incrementalConceptDriftDetector

Instantiate incremental concept drift detector

Since R2022a

Syntax

IncCDDetector = incrementalConceptDriftDetector()

IncCDDetector = incrementalConceptDriftDetector(DetectionMethod)

IncCDDetector = incrementalConceptDriftDetector(DetectionMethod,Name=Value)

Description

IncCDDetector = incrementalConceptDriftDetector() returns an incremental concept drift detector that utilizes the default method, Hoeffding's Bounds Drift Detection Method with moving average test (HDDMA).

IncCDDetector = incrementalConceptDriftDetector(DetectionMethod) returns an incremental concept drift detector that utilizes the method DetectionMethod.

IncCDDetector = incrementalConceptDriftDetector(DetectionMethod,Name=Value) specifies additional options using one or more Name=Value arguments.

Examples

Monitor Data Stream for Potential Drift

Initiate the concept drift detector using the Drift Detection Method (DDM).

incCDDetector = incrementalConceptDriftDetector("ddm");

Create a random stream such that for the first 1000 observations, failure rate is 0.1 and after 1000 observations, failure rate increases to 0.6.

rng(1234)  % For reproducibility
numObservations = 3000;
switchPeriod = 1000;

for i = 1:numObservations
    if i <= switchPeriod
       failurerate = 0.1;
    else
       failurerate = 0.6;
    end
       X(i) = rand()<failurerate; % Value 1 represents failure
end

Preallocate variables for tracking drift status.

status = zeros(numObservations,1);
statusname = strings(numObservations,1);

Continuously feed the data to the drift detector and perform incremental drift detection. At each iteration:

• Update statistics of the drift detector and monitor for drift using the new data point with detectdrift. (Note: detectdrift checks for drift after the warm-up period.)

• Track and record the drift status for visualization purposes.

• When a drift is detected, reset the incremental concept drift detector by using reset.

for i = 1:numObservations     
    
    incCDDetector = detectdrift(incCDDetector,X(i));
    statusname(i) = string(incCDDetector.DriftStatus);
          
    if incCDDetector.DriftDetected
       status(i) = 2;
       incCDDetector = reset(incCDDetector); % If drift detected, reset the detector
       sprintf("Drift detected at Observation #%d. Detector reset.",i)
    elseif incCDDetector.WarningDetected
       status(i) = 1;
    else 
       status(i) = 0;
    end   
end

ans = 
"Drift detected at Observation #1078. Detector reset."

After the change in the failure rate at observation number 1000, detectdrift detects the shift at observation number 1078.

Plot the drift status versus the observation number.

gscatter(1:numObservations,status,statusname,'gyr','*',4,'on',"Observation number","Drift status")

Monitor Continuous Data for Drift

Create a random stream such that the observations come from a normal distribution with standard deviation 0.75, but the mean changes over time. First 1000 observations come from a distribution with mean 2, the next 1000 come from a distribution with mean 4, and the following 1000 come from a distribution with mean 7.

rng(1234) % For reproducibility
numObservations = 3000;
switchPeriod1 = 1000;
switchPeriod2 = 2000;
X = zeros([numObservations 1]);

% Generate the data
for i = 1:numObservations
   if i <= switchPeriod1
      X(i) = normrnd(2,0.75);
   elseif i <= switchPeriod2
      X(i) = normrnd(4,0.75);
   else
      X(i) = normrnd(7,0.75);
   end
end

In an incremental drift detection application, access to data stream and model update would happen consecutively. One would not collect the data first and then feed into the model. However, for the purpose of clarification, this example demonstrates the simulation of data separately.

Specify the drift warm-up period as 50 observations and estimation period for the data input bounds as 100.

driftWarmupPeriod = 50;
estimationPeriod = 100;

Initiate the incremental concept drift detector. Utilize the Hoeffding's bounds method with exponentially weighted moving average method (EWMA). Specify the input type and warm-up period.

incCDDetector = incrementalConceptDriftDetector("hddmw",InputType="continuous", ...
                WarmupPeriod=driftWarmupPeriod,EstimationPeriod=estimationPeriod)

incCDDetector = 
  HoeffdingDriftDetectionMethod

        PreviousDriftStatus: 'Stable'
                DriftStatus: 'Stable'
                     IsWarm: 0
    NumTrainingObservations: 0
                Alternative: 'greater'
                  InputType: 'continuous'
                 TestMethod: 'ewma'


  Properties, Methods

incDDetector is a HoeffdingDriftDetectionMethod object. When you first create the object, properties such as DriftStatus, IsWarm, CutMean, and NumTrainingObservations are at their initial state. detectdrift updates them as you feed the data incrementally and monitor for drift.

Preallocate the batch size and the variables to record drift status and the mean the drift detector computes with each income of data.

status = zeros([numObservations 1]);
statusname = strings([numObservations 1]);
M = zeros([numObservations 1]);

Simulate the data stream of one observation at a time and perform incremental drift detection. At each iteration:

• Monitor for drift using the new data with detectdrift.

• Track and record the drift status and the statistics for visualization purposes.

• When a drift is detected, reset the incremental concept drift detector by using the function reset.

for i = 1:numObservations
    
    incCDDetector = detectdrift(incCDDetector,X(i));
    
    M(i) = incCDDetector.Mean;
        
    if incCDDetector.DriftDetected
        status(i) = 2;
        statusname(i) = string(incCDDetector.DriftStatus);
        incCDDetector = reset(incCDDetector); % If drift detected, reset the detector
        sprintf("Drift detected at observation #%d. Detector reset.",i)
    elseif incCDDetector.WarningDetected
        status(i) = 1;
        statusname(i) = string(incCDDetector.DriftStatus);
        sprintf("Warning detected at observation #%d.",i)
    else 
        status(i) = 0;
        statusname(i) = string(incCDDetector.DriftStatus);
    end      
end

ans = 
"Warning detected at observation #1024."

ans = 
"Warning detected at observation #1025."

ans = 
"Warning detected at observation #1026."

ans = 
"Warning detected at observation #1027."

ans = 
"Warning detected at observation #1028."

ans = 
"Warning detected at observation #1029."

ans = 
"Drift detected at observation #1030. Detector reset."

ans = 
"Warning detected at observation #2012."

ans = 
"Warning detected at observation #2013."

ans = 
"Warning detected at observation #2014."

ans = 
"Drift detected at observation #2015. Detector reset."

Plot the drift status versus the observation number.

gscatter(1:numObservations,status,statusname,'gyr','*',5,'on',"Number of observations","Drift status")

Plot the mean values versus the number of observations.

scatter(1:numObservations,M)

You can see the increase in the sample mean from the plot. The mean value becomes larger and the software eventually detects the drift in the data. Once a drift is detected, reset the incremental drift detector. This also resets the mean value. In the plot, the observations where the sample mean is zero correspond to the estimation periods. There is an estimation period at the beginning and then twice after the drift detector is reset following the detection of a drift.

Monitor Data Stream for Decrease in Failure Rate

Initiate the concept drift detector using the Drift Detection Method (DDM).

incCDDetector = incrementalConceptDriftDetector("ddm",Alternative="less",WarmupPeriod=100);

Create a random stream such that for the first 1000 observations, failure rate is 0.4 and after 1000 failure rate decreases to 0.1.

rng(1234)  % For reproducibility
numObservations = 3000;
switchPeriod = 1000;
for i = 1:numObservations
    if i <= switchPeriod
       failurerate = 0.4;
    else
       failurerate = 0.125;
    end
       X(i) = rand()<failurerate; % Value 1 represents failure
end

Preallocate variables for tracking drift status and the optimal mean and optimal standard deviation value.

optmean = zeros(numObservations,1);
optstddev = zeros(numObservations,1);
status = zeros(numObservations,1);
statusname = strings(numObservations,1);

Continuously feed the data to the drift detector and monitor for any potential change. Record the drift status for visualization purposes.

for i = 1:numObservations     
    
    incCDDetector = detectdrift(incCDDetector,X(i)); 

    statusname(i) = string(incCDDetector.DriftStatus);
    optmean(i) = incCDDetector.OptimalMean;
    optstddev(i) = incCDDetector.OptimalStandardDeviation;

    if incCDDetector.DriftDetected
       status(i) = 2;
       incCDDetector = reset(incCDDetector); % If drift detected, reset the detector
       sprintf("Drift detected at Observation #%d. Detector reset.",i)
    elseif incCDDetector.WarningDetected
       status(i) = 1;
    else 
       status(i) = 0;
    end   
end

ans = 
"Drift detected at Observation #1107. Detector reset."

After the change in the failure rate at observation number 1000, detectdrift detects the shift at observation number 1096.

Plot the change in the optimal mean and optimal standard deviation.

tiledlayout(2,1);
ax1 = nexttile;
plot(ax1,1:numObservations,optmean)
ax2 = nexttile;
plot(ax2,1:numObservations,optstddev)

Plot the drift status versus the observation number.

figure();
gscatter(1:numObservations,status,statusname,'gyr','*',4,'on',"Observation number","Drift status")

detectdrift concludes on a warning status for multiple observations before it decides on a drift.

Input Arguments

DetectionMethod — Incremental drift detection method

"ddm" | "hddma" | "hddmw"

Incremental drift detection method, specified as one of the following.

Detection Method	Definition
"ddm"	Drift Detection Method (DDM)
"hddma"	Hoeffding's Bounds Drift Detection Method with moving average test (HDDMA)
"hddmw"	Hoeffding's Bounds Drift Detection Method with exponentially weighted moving average (EWMA) test (HDDMW)

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: Alternative="less",InputType="continuous",InputBounds=[-1,1],ForgettingFactor=0.075 specifies the alternative hypothesis as less, that is, left-sided, the input data type as continuous data, lower and upper bounds of the input data as [-1,1] and the value of the forgetting factor for the HDDMW method as 0.075.

General Options

Alternative — Type of alternative hypothesis

"greater" (default) | "less" | "unequal" (for HDDMA or HDDMW)

Type of alternative hypothesis for determining drift status, specified as one of "unequal", "greater", or "less". Given two test statistics $$F_1\left(x\right)$$ and $$F_2\left(x\right)$$,

• "greater" tests for a drift in the positive direction, that is, $$F_1\left(x\right)>F_2\left(x\right)$$.

  In this case, the null hypothesis is $$F_1\left(x\right)\le F_2\left(x\right)$$.

• "less" tests for a drift in the negative direction, that is, $$F_1\left(x\right)<F_2\left(x\right)$$.

  In this case, the null hypothesis is $$F_1\left(x\right)\ge F_2\left(x\right)$$.

• "unequal" tests for a drift in the either direction, that is, $$F_1\left(x\right)\ne F_2\left(x\right)$$.

  In this case, the null hypothesis is $$F_1\left(x\right)=F_2\left(x\right)$$.

  "unequal" is for the HDDMA and HDDMW methods only.

For each type of test, detectdrift updates the statistics and checks whether it can reject the null hypothesis in favor of the alternative at the significance level of WarningThreshold or DriftThreshold. If it rejects the null hypothesis at the significance level of WarningThreshold, then it updates the DriftStatus to 'Warning'. If it rejects the null hypothesis at the DriftThreshold, then it updates the DriftStatus to 'Drift'.

Example: Alternative="less"

InputType — Type of input to the drift detector

"binary" (default) | "continuous"

Type of input to the drift detector, specified as either "binary" or "continuous".

Example: InputType="continuous"

WarmupPeriod — Number of observations used for drift detector to warm up

30 (default) | nonnegative integer

Number of observations used for drift detector to warm up, specified as a nonnegative integer. Until the end of the warm-up period, detectdrift trains the drift detector using the incoming data and updates the internal statistics, but does not check for the drift status. After the software reaches the warm-up period, that is, once the drift detector is warm, it starts checking for any changes in the drift status.

Example: WarmupPeriod=50

Data Types: double | single

Options for DDM

DriftThreshold — Number of standard deviations for drift limit

3 (default) | nonnegative scalar value

Number of standard deviations for drift limit, specified as a nonnegative scalar value. This is the number of standard deviations the overall test statistic value can be away from the optimal test statistic value before the drift detector sets the drift status to drift. Default value of 3 corresponds to a 99.7% confidence level [1].

DriftThreshold value must be strictly greater than the WarningThreshold value.

Example: DriftThreshold=2.5

Data Types: double | single

WarningThreshold — Number of standard deviations for warning limit

2 (default) | nonnegative scalar value

Number of standard deviations for warning limit, specified as a nonnegative scalar value. This is the number of standard deviations the overall test statistic value can be away from the optimal test statistic value before the drift detector sets the drift status to warning. Default value of 2 corresponds to a 95% confidence level [1].

WarningThreshold value must be strictly smaller than the DriftThreshold value.

Example: WarningThreshold=1.75

Data Types: double | single

Options for HDDMA and HDDMW

DriftThreshold — Threshold to determine if drift exists

0.001 (default) | nonnegative scalar value from 0 to 1

Threshold to determine if drift exists, specified as a nonnegative scalar value from 0 to 1. It is the significance level the drift detector uses for calculating the allowed error between a random variable and its expected value in Hoeffding's inequality and McDiarmid's inequality before it sets the drift status to drift [2].

DriftThreshold value must be strictly smaller than the WarningThreshold value.

Example: DriftThreshold=0.003

Data Types: double | single

EstimationPeriod — Number of observations used to estimate the input bounds for continuous data

nonnegative integer

Number of observations used to estimate the input bounds for continuous data, specified as a nonnegative integer. That is, when InputType is "continuous" and you did not specify the InputBounds value, the software uses EstimationPeriod number of observations to estimate the input bounds. After the estimation period, the software starts the warm-up period.

If you specify the InputBounds value or InputType is "binary", then the software ignores EstimationPeriod.

Default value is 100 when there is a need for estimating the input bounds. Otherwise, default value is 0.

Example: EstimationPeriod=150

Data Types: double | single

InputBounds — Lower and upper bounds of continuous input data

numeric vector of size 2

Lower and upper bounds of continuous input data, specified as a numeric vector of size 2.

If InputType is "continuous" and you do not specify the InputBounds value, then detectdrift estimates the bounds from the data during the estimation period. Specify the number of observations to estimate the data input bounds by using EstimationPeriod.

If InputType is "binary", then the drift detector sets the InputBounds value to [0,1] and the software ignores the InputBounds name-value argument.

HDDM uses Hoeffding's inequality and McDiarmid's inequality for drift detection and these inequalities assume bounded inputs [2].

Example: InputBounds=[-1 1]

Data Types: double | single

ForgettingFactor — Forgetting factor for HDDMW method

0.05 (default) | scalar value from 0 to 1

Note

This option is only for the exponentially weighted moving average (EWMA) method (corresponding to DetectionMethod value set as "hddmw").

Forgetting factor in the HDDMW method, specified as a scalar value from 0 to 1. The value of the forgetting factor determines the rate of change of the weighting factors. A forgetting factor of 0.1 gives more weight to the older data than does a forgetting factor of 0.9. A forgetting factor of 0 indicates infinite memory, where all the previous samples have equal weight.

In the exponential weighting method, the moving average is computed recursively using these formulas:

$$\begin{array}{l}{w}_{N,\varphi }=(1-\varphi )w_{N-1,\varphi }+1\\ {\overline{x}}_{N,\varphi }=\left(1-\frac{1}{w_{N,\varphi }}\right){\overline{x}}_{N-1,\varphi }+\left(\frac{1}{w_{N,\varphi }}\right)x_N\end{array}$$

• $${\overline{x}}_{N,\varphi }$$ — Moving average at the current sample

• $$\varphi$$ — Forgetting factor

• $$x_N$$ — Current data input sample

• $${\overline{x}}_{N-1,\varphi }$$ — Moving average at the previous sample

• $$w_{N,\varphi }$$ — Weighting factor applied to the current data sample

• $$\left(1-\frac{1}{w_{N,\varphi }}\right){\overline{x}}_{N-1,\varphi }$$ — Effect of the previous data on the average

For the first sample, where N = 1, the algorithm chooses $$w_{N,\varphi }$$ = 1. For the next sample, the weighting factor is updated and used to compute the average, as per the recursive equation. As the age of the data increases, the magnitude of the weighting factor decreases exponentially and never reaches zero. In other words, the recent data has more influence on the current average than the older data.

Example: ForgettingFactor=0.075

Data Types: double | single

WarningThreshold — Threshold to determine warning versus drift

0.005 (default) | nonnegative scalar value from 0 to 1

Threshold to determine warning versus drift, specified as a nonnegative scalar value from 0 to 1. It is the significance level the drift detector uses for calculating the allowed error between a random variable and its expected value in Hoeffding's inequality and McDiarmid's inequality before it sets the drift status to warning [2].

WarningThreshold value must be strictly greater than DriftThreshold value.

Example: WarningThreshold=0.007

Data Types: single | double

Output Arguments

IncCDDetector — Incremental concept drift detector

DriftDetectionMethod | HoeffdingDriftDetectionMethod

Incremental concept drift detector, specified as either DriftDetectionMethod or HoeffdingDriftDetectionMethod object. For more information on these objects and their properties, see the corresponding reference pages.

References

[1] Gama, Joao, Pedro Medas, Gladys Castillo, and Pedro P. Rodrigues. “Learning with drift detection.“ In Brazilian symposium on artificial intelligence, pp. 286-295. Berlin, Heidelberg: Springer. 2004, September.

[2] Frias-Blanco, Isvani, Jose del Campo-Ávila, Ramos-Jimenez Gonzalo, Rafael Morales-Bueno, Augustin Ortiz-Diaz, and Yaile Caballero-Mota. “Online and non-parametric drift detection methods based on Hoeffding's bounds.“ IEEE Transactions on Knowledge and Data Engineering, Vol. 27, No. 3, pp.810-823. 2014.

Version History

Introduced in R2022a