# HoeffdingDriftDetectionMethod

Incremental concept drift detector that utilizes Hoeffding's Bounds Drift Detection Method (HDDM)

## Description

`HoeffdingDriftDetectionMethod`

model object represents an incremental
concept drift detector that uses the Hoeffding's Bounds nonparametric drift detection methods
based on moving averages (A-test) or exponentially weighted moving averages (W-test) [1]. After creating the object,
you can use the `detectdrift`

object
function to update the statistics and check for any drift in the concept data (for example,
failure rate, regression loss, and so on).

`HoeffdingDriftDetectionMethod`

is suitable for incremental concept drift detection. For
drift detection on raw data, see `detectdrift`

for
batch drift detection.

## Creation

You can create `HoeffdingDriftDetectionMethod`

by specifying the
`DetectionMethod`

argument as `"hddma"`

or
`"hddmw"`

in the call to `incrementalConceptDriftDetector`

.

## Properties

`Alternative`

— Type of alternative hypothesis

`'greater'`

(default) | `'less'`

| `'unequal'`

This property is read-only.

Type of alternative hypothesis for determining the drift status, specified as
`'greater'`

, `'less'`

, or
`'unequal'`

.

**Data Types: **`char`

`CutHoeffdingBound`

— Hoeffding's bound for input data observed up to the cut point

numeric value

This property is read-only.

Hoeffding's bound for input data observed up to the cut point, specified as a numeric value.

`detectdrift`

updates `CutMean`

and `CutHoeffdingBound`

and resets `PostCutMean`

and `PostCutHoeffdingBound`

when any one of these conditions is satisfied:

`Alternative`

is`"greater"`

and`Mean`

+`HoeffdingBound`

is less than or equal to`CutMean`

+`CutHoeffdingBound`

.`Alternative`

is`"less"`

and`Mean`

-`HoeffdingBound`

is greater than or equal to`CutMean`

-`CutHoeffdingBound`

.`Alternative`

is`"unequal"`

and`Mean`

+`HoeffdingBound`

is less than or equal to`CutMean`

-`CutHoeffdingBound`

or`Mean`

-`HoeffdingBound`

is greater than or equal to`CutMean`

+`CutHoeffdingBound`

.

**Data Types: **`double`

`CutMean`

— Weighted average

numeric value

This property is read-only.

Weighted average of data observed up to the cut point, specified as a numeric value.

`detectdrift`

updates `CutMean`

and `CutHoeffdingBound`

and resets `PostCutMean`

and `PostCutHoeffdingBound`

when any one of these conditions is satisfied:

`Alternative`

is`"greater"`

and`Mean`

+`HoeffdingBound`

is less than or equal to`CutMean`

+`CutHoeffdingBound`

.`Alternative`

is`"less"`

and`Mean`

-`HoeffdingBound`

is greater than or equal to`CutMean`

-`CutHoeffdingBound`

.`Alternative`

is`"unequal"`

and`Mean`

+`HoeffdingBound`

is less than or equal to`CutMean`

-`CutHoeffdingBound`

or`Mean`

-`HoeffdingBound`

is greater than or equal to`CutMean`

+`CutHoeffdingBound`

.

**Data Types: **`double`

`DriftDetected`

— Flag indicating whether software detects drift

`1`

| `0`

This property is read-only.

Flag indicating whether software detects drift or not, specified as either
`1`

or `0`

. Value of `1`

means
`DriftStatus`

is `'Drift'`

.

**Data Types: **`logical`

`DriftStatus`

— Current drift status

`'Stable'`

| `'Warning'`

| `'Drift'`

This property is read-only.

Current drift status, specified as `'Stable'`

,
`'Warning'`

, or `'Drift'`

. You can see the
transition in the drift status by comparing `DriftStatus`

and
`PreviousDriftStaus`

.

**Data Types: **`char`

`DriftThreshold`

— Threshold to determine if drift exists

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

This property is read-only.

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

to
`'Drift'`

.

**Data Types: **`double`

`EstimationPeriod`

— Number of observations used for estimating the input bound

nonnegative integer

This property is read-only.

Number of observations used for estimating the input bound for continuous variables, specified as a nonnegative integer.

**Data Types: **`double`

`ForgettingFactor`

— Forgetting factor for HDDMW method

0.05 (default) | scalar value from 0 to 1

This property is read-only.

**Note**

This option is for the exponentially weighted moving average method
(`ewma`

) only.

Forgetting factor for the exponentially weighted moving average (EWMA) method (HDDMW), specified as a scalar value from 0 to 1.

**Data Types: **`double`

`HoeffdingBound`

— Hoeffding's bound for all input data

numeric value

This property is read-only.

Hoeffding's bound for all input data used for training the drift detector, specified as a numeric value.

**Data Types: **`double`

`InputBounds`

— Bounds of input data

numeric vector of size 2

This property is read-only.

Bounds of input data, specified as a numeric vector of size 2.

**Data Types: **`double`

`InputType`

— Type of input data

`'binary'`

(default) | `'continuous'`

This property is read-only.

Type of input data, specified as either `'binary'`

or
`'continuous'`

.

**Data Types: **`char`

`IsWarm`

— Flag indicating whether warmup period is over

`1`

| `0`

This property is read-only.

Flag indicating whether the warmup period is over or not, specified as
`1`

(`true`

) or
`0`

(`false`

).

**Data Types: **`logical`

`Mean`

— Weighted average of all input data

numeric value

This property is read-only.

Weighted average of all input data used for training the drift detector, specified as a numeric value.

**Data Types: **`double`

`NumTrainingObservations`

— Number of observations used for training

nonnegative integer value

This property is read-only.

Number of observations used for training the drift detector, specified as a nonnegative integer value.

**Data Types: **`double`

`PostCutHoeffdingBound`

— Hoeffding's bound for data observed after the cut point

numeric value

This property is read-only.

Hoeffding's bound for data observed after the cut point, specified as a numeric value.

`detectdrift`

updates `CutMean`

and `CutHoeffdingBound`

and resets `PostCutMean`

and `PostCutHoeffdingBound`

when any one of these conditions is satisfied:

`Alternative`

is`"greater"`

and`Mean`

+`HoeffdingBound`

is less than or equal to`CutMean`

+`CutHoeffdingBound`

.`Alternative`

is`"less"`

and`Mean`

-`HoeffdingBound`

is greater than or equal to`CutMean`

-`CutHoeffdingBound`

.`Alternative`

is`"unequal"`

and`Mean`

+`HoeffdingBound`

is less than or equal to`CutMean`

-`CutHoeffdingBound`

or`Mean`

-`HoeffdingBound`

is greater than or equal to`CutMean`

+`CutHoeffdingBound`

.

**Data Types: **`double`

`PostCutMean`

— Weighted average of data observed after the cut point

numeric value

This property is read-only.

Weighted average of data observed after the cut point, specified as a numeric value.

`detectdrift`

updates `CutMean`

and `CutHoeffdingBound`

and resets `PostCutMean`

and `PostCutHoeffdingBound`

when any one of these conditions is satisfied:

`Alternative`

is`"greater"`

and`Mean`

+`HoeffdingBound`

is less than or equal to`CutMean`

+`CutHoeffdingBound`

.`Alternative`

is`"less"`

and`Mean`

-`HoeffdingBound`

is greater than or equal to`CutMean`

-`CutHoeffdingBound`

.`Alternative`

is`"unequal"`

and`Mean`

+`HoeffdingBound`

is less than or equal to`CutMean`

-`CutHoeffdingBound`

or`Mean`

-`HoeffdingBound`

is greater than or equal to`CutMean`

+`CutHoeffdingBound`

.

**Data Types: **`double`

`PreviousDriftStatus`

— Drift status prior to the latest training

`'Stable'`

| `'Warning'`

| `'Drift'`

This property is read-only.

Drift status prior to the latest training using the most recent batch of data,
specified as `'Stable'`

, `'Warning'`

, or
`'Drift'`

. You can see the transition in the drift status by
comparing `DriftStatus`

and
`PreviousDriftStaus`

.

**Data Types: **`char`

`TestMethod`

— Test method used for drift detection

`'ewma'`

| `'average'`

This property is read-only.

Test method used for drift detection, specified as either `'ewma'`

or `'average'`

corresponding to the `"hddmw"`

and
`"hddma"`

detection methods, respectively, in the call to
`incrementalConceptDriftDetector`

.

**Data Types: **`char`

`WarmupPeriod`

— Number of observations for drift detector warmup

nonnegative integer value

This property is read-only.

Number of observations for drift detector warmup, specified as a nonnegative integer.

**Data Types: **`double`

`WarningDetected`

— Flag indicating whether there is warning

`1`

| `0`

This property is read-only.

Flag indicating whether there is warning or not, specified as either
`1`

or `0`

. Value of `1`

means
`DriftStatus`

is `'Warning'`

.

**Data Types: **`logical`

`WarningThreshold`

— Threshold to determine warning versus drift

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

This property is read-only.

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

to
`'Warning'`

.

**Data Types: **`double`

## Object Functions

`detectdrift` | Update drift detector states and drift status with new data |

`reset` | Reset incremental concept drift detector |

## Examples

### 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 warmup 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 warmup 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.

## References

[1] 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**

## See Also

`incrementalConceptDriftDetector`

| `DriftDetectionMethod`

| `detectdrift`

| `reset`

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