# deepSignalAnomalyDetector

## Syntax

## Description

creates a signal anomaly detector object `d`

= deepSignalAnomalyDetector(`numChannels`

)`d`

based on a 1-D convolutional
autoencoder.

specifies the type of deep learning model implemented by the detector.`d`

= deepSignalAnomalyDetector(`numChannels`

,`modelType`

)

specifies additional options using name-value arguments.`d`

= deepSignalAnomalyDetector(___,`Name=Value`

)

## Examples

### Detect Anomalies in Sinusoids

Load the file `sineWaveAnomalyData.mat`

, which contains two sets of synthetic three-channel sinusoidal signals.

`sineWaveNormal`

contains 10 sinusoids of stable frequency and amplitude. Each signal has a series of small-amplitude impact-like imperfections. The signals have different lengths and initial phases. Plot the first three normal signals.

load sineWaveAnomalyData.mat sl = 3; tiledlayout("vertical") ax = zeros(sl,1); for kj = 1:sl ax(kj) = nexttile; plot(sineWaveNormal{kj}) title("Normal Signal") end

`sineWaveAbnormal`

contains three signals, all of the same length. Each signal in the set has one or more anomalies.

All channels of the first signal have an abrupt change in frequency that lasts for a finite time.

The second signal has a finite-duration amplitude change in one of its channels.

The third signal has spikes at random times in all channels.

Plot the three signals with anomalies.

for kj = 1:sl plot(ax(kj),sineWaveAbnormal{kj}) title(ax(kj),"Signal with Anomalies") end

Create an autoencoder object to detect the anomalies in the abnormal signals. The object contains a neural network that you can train to best reproduce an input set of anomaly-free data. The trained object encodes the patterns inherent in the data and can recognize if a signal contains regions that deviate from the patterns. You do not need to label any data to train the detector. The training process is unsupervised.

By default, the `deepSignalAnomalyDetector`

function creates objects with convolutional autoencoders. The only mandatory argument is the number of channels in the training and testing signals.

D = deepSignalAnomalyDetector(sl)

D = deepSignalAnomalyDetectorCNN with properties: IsTrained: 0 NumChannels: 3 Model Information ModelType: 'convautoencoder' FilterSize: 8 NumFilters: 32 NumDownsampleLayers: 2 DownsampleFactor: 2 DropoutProbability: 0.2000 Threshold Information Threshold: [] ThresholdMethod: 'contaminationFraction' ThresholdParameter: 0.0100 Window Information WindowLength: 1 OverlapLength: 'auto' WindowLossAggregation: 'mean'

Use the `trainDetector`

function to train the convolutional neural network with the normal data. Use the training options for the adaptive moment estimation (Adam) optimizer. Specify a maximum number of 100 epochs to use for training. For more information, see `trainingOptions`

(Deep Learning Toolbox).

```
opts = trainingOptions("adam",MaxEpochs=100);
trainDetector(D,sineWaveNormal,opts)
```

Iteration Epoch TimeElapsed LearnRate TrainingLoss _________ _____ ___________ _________ ____________ 1 1 00:00:04 0.001 0.49381 50 50 00:00:16 0.001 0.065911 100 100 00:00:26 0.001 0.047147 Training stopped: Max epochs completed Computing threshold... Threshold computation completed.

Use the trained detector to detect the anomalies in the abnormal data. The `detect`

function outputs two cell arrays, with each array element corresponding to a signal in the testing data.

[lbls,loss] = detect(D,sineWaveAbnormal);

The first output of `detect`

is a categorical array that declares each sample of a signal as being anomalous or not. A sample can be either a point, a signal region, or an entire signal. An anomaly is detected when the *reconstruction loss*, or the difference between the value of a signal and the value reconstructed by the detector based on the training data, exceeds a given *threshold*. You can set a threshold manually or you can direct the detector to compute a threshold based on a specified statistic of loss values computed on training data.

for kj = 1:sl hold(ax(kj),"on") plot(ax(kj),lbls{kj},LineWidth=2) title(ax(kj),"Signal with Anomalies") hold(ax(kj),"off") end

Alternatively, use the `plotAnomalies`

function to plot each channel of each signal and the anomalies found by the detector. The detector decides that there is an anomaly in a signal if it detects one in any of the signal channels. `plotAnomalies`

plots the anomaly locations in all channels.

for kj = 1:sl figure plotAnomalies(D,sineWaveAbnormal{kj}) end

The second output of `detect`

is the computed reconstruction loss that the object uses to determine the labeling. You can plot the reconstruction loss directly from the output of `detect`

, but it is more convenient to use the `plotLoss`

function, which also displays the the threshold value above which a sample is declared to be anomalous.

tiledlayout("vertical") for kj = 1:sl nexttile plotLoss(D,sineWaveAbnormal{kj}) end

The `plotLossDistribution`

function displays the reconstruction loss distribution and gives insight into the way the detector chooses the threshold. You can plot the distribution loss for the normal data alongside the distribution loss for the abnormal data. The threshold chosen by the detector is larger than the loss values for most of the normal-data samples but smaller than an appreciable number of abnormal-data losses that signal the possible presence of anomalies. You can improve the choice of threshold by using the `updateDetector`

function.

clf plotLossDistribution(D,sineWaveNormal,sineWaveAbnormal)

Use the `getModel`

function to obtain the underlying neural network model corresponding to the detector. You can then inspect the model using `analyzeNetwork`

(Deep Learning Toolbox).

M = getModel(D); analyzeNetwork(M)

## Input Arguments

`numChannels`

— Number of channels

positive integer

Number of channels in each signal input to the detector `d`

,
specified as a positive integer.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`modelType`

— Type of deep learning model

`"convautoencoder"`

(default) | `"lstmautoencoder"`

| `"lstmforecaster"`

Type of deep learning model implemented by the detector `d`

,
specified as one of these:

`"convautoencoder"`

— Implement a 1-D convolutional autoencoder.`"lstmautoencoder"`

— Implement a long short-term memory (LSTM) autoencoder.`"lstmforecaster"`

— Implement a long short-term memory (LSTM) forecaster.

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

**Example: **`ThresholdMethod="manual",Threshold=0.4`

specifies that the
threshold value above which a sample is declared to be anomalous is set manually to
`0.4`

.

**Window**

`WindowLength`

— Window length

`1`

(default) | positive integer | `"fullSignal"`

Window length of each signal segment, specified as a positive integer or as `"fullSignal"`

.

If you specify

`WindowLength`

as an integer, the detector divides each input signal into segments. The length of each segment is equal to the specified value in samples.If you specify

`WindowLength`

as`"fullSignal"`

, the detector treats each input signal as a single segment.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `char`

| `string`

`OverlapLength`

— Number of overlapped samples

`"auto"`

(default) | positive integer

Number of overlapped samples between window segments, specified as a positive integer or as `"auto"`

.

If you specify

`WindowLength`

and`OverlapLength`

as integers, the detector sets the number of overlapped samples to the specified value. The number of overlapped samples must be less than the window length.If you specify

`WindowLength`

as an integer and`OverlapLength`

as`"auto"`

, the detector sets the number of overlapped samples to`WindowLength`

– 1.If you specify

`WindowLength`

as`"fullSignal"`

, you cannot specify`OverlapLength`

as an integer.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

| `logical`

| `char`

| `string`

`WindowLossAggregation`

— Method to aggregate sample loss

`"mean"`

(default) | `"max"`

| `"min"`

| `"median"`

Method to aggregate sample loss within each window segment, specified as one of these:

`"max"`

— Compute the aggregated window loss as the maximum value of all the sample losses within the window.`"mean"`

— Compute the aggregated window loss as the mean value of all the sample losses within the window.`"median"`

— Compute the aggregated window loss as the median value of all the sample losses within the window.`"min"`

— Compute the aggregated window loss as the minimum value of all the sample losses within the window.

The detector computes the detection loss of each sample within a window segment and aggregates the loss values over each window.

**Threshold**

`ThresholdMethod`

— Method to compute detection threshold

`"contaminationFraction"`

(default) | `"max"`

| `"mean"`

| `"median"`

| `"manual"`

| `"customFunction"`

Method to compute the detection threshold, specified as one of these:

`"contaminationFraction"`

— Value corresponding to the detection of anomalies within a specified fraction of windows. The fraction value is specified by`ThresholdParameter`

.`"max"`

— Maximum window loss measured over the entire training data set and multiplied by`ThresholdParameter`

.`"median"`

— Median window loss measured over the entire training data set and multiplied by`ThresholdParameter`

.`"mean"`

— Mean window loss measured over the entire training data set and multiplied by`ThresholdParameter`

.`"manual"`

— Manual detection threshold value based on`Threshold`

.`"customFunction"`

— Custom detection threshold value based on`ThresholdFunction`

.

If you specify `ThresholdMethod`

, you can also specify `ThresholdParameter`

, `Threshold`

, or `ThresholdFunction`

. The available threshold parameter depends on the specified detection method.

`ThresholdParameter`

— Detection threshold

real scalar

Detection threshold, specified as a real scalar.

If

`ThresholdMethod`

is specified as`"max"`

,`"mean"`

, or`"median"`

, specify`ThresholdParameter`

as a positive scalar. If you do not specify`ThresholdParameter`

, the detector sets the threshold to 1.If

`ThresholdMethod`

is specified as`"contaminationFraction"`

, specify`ThresholdParameter`

as a nonnegative scalar less than 0.5. If you do not specify`ThresholdParameter`

, the detector sets the threshold to 0.01.If

`ThresholdMethod`

is specified as`"customFunction"`

or`"manual"`

, this argument does not apply.

`Threshold`

— Manual detection threshold

positive scalar

Manual detection threshold, specified as a positive scalar. This argument applies only when `ThresholdMethod`

is specified as `"manual"`

.

Use this option when you do not want the detector to compute a threshold based on training data.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`ThresholdFunction`

— Function to compute custom detection threshold

function handle

Function to compute custom detection threshold, specified as a function handle. This argument applies only when `ThresholdMethod`

is specified as `"customFunction"`

.

The function must have two inputs:

The first input is a cell array of aggregated window loss values.

The second input is a cell array of sample loss values before aggregation.

Each cell contains a loss vector for one signal observation.

The function must return a positive scalar corresponding to the detection threshold.

Use this option when you want to compute a threshold based on training data.

**Data Types: **`function_handle`

**Convolutional Encoder**

`NumDownsampleLayers`

— Number of convolutional layers in downsampling section

`2`

(default) | positive integer

Number of convolutional layers in the downsampling section of the model, specified as a positive integer.

The model uses the same number of transposed convolutional layers in the upsampling section, with the parameters in reverse order.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`DownsampleFactor`

— Downsampling factor

`2`

(default) | positive integer | vector of positive integers

Downsampling factor used by convolutional layers, specified as a positive integer or a vector of positive integers.

If you specify

`DownsampleFactor`

as a scalar, each layer uses the same downsampling factor.If you specify

`DownsampleFactor`

as a vector, the*i*th layer uses a downsampling factor equal to the value of the*i*th vector element. The length of the vector must be equal to the number of layers specified by`NumDownsampleLayers`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`NumFilters`

— Number of filters

`32`

(default) | positive integer | vector of positive integers

Number of filters in convolutional layers, specified as a positive scalar integer or a vector of positive integers.

If you specify

`NumFilters`

as a scalar, each layer has the same number of filters.If you specify

`NumFilters`

as a vector, the*i*th layer has a number of filters equal to the value of the*i*th vector element. The length of the vector must be equal to the number of layers specified by`NumDownsampleLayers`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`FilterSize`

— Size of filters

`8`

(default) | positive integer | vector of positive integers

Size of filters in convolutional layers, specified as a positive integer or a vector of positive integers.

If you specify

`FilterSize`

as a scalar, the size of each filter is the same in all layers.If you specify

`FilterSize`

as a vector, the size of the filters in the*i*th layer is equal to the value of the*i*th vector element. The length of the vector must be equal to the number of layers specified by`NumDownsampleLayers`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`DropoutProbability`

— Dropout probability

`0.2`

(default) | nonnegative scalar

Dropout probability used to avoid overfitting, specified as a nonnegative scalar less than 1.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

**LSTM Autoencoder**

`EncoderHiddenUnits`

— Number of hidden units in encoder

`[32 16]`

(default) | vector of positive integers

Number of hidden units for each LSTM layer in the encoder, specified as a vector
of positive integers. The *i*th element of the vector sets the number
of hidden units in the *i*th layer.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`DecoderHiddenUnits`

— Number of hidden units in decoder

`[32 16]`

(default) | vector of positive integers

Number of hidden units in each LSTM layer of the decoder, specified as a vector of
positive integers. The *i*th element of the vector sets the number of
hidden units in the *i*th layer.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

**LSTM Forecaster**

*Since R2024a*

`ForecastSteps`

— Number of steps ahead for forecasting

`1`

(default) | positive integer scalar

This property is read-only.

Number of steps ahead for forecasting, specified as a positive integer scalar.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`NumHiddenUnits`

— Number of hidden units of LSTM layers

`16`

(default) | positive integer scalar | vector of positive integers

This property is read-only.

Number of hidden units of LSTM layers, specified as a positive integer scalar or a
vector of positive integers. The *i*th element of the vector sets the
number of hidden units in the *i*th layer.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

## Output Arguments

`d`

— Signal anomaly detector

`deepSignalAnomalyDetectorCNN`

object | `deepSignalAnomalyDetectorLSTM`

object | `deepSignalAnomalyDetectorLSTMForecaster`

object

Signal anomaly detector, returned as a `deepSignalAnomalyDetectorCNN`

object, a `deepSignalAnomalyDetectorLSTM`

object, or a `deepSignalAnomalyDetectorLSTMForecaster`

object. You must train
`d`

with data before you can use it to detect anomalies.

## Algorithms

### Windows

To detect anomalies, `deepSignalAnomalyDetector`

divides each channel
of each signal into possibly overlapping windows. You can specify the window length using
`WindowLength`

and the number of overlap samples using
`OverlapLength`

.

By default, the detector uses signals with a length of one sample and zero samples of overlap between adjoining windows. These settings detect

*point anomalies*.You can also set

`WindowLength`

to`"fullSignal"`

to detect*whole-signal anomalies*.

### Aggregated Loss

For each window, `deepSignalAnomalyDetector`

computes
sample-by-sample *losses*, defined as the square of the difference in
value between the original signal and the reconstructed signal. The detector then aggregates
the losses using the method specified using `WindowLossAggregation`

. You
can use the maximum sample loss, the minimum sample loss, the mean of the losses, or the
median of the losses.

If the aggregated loss for a window is larger than a specified threshold, the object detects the whole window as abnormal.

### Threshold

To determine the threshold, `deepSignalAnomalyDetector`

finds the
aggregated losses for all the windows in the training data and combines them into a
statistic. You can specify the method that the detector uses to compute the threshold using
`ThresholdMethod`

.

The statistic can be the maximum value of the losses across the data, the minimum value, the mean value, or the median value. The threshold is the statistic multiplied by

`ThresholdParameter`

.If you expect a given fraction of windows in your data to be abnormal, you can instead specify

`ThresholdMethod`

as`contaminationFraction`

and`ThresholdParameter`

as the expected fraction. In that case, the object sets the threshold to the loss value such that the number of windows with greater losses is equal to the specified fraction of the total.If you prefer, you can specify a threshold manually by specifying

`ThresholdMethod`

as`"manual"`

and using the`Threshold`

argument. You can also use your own custom function to compute the threshold.

### Overlap Priority

When the trained object detects a window as normal or abnormal, you can specify whether
to associate the label with the whole window or with each of its samples. If you choose to
divide your signals into overlapping windows, a conflict can arise because some signal
samples can at the same time be in a window detected as normal and in a window detected as
abnormal. In that case, you can use the `OverlapPriority`

argument of the `detect`

function
to declare samples with conflicting labels as either normal or abnormal.

## Extended Capabilities

### GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

## Version History

**Introduced in R2023a**

### R2024a: Segmentation with integer `SequenceLength`

results in fewer
batches

Using `trainingOptions`

with an integer
`SequenceLength`

value produces fewer batches than in previous releases
and the training results can be different. To achieve a similar number of iterations as
before, increase the number of epochs.

### R2024a: Perform streaming anomaly detection

`deepSignalAnomalyDetector`

has a third mode,
`deepSignalAnomalyDetectorLSTMForecaster`

, that uses a long short-term
memory network to detect anomalies in streaming workflows and thus in real time.

### R2024a: Save models for use with Simulink block

The `saveModel`

object function creates a MAT-file containing the trained network and parameters
corresponding to any object generated by `deepSignalAnomalyDetector`

. Use the generated
file with the Deep Signal Anomaly Detector
Simulink^{®} block.

## See Also

### Objects

`deepSignalAnomalyDetectorCNN`

|`deepSignalAnomalyDetectorLSTM`

|`deepSignalAnomalyDetectorLSTMForecaster`

### Functions

### Blocks

- Deep Signal Anomaly Detector (DSP System Toolbox)

### Topics

- Detect Anomalies in Signals Using deepSignalAnomalyDetector
- Detect Anomalies in Machinery Using LSTM Autoencoder
- Detect Anomalies in ECG Data Using Wavelet Scattering and LSTM Autoencoder in Simulink
- Anomaly Detection in Industrial Machinery Using Three-Axis Vibration Data (Predictive Maintenance Toolbox)
- Anomaly Detection Using Convolutional Autoencoder with Wavelet Scattering Sequences

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