fit

Train one-class SVM model for incremental anomaly detection

Since R2023b

Syntax

Mdl = fit(Mdl,Tbl)

Mdl = fit(Mdl,X)

[Mdl,tf] = fit(___)

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

Description

The fit function fits a configured one-class support vector machine (SVM) model for incremental anomaly detection (incrementalOneClassSVM object) to streaming data.

To fit a one-class SVM model to an entire batch of data at once, see ocsvm.

Mdl = fit(Mdl,Tbl) returns an incremental learning model Mdl, which represents the input incremental learning model Mdl 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 Mdl.

Mdl = fit(Mdl,X) fits the incremental learning model Mdl using the predictor data in the matrix X.

[Mdl,tf] = fit(___) additionally returns the logical array tf with N elements for N observations, using any of the input argument combinations in the previous syntaxes.

[Mdl,tf,scores] = fit(___) additionally returns the numeric array scores containing anomaly scores with N elements for N observations. The values in this array are in the range (–Inf,Inf). A negative score value with large magnitude indicates a normal observation, and a large positive value indicates an anomaly.

Examples

Create Incremental Anomaly Detector Without Any Prior Information

Create a default one-class support vector machine (SVM) model for incremental anomaly detection.

Mdl = incrementalOneClassSVM;
Mdl.ScoreWarmupPeriod

ans = 0

Mdl.ContaminationFraction

ans = 0

Mdl is an incrementalOneClassSVM model object. All its properties are read-only. By default, the software sets the score warm-up period to 0 and the anomaly contamination fraction to 0.

Mdl must be fit to data before you can use it to perform any other operations.

Load Data

Load the 1994 census data stored in census1994.mat. The data set consists of demographic data from the US Census Bureau.

load census1994.mat

incrementalOneClassSVM does not support categorical predictors and does not use observations with missing values. Remove missing values in the data to reduce memory consumption and speed up training. Remove the categorical predictors.

adultdata = rmmissing(adultdata);
adultdata = removevars(adultdata,["workClass","education","marital_status", ...
    "occupation","relationship","race","sex","native_country","salary"]);

Fit Incremental Model

Fit the incremental model Mdl to the data in the adultdata table 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(adultdata(:,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;    
    Mdl = fit(Mdl,adultdata(idx,:));
    [isanom,scores] = isanomaly(Mdl,adultdata(idx,:));
    medianscore(j) = median(scores);
    allscores = [allscores scores'];    
    numAnom(j) = sum(isanom);
    threshold(j) = Mdl.ScoreThreshold;
end

Mdl is an incrementalOneClassSVM 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")
xlim([0 n])

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.

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=Mdl.ScoreThreshold

finalScoreThreshold = 0.1799

The median score is negative for the first several iterations, then rapidly approaches zero. The anomaly score threshold immediately rises from its (default) starting value of 0 to 1.3, and then gradually approaches 0.18. Because ContaminationFraction = 0, incrementalOneClassSVM 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.

Incrementally Train One-Class SVM Model on Shingled Data

Train a one-class SVM model on a simulated noisy periodic shingled time series containing no anomalies by using ocsvm. Convert the trained model to an incremental learner object, and 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 = 5001+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 which contains the anomalous region, and circle the anomalous data points.

c = 2*(sin(2*pi*(a-35)/period)+sigma*randn(n,1));

b(2150:2170) = c(2150:2170);
scatter(a,b,".")
xlim([1900,2200])
xlabel("Observation")
hold on
scatter(a(2150:2170),b(2150:2170),"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 one-class SVM model to the first 1000 shingled observations, specifying a contamination fraction of zero. Convert it to an incrementalOneClassSVM model object.

Mdl = ocsvm(X(1:1000,:),ContaminationFraction=0);
IncrementalMdl = incrementalLearner(Mdl);

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(0,"twister"); % 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(1:5000),allscores,".")
hold on
scatter(a(anomIdx),allscores(anomIdx),20,"or")
xlim([1900,2200])
xlabel("Shingle")
ylabel("Score")
hold off

Because the introduced anomalous region begins at observation 2150, and the shingle size is 100, shingle 2051 is the first one to show a high anomaly score. Some shingles between 2050 and 2170 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 that the software returned as anomalous.

figure
xlim([1900,2200])
ylim([-1.5 2])
rectangle(Position=[2150 -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 Anomaly Detection with Categorical Predictor Data

Train a one-class SVM model and perform anomaly detection on a data set with categorical predictors.

Load Data

Load the 1994 census data stored in census1994.mat. The data set consists of demographic data from the US Census Bureau.

load census1994.mat

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

adultdata = rmmissing(adultdata);
adulttest = rmmissing(adulttest);

The census data set contains nine categorical variables. Because the fit function of incrementalOneClassSVM does not support categorical variables, you need to convert them to dummy variables. Remove all of the noncategorical variables, and remove the categorical variables that have more than 10 unique categories. Convert the remaining categorical variables to dummy variables using onehotencode.

adultdata = removevars(adultdata,["age","fnlwgt","capital_gain", ...
    "capital_loss","hours_per_week","occupation","education", ...
    "education_num","native_country"]);
adulttest = removevars(adulttest,["age","fnlwgt","capital_gain", ...
    "capital_loss","hours_per_week","occupation","education", ...
    "education_num","native_country"]);
Xtrain = table();
Xstream = table();
for i=1:width(adultdata)
    Xtrain = [Xtrain onehotencode(adultdata(:,i))];
    Xstream = [Xstream onehotencode(adulttest(:,i))];
end

Train One-Class SVM Model

Fit a one-class SVM model to the training data. Specify a random stream for reproducibility, and an anomaly contamination fraction of 0.001. Set KernelScale to "auto" so that the software selects an appropriate kernel scale parameter using a heuristic procedure.

rng(0,"twister"); % For reproducibility
TTMdl = ocsvm(Xtrain,ContaminationFraction=0.001, ...
    KernelScale="auto",RandomStream=RandStream("mlfg6331_64"))

TTMdl = 
  OneClassSVM

    CategoricalPredictors: []
    ContaminationFraction: 1.0000e-03
           ScoreThreshold: -0.6840
           PredictorNames: {1x30 cell}
              KernelScale: 2.4495
                   Lambda: 0.0727

TTMdl is a OneClassSVM model object representing a traditionally trained one-class SVM model.

Convert Trained Model

Convert the traditionally trained one-class SVM model to a one-class SVM model for incremental learning.

IncrementalMdl = incrementalLearner(TTMdl);

IncrementalMdl is an incrementalOneClassSVM 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;    
    [IncrementalMdl,tf,scores] = fit(IncrementalMdl,Xstream(idx,:));
    medianscore(j) = median(scores);
    numAnom(j) = sum(tf);
    threshold(j) = IncrementalMdl.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 = 11

anomfrac= totalanomalies/n

anomfrac = 7.3041e-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 negative score value with large magnitude indicates a normal observation, and a large positive value indicates an anomaly. The median score fluctuates between approximately $$-$$58 and $$-$$55. After the 10th iteration, the score threshold fluctuates between $$-$$28 and $$-$$21. The software detects 11 anomalies in the Xstream data, yielding a total contamination fraction of approximately 0.0007.

Input Arguments

Mdl — Incremental anomaly detection model

incrementalOneClassSVM model object

Incremental anomaly detection model to fit to streaming data, specified as an incrementalOneClassSVM model object. You can create Mdl by calling incrementalOneClassSVM directly, or by converting a traditionally trained OneClassSVM 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 Mdl 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 at least one missing value (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.

• Incremental learning functions support only numeric input predictor data. You must prepare an encoded version of categorical data to use incremental learning functions. Use dummyvar to convert each categorical variable to a dummy variable. For more details, see Dummy Variables.

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 Mdl 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 columns in the training data.

Note

• If an observation contains at least one missing (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.

• Incremental learning functions support only numeric input predictor data. You must prepare an encoded version of categorical data to use incremental learning functions. Use dummyvar to convert each categorical variable to a numeric matrix of dummy variables. Then, concatenate all dummy variable matrices and any other numeric predictors, in the same way that the training function encodes categorical data. For more details, see Dummy Variables.

Data Types: single | double

Output Arguments

Mdl — Updated one-class SVM model for incremental anomaly detection

incrementalOneClassSVM model object

Updated one-class SVM model for incremental anomaly detection, returned as an incrementalOneClassSVM 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 Mdl and then detects 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 with at least one missing value.

Data Types: logical

scores — Anomaly scores

numeric column vector

Anomaly scores, returned as a numeric column vector whose values are in the range (–Inf,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 Mdl. A negative score value with large magnitude 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 with at least one missing value.

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.

Version History

Introduced in R2023b