themodwtLayer
. For more information, seeflattenLayer
(Deep Learning Toolbox).You can feed the output of
modwtLayer
unchanged to a 2-D convolutional layer when you want to convolve along the level ("S"
) and time ("T"
) dimensions jointly. For more information, seeconvolution2dLayer
(Deep Learning Toolbox).To use
modwtLayer
as part of a recurrent neural network, you must place a flatten layer after themodwtLayer
. For more information, seelstmLayer
(Deep Learning Toolbox) andgruLayer
(Deep Learning Toolbox).To use the output of
modwtLayer
with a fully connected layer as part of a classification workflow, you must reduce the time ("T"
) dimension of the output so that it is of size 1. To reduce the time dimension of the output, place a global pooling layer before the fully connected layer. For more information, seeglobalAveragePooling2dLayer
(Deep Learning Toolbox) andfullyConnectedLayer
(Deep Learning Toolbox).
Version History
Introduced in R2022b
See Also
Apps
- Deep Network Designer (Deep Learning Toolbox)
Functions
Objects
cwtLayer
|stftLayer
(Signal Processing Toolbox) |dlarray
(Deep Learning Toolbox) |dlnetwork
(Deep Learning Toolbox)
Topics
- Practical Introduction to Multiresolution Analysis
- Comparing MODWT and MODWTMRA
- Deep Learning in MATLAB (Deep Learning Toolbox)
- List of Deep Learning Layers (Deep Learning Toolbox)
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