incrementalRobustRandomCutForest

Robust random cut forest model for incremental anomaly detection

Since R2023b

Description

The incrementalRobustRandomCutForest function creates an incrementalRobustRandomCutForest model object, which represents a robust random cut forest (RRCF) model for incremental anomaly detection.

Unlike other Statistics and Machine Learning Toolbox™ model objects, incrementalRobustRandomCutForest can be called directly. Also, you can specify learning options, such as the number of robust random cut trees, the contamination fraction in the training data, and whether to standardize the predictor data before fitting the model to data. After you create an incrementalRobustRandomCutForest object, it is prepared for incremental learning (see Incremental Learning for Anomaly Detection).

incrementalRobustRandomCutForest is best suited for incremental learning. For a traditional approach to anomaly detection when all the data is provided in advance, see rrcforest.

Creation

You can create an incrementalRobustRandomCutForest model object in several ways:

• Call the function directly — Configure incremental learning options, or specify learner-specific options, by calling incrementalRobustRandomCutForest directly. This approach is best when you do not have data yet or you want to start incremental learning immediately.

• Convert a traditionally trained model — To initialize a RRCF model for incremental learning using the model parameters and hyperparameters of a trained model object, you can convert the traditionally trained model to an incrementalRobustRandomCutForest model object by passing it to the incrementalLearner function.

• Call an incremental learning function — fit accepts a configured incrementalRobustRandomCutForest model object and data as input, and returns an incrementalRobustRandomCutForest model object updated with information learned from the input model and data.

Syntax

forest = incrementalRobustRandomCutForest

forest = incrementalRobustRandomCutForest(Name,Value)

Description

forest = incrementalRobustRandomCutForest returns an incremental RRCF model object forest for anomaly detection with default parameters. Properties of a default model contain placeholders for unknown model parameters. You must train a default model before you can use it to detect anomalies.

forest = incrementalRobustRandomCutForest(Name,Value) sets properties and additional options using one or more name-value arguments. For example, incrementalRobustRandomCutForest(ContaminationFraction=0.1,ScoreWarmupPeriod=1000) sets the anomaly contamination fraction to 0.1 and the score warm-up period to 1000.

Input Arguments

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: incrementalRobustRandomCutForest(StandardizeData=true) specifies to standardize the predictor data.

StandardizeData — Flag to standardize predictor data

false or 0 (default) | true or 1

Flag to standardize the predictor data, specified as a numeric or logical 1 (true) or 0 (false).

If you set StandardizeData=true, the incrementalRobustRandomCutForest function centers and scales each predictor variable (X or Tbl) by the corresponding column mean and standard deviation. The function does not standardize the data contained in the dummy variable columns generated for categorical predictors.

Example: StandardizeData=true

Data Types: logical

Options — Options for computing in parallel and setting random streams

structure

Options for computing in parallel and setting random streams, specified as a structure. Create the Options structure using statset. This table lists the option fields and their values.

Field Name	Value	Default
UseParallel	Set this value to true to run computations in parallel.	false
UseSubstreams	Set this value to true to run computations in a reproducible manner. To compute reproducibly, set Streams to a type that allows substreams: "mlfg6331_64" or "mrg32k3a".	false
Streams	Specify this value as a RandStream object or cell array of such objects. Use a single object except when the UseParallel value is true and the UseSubstreams value is false. In that case, use a cell array that has the same size as the parallel pool.	If you do not specify Streams, then incrementalRobustRandomCutForest uses the default stream or streams.

Note

You need Parallel Computing Toolbox™ to run computations in parallel.

Example: Options=statset(UseParallel=true,UseSubstreams=true,Streams=RandStream("mlfg6331_64"))

Data Types: struct

ScoreWarmupPeriod — Warm-up period before score computation and anomaly detection

0 (default) | nonnegative integer

Warm-up period before score computation and anomaly detection, specified as a nonnegative integer. This option specifies the number of observations used by the incremental fit function to train the model and estimate the score threshold.

Note

When processing observations during the score warm-up period, the software ignores observations that contain missing values for all predictors.

Example: ScoreWarmupPeriod=200

Data Types: single | double

ScoreWindowSize — Running window size used to estimate score threshold

1000 (default) | positive integer

Running window size used to estimate the score threshold (ScoreThreshold), specified as a positive integer. The default ScoreWindowSize value is 1000.

If ScoreWindowSize is greater than the number of observations in the training data, the software determines ScoreThreshold by subsampling from the training data. Otherwise, ScoreThreshold is set to forest.ScoreThreshold.

Example: ScoreWindowSize=100

Data Types: single | double

Properties

You can set most properties by using name-value argument syntax when you call incrementalRobustRandomCutForest directly. You can set some properties when you call incrementalLearner to convert a traditionally trained model object. You cannot set the properties Mu, NumTrainingObservations, ScoreThreshold, Sigma, and IsWarm.

CategoricalPredictors — List of categorical predictors

vector of positive integers | logical vector | character matrix | string array | cell array of character vectors | "all" | []

This property is read-only.

List of categorical predictors, specified as one of the values in this table.

Value	Description
Vector of positive integers	Each entry in the vector is an index value indicating that the corresponding predictor is categorical. The index values are between 1 and p, where p is the number of predictors used to train the model. If incrementalRobustRandomCutForest uses a subset of input variables as predictors, then the function indexes the predictors using only the subset. The CategoricalPredictors values do not count any variables that the function does not use.
Logical vector	A true entry means that the corresponding predictor is categorical. The length of the vector is p.
Character matrix	Each row of the matrix is the name of a predictor variable. The names must match the entries in PredictorNames. Pad the names with extra blanks so each row of the character matrix has the same length.
String array or cell array of character vectors	Each element in the array is the name of a predictor variable. The names must match the entries in PredictorNames.
"all"	All predictors are categorical.

Data Types: single | double | logical | char | string | cell

CollusiveDisplacement — Collusive displacement calculation method

"maximal" (default) | "average"

This property is read-only.

Collusive displacement calculation method, specified as "maximal" or "average".

The incrementalRobustRandomCutForest function finds the maximum change ("maximal") or the average change ("average") in model complexity for each tree, and computes the collusive displacement (anomaly score) for each observation.

Data Types: char | string

ContaminationFraction — Fraction of anomalies in training data

numeric scalar in the range [0,1]

This property is read-only.

Fraction of anomalies in the training data, specified as a numeric scalar in the range [0,1].

• If the ContaminationFraction value is 0, then incrementalRobustRandomCutForest treats all training observations as normal observations, and sets the ScoreThreshold value to the maximum anomaly score value of the training data.

• If the ContaminationFraction value is in the range (0,1], then incrementalRobustRandomCutForest determines the ScoreThreshold value so that the function detects the specified fraction of training observations as anomalies.

The default ContaminationFraction value depends on how you create the model:

• If you convert a traditionally trained model to create forest, then ContaminationFraction is specified by the corresponding property of the traditionally trained model.

• If you create forest by calling incrementalRobustRandomCutForest directly, then you can specify ContaminationFraction by using name-value argument syntax. If you do not specify the value, then the default value is 0.

Data Types: single | double

EstimationPeriod — Number of observations processed to estimate hyperparameters

nonnegative integer

This property is read-only.

Number of observations processed by the incremental learner to estimate hyperparameters before training, specified as a nonnegative integer.

• When processing observations during the estimation period, the software ignores observations that have missing values for all predictors.

• If you specify a positive EstimationPeriod and StandardizeData is false, incrementalRobustRandomCutForest forces EstimationPeriod to 0.

• If forest is prepared for incremental learning (all hyperparameters required for training are specified), incrementalRobustRandomCutForest forces EstimationPeriod to 0.

• If forest is not prepared for incremental learning and StandardizeData is true, incrementalRobustRandomCutForest sets EstimationPeriod to 1000 and estimates the unknown hyperparameters.

For more details, see Estimation Period.

Data Types: single | double

IsWarm — Flag indicating whether fit returns scores and detects anomalies

false or 0 | true or 1

This property is read-only.

Flag indicating whether the incremental fitting function fit returns scores and detects anomalies after training the model, specified as a numeric or logical 0 (false) or 1 (true).

The incremental model forest is warm (IsWarm becomes true) after the fit function fits the incremental model to ScoreWarmupPeriod observations.

You cannot specify IsWarm directly.

Data Types: logical

Mu — Predictor means

numeric vector | []

This property is read-only.

Predictor means of the training data, specified as a numeric vector.

• If you specify StandardizeData=true:

  • The fit function does not standardize columns that contain categorical variables. The elements in Mu for categorical variables contain NaN values.

  • The isanomaly function standardizes the input data by using the predictor means in Mu and standard deviations in Sigma.

  The length of Mu is equal to the number of predictors.

• If you set StandardizeData=false, then Mu is an empty vector ([]).

You cannot specify Mu directly.

Data Types: single | double

NumLearners — Number of robust random cut trees

100 (default) | positive integer scalar

This property is read-only.

Number of robust random cut trees (trees in the RRCF model), specified as a positive integer scalar.

Data Types: single | double

NumObservationsPerLearner — Number of observations for each robust random cut tree

min(N,256) where N is the number of training observations (default) | positive integer scalar greater than or equal to 3

This property is read-only.

Number of observations to draw from the training data without replacement for each robust random cut tree (tree in the RRCF model), specified as a positive integer scalar greater than or equal to 3.

Data Types: single | double

NumObservationsToKeep — Size of historical data

value of NumObservationsPerLearner (default) | positive integer scalar

This property is read-only.

Size of historical data that pertains to the RRCF model's knowledge, specified as a positive integer scalar.

Data Types: single | double

NumPredictors — Number of predictor variables

nonnegative numeric scalar

This property is read-only.

Number of predictor variables, specified as a nonnegative numeric scalar.

The default NumPredictors value depends on how you create the model:

• If you convert a traditionally trained model to create forest, NumPredictors is specified by the corresponding property of the traditionally trained model.

• If you create forest by calling incrementalRobustRandomCutForest directly, you can specify NumPredictors by using name-value argument syntax. If you do not specify the value, then the default value is 0, and incremental fitting functions infer NumPredictors from the predictor data during training.

Data Types: double

NumTrainingObservations — Number of observations fit to incremental model

0 (default) | nonnegative numeric scalar

This property is read-only.

Number of observations fit to the incremental model forest, specified as a nonnegative numeric scalar. NumTrainingObservations increases when you pass forest and training data to fit outside of the estimation period.

• When fitting the model, the software ignores observations that have missing values for all predictors.

• If you convert a traditionally trained model to create forest, incrementalRobustRandomCutForest does not add the number of observations fit to the traditionally trained model to NumTrainingObservations.

You cannot specify NumTrainingObservations directly.

Data Types: double

ObservationRemoval — Observation removal method

"oldest" (default) | "timedecaying" | "random"

Observation removal method, specified as "oldest", "timedecaying", or "random". When the robust random cut trees reach their capacity, the software removes old observations to accommodate the most recent data.

Value	Description
"oldest"	Oldest observations are removed first.
"timedecaying"	Observations are removed randomly in a weighted fashion. Older observations have a higher probability of being removed first.
"random"	Observations are removed in random order.

Data Types: string | char

PredictorNames — Predictor variable names

string array of unique names | cell array of unique character vectors

This property is read-only.

Predictor variable names, specified as a string array of unique names or cell array of unique character vectors. The functionality of PredictorNames depends on how you supply the predictor data.

• If you supply Tbl, then you can use PredictorNames to specify which predictor variables to use. That is, incrementalRobustRandomCutForest uses only the predictor variables in PredictorNames.

  • PredictorNames must be a subset of Tbl.Properties.VariableNames.

  • By default, PredictorNames contains the names of all predictor variables in Tbl.

• If you supply X, then you can use PredictorNames to assign names to the predictor variables in X.

  • The order of the names in PredictorNames must correspond to the column order of X. That is, PredictorNames{1} is the name of X(:,1), PredictorNames{2} is the name of X(:,2), and so on. Also, size(X,2) and numel(PredictorNames) must be equal.

  • By default, PredictorNames is {"x1","x2",...}.

Data Types: string | cell

ScoreThreshold — Threshold for anomaly score

nonnegative integer

This property is read-only.

Threshold for the anomaly score used to detect anomalies, specified as a nonnegative integer. incrementalRobustRandomCutForest detects observations with scores above the threshold as anomalies.

The default ScoreThreshold value depends on how you create the model:

• If you convert a traditionally trained model object to create forest, then ScoreThreshold is specified by the corresponding property value of the object.

• Otherwise, the default value is 0.

ScoreThreshold has the value 0 until the number of observations reaches the ScoreWarmupPeriod value. After that, the software updates the ScoreThreshold with every new observation.

You cannot specify ScoreThreshold directly.

Data Types: single | double

ScoreWarmupPeriod — Warm-up period before score computation and anomaly detection

nonnegative integer

This property is read-only.

Warm-up period before score computation and anomaly detection, specified as a nonnegative integer. This value is the number of observations used by the incremental fit function to train the model and estimate the score threshold.

• When processing observations during the score warm-up period, the software ignores observations that have missing values for all predictors.

• You can return scores and detect anomalies during the warm-up period by calling isanomaly directly.

The default ScoreWarmupPeriod value depends on how you create the model:

• If you convert a traditionally trained model to create forest, the ScoreWarmupPeriod name-value argument of the incrementalLearner function sets this property.

• Otherwise, the default value is 0.

Data Types: single | double

ScoreWindowSize — Running window size for ScoreThreshold estimation

nonnegative integer

This property is read-only.

Running window size for ScoreThreshold estimation, specified as a nonnegative integer. The software estimates the ScoreThreshold value over a running window with a window size of ScoreWindowSize.

The default ScoreWindowSize value depends on how you create the model:

• If you convert a traditionally trained model to create forest, the ScoreWindowSize name-value argument of the incrementalLearner function sets this property.

• Otherwise, the default value is 1000.

Data Types: double

Sigma — Predictor standard deviations

numeric vector | []

This property is read-only.

Predictor standard deviations of the training data, specified as a numeric vector.

• If you specify StandardizeData=true when you train an incremental RRCF model using fit:

  • The fit function does not standardize columns that contain categorical variables. The elements in Sigma for categorical variables contain NaN values.

  • The isanomaly function standardizes the input data by using the predictor means in Mu and standard deviations in Sigma.

  The length of Sigma is equal to the number of predictors.

• If you set StandardizeData=false, then Sigma is an empty vector ([]).

You cannot specify Sigma directly.

Object Functions

fit	Train robust random cut forest model for incremental anomaly detection
isanomaly	Find anomalies in data using robust random cut forest (RRCF) for incremental learning
reset	Reset incremental robust random cut forest model

Examples

Create Incremental Anomaly Detector Without Any Prior Information

Create a default robust random cut forest model for incremental anomaly detection.

forest = incrementalRobustRandomCutForest;
details(forest)

  incrementalRobustRandomCutForest with properties:

        CollusiveDisplacement: 'maximal'
                  NumLearners: 100
    NumObservationsPerLearner: 256
           ObservationRemoval: 'oldest'
        NumObservationsToKeep: 256
                           Mu: []
                        Sigma: []
        CategoricalPredictors: []
             EstimationPeriod: 0
                       IsWarm: 0
        ContaminationFraction: 0
      NumTrainingObservations: 0
                NumPredictors: 0
               ScoreThreshold: 0
            ScoreWarmupPeriod: 0
               PredictorNames: {}
              ScoreWindowSize: 1000

forest is an incrementalRobustRandomCutForest model object. All its properties are read-only. By default, the software sets the anomaly contamination fraction to 0 and the score warm-up period to 0. forest must be fit to data before you can use it to perform any other operations.

Load Data

Load the human activity data set and keep only the first 3000 observations. For details on the data set, enter Description at the command line.

load humanactivity.mat
feat = feat(1:3000,:);

Fit Incremental Model and Detect Anomalies

Fit the incremental model forest to the data by using the fit function. Because ScoreWarmupPeriod = 0, fit returns scores and detects anomalies immediately after fitting the model for the first time. To simulate a data stream, fit the model in chunks of 100 observations at a time. At each iteration:

• Process 100 observations.

• Overwrite the previous incremental model with a new one fitted to the incoming observations.

• Store medianscore, the median score value of the data chunk, to see how it evolves during incremental learning.

• Store allscores, the score values for the fitted observations.

• Store threshold, the score threshold value for anomalies, to see how it evolves during incremental learning.

• Store numAnom, the number of detected anomalies in the data chunk.

n = numel(feat(:,1));
numObsPerChunk = 100;
nchunk = floor(n/numObsPerChunk);
medianscore = zeros(nchunk,1);
threshold = zeros(nchunk,1);    
numAnom = zeros(nchunk,1);
allscores = [];

% Incremental fitting
rng(0,"twister"); % For reproducibility
for j = 1:nchunk
    ibegin = min(n,numObsPerChunk*(j-1) + 1);
    iend = min(n,numObsPerChunk*j);
    idx = ibegin:iend;    
    forest = fit(forest,feat(idx,:));
    [isanom,scores] = isanomaly(forest,feat(idx,:));
    medianscore(j) = median(scores);
    allscores = [allscores scores'];    
    numAnom(j) = sum(isanom);
    threshold(j) = forest.ScoreThreshold;
end

forest is an incrementalRobustRandomCutForest model object trained on all the data in the stream. The fit function fits the model to the data chunk, and the isanomaly function returns the observation scores and the indices of observations in the data chunk with scores above the score threshold value.

Analyze Incremental Model During Training

Plot the anomaly score for every observation.

plot(allscores,".-")
xlabel("Observation")
ylabel("Score")

At each iteration, the software calculates a score value for each observation in the data chunk. A low score value indicates a normal observation, and a high score value indicates an anomaly.

To see how the score threshold and median score per data chunk evolve during training, plot them on separate tiles.

figure
tiledlayout(2,1);
nexttile
plot(medianscore,".-")
ylabel("Median Score")
xlabel("Iteration")
xlim([0 nchunk])
nexttile
plot(threshold,".-")
ylabel("Score Threshold")
xlabel("Iteration")
xlim([0 nchunk])

finalScoreThreshold=forest.ScoreThreshold

finalScoreThreshold = 
93.7052

The median score fluctuates between 4 and 20. The anomaly score threshold has a value of 20 after the first iteration and steadily approaches a value of 94 by the 22nd iteration. Because ContaminationFraction = 0, incrementalRobustRandomCutForest treats all training observations as normal observations, and at each iteration sets the score threshold to the maximum score value in the data chunk.

totalAnomalies = sum(numAnom)

totalAnomalies = 
0

No anomalies are detected at any iteration, because ContaminationFraction = 0.

Configure Incremental Learning Options and Analyze Model During Training

Prepare an incremental robust random cut forest model by specifying an anomaly contamination fraction of 0.001, and standardize the data using an initial estimation period of 500 observations. Specify a score warm-up period of 1000 observations, during which the fit function updates the score threshold and trains the model but does not return scores or identify anomalies.

forest = incrementalRobustRandomCutForest(ContaminationFraction=0.001, ...
    StandardizeData=true,ScoreWarmupPeriod=1000,EstimationPeriod=500);

forest is an incrementalRobustRandomCutForest model object. All its properties are read-only. forest must be fit to data before you can use it to perform any other operations.

Load Data

Load the credit rating data stored in CreditRating_Historical.dat. Remove the ID column and the categorical variables.

creditrating = readtable("CreditRating_Historical.dat");
creditrating = removevars(creditrating,["ID","Industry","Rating"]);

The fit function of incrementalRobustRandomCutForest does not use observations with missing values. Remove missing values in the data sets to reduce memory consumption and speed up training.

creditrating = rmmissing(creditrating);

Fit Incremental Model and Detect Anomalies

Fit the incremental model Mdl to the data by using the fit function. To simulate a data stream, fit the model in chunks of 100 observations at a time. Because EstimationPeriod = 500 and ScoreWarmupPeriod = 1000, fit only returns scores and detects anomalies after 15 iterations. At each iteration:

• Process 100 observations.

• Overwrite the previous incremental model with a new one fitted to the incoming observations.

• Store meanscore, the mean score value of the data chunk, to see how it evolves during incremental learning.

• Store threshold, the score threshold value for anomalies, to see how it evolves during incremental learning.

• Store numAnom, the number of detected anomalies in the chunk, to see how it evolves during incremental learning.

n = numel(creditrating(:,1));
numObsPerChunk = 100;
nchunk = floor(n/numObsPerChunk);
meanscore = zeros(nchunk,1);
threshold = zeros(nchunk,1);    
numAnom = zeros(nchunk,1);

% Incremental fitting
rng(0,"twister"); % For reproducibility
for j = 1:nchunk
    ibegin = min(n,numObsPerChunk*(j-1) + 1);
    iend = min(n,numObsPerChunk*j);
    idx = ibegin:iend;    
    [forest,tf,scores] = fit(forest,creditrating(idx,:));
    meanscore(j) = mean(scores);
    numAnom(j) = sum(tf);
    threshold(j) = forest.ScoreThreshold;
end

forest is an incrementalRobustRandomCutForest model object trained on all the data in the stream.

Analyze Incremental Model During Training

To see how the mean score, score threshold and number of detected anomalies per chunk evolve during training, plot them on separate tiles.

tiledlayout(3,1);
nexttile
plot(meanscore)
ylabel("Mean Score")
xlabel("Iteration")
xlim([0 nchunk])
xline(forest.EstimationPeriod/numObsPerChunk,"r-.")
xline((forest.EstimationPeriod+forest.ScoreWarmupPeriod)/numObsPerChunk,"r")
nexttile
plot(threshold)
ylabel("Score Threshold")
xlabel("Iteration")
xlim([0 nchunk])
xline(forest.EstimationPeriod/numObsPerChunk,"r-.")
xline((forest.EstimationPeriod+forest.ScoreWarmupPeriod)/numObsPerChunk,"r")
nexttile
plot(numAnom,"+")
ylabel("Anomalies")
xlabel("Iteration")
xlim([0 nchunk])
ylim([0 max(numAnom)+0.2])
xline(forest.EstimationPeriod/numObsPerChunk,"r-.")
xline((forest.EstimationPeriod+forest.ScoreWarmupPeriod)/numObsPerChunk,"r")

During the estimation period, fit estimates means and standard deviations using the observations, and does not fit the model or update the score threshold. During the warm-up period, fit fits the model and updates the score threshold, but returns all scores as NaN and all anomaly values as false. After the warm-up period, fit returns the observation scores and the indices of observations with scores above the score threshold value. A small score value indicates a normal observation, and a large score value indicates an anomaly.

totalAnomalies=sum(numAnom)

totalAnomalies = 
3

anomfrac= totalAnomalies/(n-forest.EstimationPeriod-forest.ScoreWarmupPeriod)

anomfrac = 
0.0012

The software detects 3 anomalies after the warm-up and estimation periods. The contamination fraction after the estimation and warm-up periods is approximately 0.001.

More About

Incremental Learning for Anomaly Detection

Incremental learning, or online learning, is a branch of machine learning concerned with processing incoming data from a data stream, possibly given little to no knowledge of the distribution of the predictor variables, aspects of the prediction or objective function (including tuning parameter values), or whether the observations contain anomalies. Incremental learning differs from traditional machine learning, where enough data is available to fit to a model, perform cross-validation to tune hyperparameters, and infer the predictor distribution.

Anomaly detection is used to identify unexpected events and departures from normal behavior. In situations where the full data set is not immediately available, or new data is arriving, you can use incremental learning for anomaly detection to incrementally train a model so it adjusts to the characteristics of the incoming data.

Given incoming observations, an incremental learning model for anomaly detection does the following:

• Computes anomaly scores

• Updates the anomaly score threshold

• Detects data points above the score threshold as anomalies

• Fits the model to the incoming observations

For more information, see Incremental Anomaly Detection with MATLAB.

Algorithms

Estimation Period

During the estimation period, the incremental fitting function fit does not fit the model. The function uses the first incoming EstimationPeriod observations to estimate the predictor means (Mu) and standard deviations (Sigma). At the end of the estimation period, the function updates the properties that store the hyperparameters.

Estimation occurs only when:

• EstimationPeriod is positive.

• forest.Mu and forest.Sigma are empty arrays [].

• Incremental fitting functions are configured to standardize predictor data (see Standardize Data).

Note

If you specify a positive EstimationPeriod and StandardizeData is false, then EstimationPeriod is reset to 0.

Standardize Data

If incremental learning functions are configured to standardize predictor variables, they do so using the means and standard deviations stored in the Mu and Sigma properties of the incremental learning model forest.

• When you set StandardizeData=true and a positive estimation period (see EstimationPeriod), and forest.Mu and forest.Sigma are empty, the incremental fit function estimates means and standard deviations using the estimation period observations.

• When the incremental fitting function estimates predictor means and standard deviations, the function computes weighted means and weighted standard deviations using the estimation period observations. Specifically, the function standardizes predictor j (x_j) using

  $$x_j^{\ast }=\frac{x_j-{\mu }_j^{\ast }}{{\sigma }_j^{\ast }}.$$

  • x_j is predictor j, and x_jk is observation k of predictor j in the estimation period.

  • $${\mu }_j^{\ast }=\frac{1}{{\displaystyle \sum _k{w}_k}}{\displaystyle \sum _k{w}_k{x}_{jk}}.$$

  • $${\left({\sigma }_j^{\ast }\right)}^2=\frac{1}{{\displaystyle \sum _k{w}_k}}{\displaystyle \sum _k{w}_k{\left(x_{jk}-{\mu }_j^{\ast }\right)}^2}.$$

  • w_j is observation weight j.

  • The observation weights w_j are all equal to one and cannot be specified.

References

[1] Guha, Sudipto, N. Mishra, G. Roy, and O. Schrijvers. "Robust Random Cut Forest Based Anomaly Detection on Streams," Proceedings of The 33rd International Conference on Machine Learning 48 (June 2016): 2712–21.

[2] Bartos, Matthew D., A. Mullapudi, and S. C. Troutman. "rrcf: Implementation of the Robust Random Cut Forest Algorithm for Anomaly Detection on Streams." Journal of Open Source Software 4, no. 35 (2019): 1336.

Extended Capabilities

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To run in parallel, specify the Options name-value argument in the call to this function and set the UseParallel field of the options structure to true using statset:

Options=statset(UseParallel=true)

For more information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).

Version History

Introduced in R2023b