fit

Train robust random cut forest model for incremental anomaly detection

Since R2023b

Syntax

forest = fit(forest,Tbl)

forest = fit(forest,X)

[forest,tf] = fit(___)

[forest,tf,scores] = fit(___)

Description

The fit function fits a configured robust random cut forest (RRCF) model for incremental anomaly detection (incrementalRobustRandomCutForest object) to streaming data.

To fit a RRCF model to an entire batch of data at once, see rrcforest.

forest = fit(forest,Tbl) returns an incremental learning model forest, which represents the input incremental learning model forest trained using the predictor data in Tbl. Specifically, the fit function fits the model to the incoming data and stores the updated score threshold and configurations in the output model forest.

forest = fit(forest,X) fits the incremental learning model forest using the predictor data in the matrix X. You must use this syntax if you initially trained forest on a predictor matrix in your first call to fit.

[forest,tf] = fit(___) additionally returns the logical array tf, whose elements are true when an anomaly is detected in the corresponding row of Tbl or X, using any of the input argument combinations in the previous syntaxes.

[forest,tf,scores] = fit(___) also returns an anomaly score in the range [0,Inf) for each observation in Tbl or X. A small positive value indicates a normal observation, and a large positive value indicates an anomaly.

Examples

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.

Incrementally Train RRCF Model on Shingled Data

Train a robust random cut forest (RRCF) model on a simulated, noisy, periodic shingled time series containing no anomalies by using rrcforest. Convert the trained model to an incremental learner object, and then incrementally fit the time series and detect anomalies.

Create Simulated Data Stream

Create a simulated data stream of observations representing a noisy sinusoid signal.

rng(0,"twister"); % For reproducibility
period = 100;
n = 2001+period;
sigma = 0.04;
a = linspace(1,n,n)';
b = sin(2*pi*(a-1)/period)+sigma*randn(n,1);

Introduce an anomalous region into the data stream. Plot the data stream portion that contains the anomalous region, and circle the anomalous data points.

c = 2*(sin(2*pi*(a-35)/period)+sigma*randn(n,1));
b(1150:1170) = c(1150:1170);
scatter(a,b,".")
xlim([900,1200])
xlabel("Observation")
hold on
scatter(a(1150:1170),b(1150:1170),"r")
hold off

Convert the single-featured data set b into a multi-featured data set by shingling [1] with a shingle size equal to the period of the signal. The $$i$$th shingled observation is a vector of $$k$$ features with values $$b_i$$, $$b_{i+1}$$, ..., $$b_{i+k-1}$$, where $$k$$ is the shingle size.

X = [];
shingleSize = period;
for i = 1:n-shingleSize
    X = [X;b(i:i+shingleSize-1)'];
end

Train Model and Perform Incremental Anomaly Detection

Fit a robust random cut forest model to the first 1000 shingled observations, specifying a contamination fraction of 0. Convert the model to an incrementalRobustRandomCutForest model object. Specify to keep the 100 most recent observations relevant for anomaly detection.

Mdl = rrcforest(X(1:1000,:),ContaminationFraction=0);
IncrementalMdl = incrementalLearner(Mdl,NumObservationsToKeep=100);

To simulate a data stream, process the full shingled data set in chunks of 100 observations at a time. At each iteration:

• Process 100 observations.

• Calculate scores and detect anomalies using the isanomaly function.

• Store anomIdx, the indices of shingled observations marked as anomalies.

• If the chunk contains fewer than three anomalies, fit and update the previous incremental model.

n = numel(X(:,1));
numObsPerChunk = 100;
nchunk = floor(n/numObsPerChunk);
anomIdx = [];
allscores = [];

% Incremental fitting
rng("default"); % For reproducibility
for j = 1:nchunk
    ibegin = min(n,numObsPerChunk*(j-1) + 1);
    iend = min(n,numObsPerChunk*j);
    idx = ibegin:iend;
    [isanom,scores] = isanomaly(IncrementalMdl,X(idx,:));
    allscores = [allscores;scores];
    anomIdx = [anomIdx;find(isanom)+ibegin-1];
    if (sum(isanom) < 3)
        IncrementalMdl = fit(IncrementalMdl,X(idx,:));
    end
end

Analyze Incremental Model During Training

At each iteration, the software calculates a score value for each observation in the data chunk. A negative score value with large magnitude indicates a normal observation, and a large positive value indicates an anomaly. Plot the anomaly score for the observations in the vicinity of the anomaly. Circle the scores of shingles that the software returns as anomalous.

figure
scatter(a(1:2000),allscores,".")
hold on
scatter(a(anomIdx),allscores(anomIdx),20,"or")
xlim([900,1200])
xlabel("Shingle")
ylabel("Score")
hold off

Because the introduced anomalous region begins at observation 1150, and the shingle size is 100, shingle 1051 is the first to show a high anomaly score. Some shingles between 1050 and 1170 have scores lying just below the anomaly score threshold, due to the noise in the sinusoidal signal. The shingle size affects the performance of the model by defining how many subsequent consecutive data points in the original time series the software uses to calculate the anomaly score for each shingle.

Plot the unshingled data and highlight the introduced anomalous region. Circle the observation number of the first element in each shingle returned by that the software as anomalous.

figure
xlim([900,1200])
ylim([-1.5 2])
rectangle(Position=[1150 -1.5 20 3.5],FaceColor=[0.9 0.9 0.9], ...
    EdgeColor=[0.9 0.9 0.9])
hold on
scatter(a,b,".")
scatter(a(anomIdx),b(anomIdx),20,"or")
xlabel("Observation")
hold off

Perform Incremental RRCF Anomaly Detection with Categorical Predictor Data

Train an incremental robust random cut forest (RRCF) model and perform anomaly detection on a data set with categorical predictors.

Load Data

Load census1994.mat. The data set consists of demographic data from the US Census Bureau.

load census1994.mat

incrementalRobustRandomCutForest does not use observations with missing values. Remove missing values in the data to reduce memory consumption and speed up training. Keep only the first 1000 observations in the training data set and the first 2000 observations in the test data set.

adultdata = rmmissing(adultdata);
adulttest = rmmissing(adulttest);
Xtrain = adultdata(1:1000,:);
Xstream = adulttest(1:2000,:);

Train RRCF Model

Fit an RRCF model to the training data. Specify an anomaly contamination fraction of 0.001.

rng(0,"twister"); % For reproducibility
TTforest = rrcforest(Xtrain,ContaminationFraction=0.001);
details(TTforest)

  RobustRandomCutForest with properties:

        CollusiveDisplacement: 'maximal'
                  NumLearners: 100
    NumObservationsPerLearner: 256
                           Mu: []
                        Sigma: []
        CategoricalPredictors: [2 4 6 7 8 9 10 14 15]
        ContaminationFraction: 1.0000e-03
               ScoreThreshold: 55.5745
               PredictorNames: {'age'  'workClass'  'fnlwgt'  'education'  'education_num'  'marital_status'  'occupation'  'relationship'  'race'  'sex'  'capital_gain'  'capital_loss'  'hours_per_week'  'native_country'  'salary'}

TTforest is a RobustRandomCutForest model object representing a traditionally trained RRCF model. The software identifies nine variables in the data as categorical predictors because they contain string arrays.

Convert Trained Model

Convert the traditionally trained RRCF model to an RRCF model for incremental learning.

Incrementalforest = incrementalLearner(TTforest);

Incrementalforest is an incrementalRobustRandomCutForest model object that is ready for incremental learning and anomaly detection.

Fit Incremental Model and Detect Anomalies

Perform incremental learning on the Xstream data by using the fit function. 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 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(Xstream(:,1));
numObsPerChunk = 100;
nchunk = floor(n/numObsPerChunk);
medianscore = zeros(nchunk,1);
numAnom = zeros(nchunk,1);
threshold = zeros(nchunk,1);

% Incremental fitting
for j = 1:nchunk
    ibegin = min(n,numObsPerChunk*(j-1) + 1);
    iend = min(n,numObsPerChunk*j);
    idx = ibegin:iend;    
    [Incrementalforest,tf,scores] = fit(Incrementalforest,Xstream(idx,:));
    medianscore(j) = median(scores);
    numAnom(j) = sum(tf);
    threshold(j) = Incrementalforest.ScoreThreshold;
end

Analyze Incremental Model During Training

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

tiledlayout(3,1);
nexttile
plot(medianscore)
ylabel("Median Score")
xlabel("Iteration")
xlim([0 nchunk])
nexttile
plot(threshold)
ylabel("Score Threshold")
xlabel("Iteration")
xlim([0 nchunk])
nexttile
plot(numAnom,"+")
ylabel("Anomalies")
xlabel("Iteration")
xlim([0 nchunk])
ylim([0 max(numAnom)+0.2])

totalanomalies=sum(numAnom)

totalanomalies = 
1

anomfrac= totalanomalies/n

anomfrac = 
5.0000e-04

fit updates the model and returns the observation scores and the indices of observations with scores above the score threshold value as anomalies. A high score value indicates a normal observation, and a low value indicates an anomaly. The median score fluctuates between approximately 230 and 270. The score threshold rises from a value of 260 after the first iteration and steadily approaches 285 after 12 iterations. The software detected 4 anomalies in the Xstream data, yielding a total contamination fraction of 0.002.

Input Arguments

forest — Incremental anomaly detection model

incrementalRobustRandomCutForest model object

Incremental anomaly detection model to fit to streaming data, specified as an incrementalRobustRandomCutForest model object. You can create forest by calling incrementalRobustRandomCutForest directly, or by converting a supported, traditionally trained RRCF model using the incrementalLearner function.

Tbl — Predictor data

table

Predictor data, specified as a table. Each row of Tbl corresponds to one observation, and each column corresponds to one predictor variable. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

If you train forest using a table, then you must provide predictor data by using Tbl, not X. All predictor variables in Tbl must have the same variable names and data types as those in the training data. However, the column order in Tbl does not need to correspond to the column order of the training data.

Note

If an observation contains missing values for all predictors (NaN, '' (empty character vector), "" (empty string), <missing>, or <undefined>) , fit ignores the observation. Consequently, fit uses fewer than n observations to create an updated model, where n is the number of observations in Tbl.

Data Types: table

X — Predictor data

numeric matrix

Predictor data, specified as a numeric matrix. Each row of X corresponds to one observation, and each column corresponds to one predictor variable.

If you train forest using a matrix, then you must provide predictor data by using X, not Tbl. The variables that make up the columns of X must have the same order as the variables in the training data. If forest.NumPredictors is not specified, then fit infers it from the data.

Note

If an observation contains missing values for all predictors (NaN) value, fit ignores the observation. Consequently, fit uses fewer than n observations to create an updated model, where n is the number of observations in X.

Data Types: single | double

Output Arguments

forest — Updated RRCF model for incremental anomaly detection

incrementalRobustRandomCutForest model object

Updated RRCF model for incremental anomaly detection, returned as an incrementalRobustRandomCutForest model object.

tf — Anomaly indicators

logical column vector

Anomaly indicators, returned as a logical column vector. An element of tf is true when the observation in the corresponding row of Tbl or X is an anomaly, and false otherwise. tf has the same length as Tbl or X.

fit updates forest and then identifies the observations with scores above the threshold (the ScoreThreshold value) as anomalies.

Note

• If the model is not warm (IsWarm = false), then fit returns all tf as false.

• fit assigns the anomaly indicator of false (logical 0) to observations that have missing values for all predictors.

Data Types: logical

scores — Anomaly scores

numeric column vector

Anomaly scores, returned as a numeric column vector whose values are in the range [0,Inf). scores has the same length as Tbl or X, and each element of scores contains an anomaly score for the observation in the corresponding row of Tbl or X. fit calculates scores after updating forest. A small positive value indicates a normal observation, and a large positive value indicates an anomaly.

Note

• If the model is not warm (IsWarm = false), then fit returns all scores as NaN.

• fit assigns the anomaly score of NaN to observations that have missing values for all predictors.

Data Types: single | double

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.

Version History

Introduced in R2023b