rrcforest
Syntax
Description
Use the rrcforest
function to fit a robust random cut forest model for outlier detection and novelty
detection.
Outlier detection (detecting anomalies in training data) — Use the output argument
tf
ofrrcforest
to identify anomalies in training data.Novelty detection (detecting anomalies in new data with uncontaminated training data) — Create a
RobustRandomCutForest
model object by passing uncontaminated training data (data with no outliers) torrcforest
. Detect anomalies in new data by passing the object and the new data to the object functionisanomaly
.
returns a forest
= rrcforest(Tbl
)RobustRandomCutForest
model object for the predictor data in the table
Tbl
.
specifies options using one or more name-value arguments in addition to any of the input
argument combinations in the previous syntaxes. For example, specify
forest
= rrcforest(___,Name=Value
)
to process 10% of the
training data as anomalies.ContaminationFraction
=0.1
Examples
Detect Outliers
Detect outliers (anomalies in training data) by using the rrcforest
function.
Load the sample data set NYCHousing2015
.
load NYCHousing2015
The data set includes 10 variables with information on the sales of properties in New York City in 2015. Display a summary of the data set.
summary(NYCHousing2015)
NYCHousing2015: 91446x10 table Variables: BOROUGH: double NEIGHBORHOOD: cell array of character vectors BUILDINGCLASSCATEGORY: cell array of character vectors RESIDENTIALUNITS: double COMMERCIALUNITS: double LANDSQUAREFEET: double GROSSSQUAREFEET: double YEARBUILT: double SALEPRICE: double SALEDATE: datetime Statistics for applicable variables: NumMissing Min Median Max Mean Std BOROUGH 0 1 3 5 2.8431 1.3343 NEIGHBORHOOD 0 BUILDINGCLASSCATEGORY 0 RESIDENTIALUNITS 0 0 1 8759 2.1789 32.2738 COMMERCIALUNITS 0 0 0 612 0.2201 3.2991 LANDSQUAREFEET 0 0 1700 29305534 2.8752e+03 1.0118e+05 GROSSSQUAREFEET 0 0 1056 8942176 4.6598e+03 4.3098e+04 YEARBUILT 0 0 1939 2016 1.7951e+03 526.9998 SALEPRICE 0 0 333333 4.1111e+09 1.2364e+06 2.0130e+07 SALEDATE 0 01-Jan-2015 09-Jul-2015 31-Dec-2015 07-Jul-2015 2470:47:17
The SALEDATE
column is a datetime
array, which is not supported by rrcforest
. Create columns for the month and day numbers of the datetime
values, and then delete the SALEDATE
column.
[~,NYCHousing2015.MM,NYCHousing2015.DD] = ymd(NYCHousing2015.SALEDATE); NYCHousing2015.SALEDATE = [];
The columns BOROUGH
, NEIGHBORHOOD
, and BUILDINGCLASSCATEGORY
contain categorical predictors. Display the number of categories for the categorical predictors.
length(unique(NYCHousing2015.BOROUGH))
ans = 5
length(unique(NYCHousing2015.NEIGHBORHOOD))
ans = 254
length(unique(NYCHousing2015.BUILDINGCLASSCATEGORY))
ans = 48
For a categorical variable with more than 64 categories, the rrcforest
function uses an approximate splitting method that can reduce the accuracy of the robust random cut forest model. Remove the NEIGHBORHOOD
column, which contains a categorical variable with 254 categories.
NYCHousing2015.NEIGHBORHOOD = [];
Train a robust random cut forest model for NYCHousing2015
. Specify the fraction of anomalies in the training observations as 0.1, and specify the first variable (BOROUGH
) as a categorical predictor. The first variable is a numeric array, so rrcforest
assumes it is a continuous variable unless you specify the variable as a categorical variable.
rng("default") % For reproducibility [Mdl,tf,scores] = rrcforest(NYCHousing2015, ... ContaminationFraction=0.1,CategoricalPredictors=1);
Mdl
is a RobustRandomCutForest
model object. rrcforest
also returns the anomaly indicators (tf
) and anomaly scores (scores
) for the training data NYCHousing2015
.
Plot a histogram of the score values. Create a vertical line at the score threshold corresponding to the specified fraction.
histogram(scores) xline(Mdl.ScoreThreshold,"r-",["Threshold" Mdl.ScoreThreshold])
If you want to identify anomalies with a different contamination fraction (for example, 0.01), you can train a new robust random cut forest model.
rng("default") % For reproducibility [newMdl,newtf,scores] = rrcforest(NYCHousing2015, ... ContaminationFraction=0.01,CategoricalPredictors=1);
If you want to identify anomalies with a different score threshold value (for example, 65), you can pass the RobustRandomCutForest
model object, the training data, and a new threshold value to the isanomaly
function.
[newtf,scores] = isanomaly(Mdl,NYCHousing2015,ScoreThreshold=65);
Note that changing the contamination fraction or score threshold changes the anomaly indicators only, and does not affect the anomaly scores. Therefore, if you do not want to compute the anomaly scores again by using rrcforest
or isanomaly
, you can obtain a new anomaly indicator using the existing score values.
Change the fraction of anomalies in the training data to 0.01
.
newContaminationFraction = 0.01;
Find a new score threshold by using the quantile
function.
newScoreThreshold = quantile(scores,1-newContaminationFraction)
newScoreThreshold = 63.2642
Obtain a new anomaly indicator.
newtf = scores > newScoreThreshold;
Detect Novelties
Create a RobustRandomCutForest
model object for uncontaminated training observations by using the rrcforest
function. Then detect novelties (anomalies in new data) by passing the object and the new data to the object function isanomaly
.
Load the 1994 census data stored in census1994.mat
. The data set contains demographic data from the US Census Bureau to predict whether an individual makes over $50,000 per year.
load census1994
census1994
contains the training data set adultdata
and the test data set adulttest
.
Assume that adultdata
does not contain outliers. Train a robust random cut forest model for adultdata
. Specify StandardizeData
as true
to standardize the input data.
rng("default") % For reproducibility [Mdl,tf,s] = rrcforest(adultdata,StandardizeData=true);
Mdl
is a RobustRandomCutForest
model object. rrcforest
also returns the anomaly indicators tf
and anomaly scores s
for the training data adultdata
. If you do not specify the ContaminationFraction
name-value argument as a value greater than 0, then rrcforest
treats all training observations as normal observations, meaning all the values in tf
are logical 0 (false
). The function sets the score threshold to the maximum score value. Display the threshold value.
Mdl.ScoreThreshold
ans = 86.5315
Find anomalies in adulttest
by using the trained robust random cut forest model. Because you specified StandardizeData=true
when you trained the model, the isanomaly
function standardizes the input data by using the predictor means and standard deviations of the training data stored in the Mu
and Sigma
properties, respectively.
[tf_test,s_test] = isanomaly(Mdl,adulttest);
The isanomaly
function returns the anomaly indicators tf_test
and scores s_test
for adulttest
. By default, isanomaly
identifies observations with scores above the threshold (Mdl.ScoreThreshold
) as anomalies.
Create histograms for the anomaly scores s
and s_test
. Create a vertical line at the threshold of the anomaly scores.
histogram(s,Normalization="probability") hold on histogram(s_test,Normalization="probability") xline(Mdl.ScoreThreshold,"r-",join(["Threshold" Mdl.ScoreThreshold])) legend("Training Data","Test Data",Location="northwest") hold off
Display the observation index of the anomalies in the test data.
find(tf_test)
ans = 3541
The anomaly score distribution of the test data is similar to that of the training data, so isanomaly
detects a small number of anomalies in the test data with the default threshold value.
Zoom in to see the anomaly and the observations near the threshold.
xlim([50 92]) ylim([0 0.001])
You can specify a different threshold value by using the ScoreThreshold
name-value argument. For an example, see Specify Anomaly Score Threshold.
Input Arguments
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.
To use a subset of the variables in Tbl
, specify the variables by using the PredictorNames
name-value argument.
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.
You can use the PredictorNames
name-value argument to assign names to the predictor variables in X
.
Data Types: single
| double
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: NumLearners=50,NumObservationsPerLearner=100
specifies to
train a robust random cut forest model using 50 trees and 100 observations for each
tree.
CategoricalPredictors
— List of categorical predictors
vector of positive integers | logical vector | character matrix | string array | cell array of character vectors | "all"
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 If |
Logical vector | A |
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. |
By default, if the predictor data is a table
(Tbl
), rrcforest
assumes that a variable is
categorical if it is a logical vector, unordered categorical vector, character array, string
array, or cell array of character vectors. If the predictor data is a matrix
(X
), rrcforest
assumes that all predictors are
continuous. To identify any other predictors as categorical predictors, specify them by using
the CategoricalPredictors
name-value argument.
For a categorical variable with more than 64 categories, the
rrcforest
function uses an approximate splitting method that can
reduce the accuracy of the model.
Example: CategoricalPredictors="all"
Data Types: single
| double
| logical
| char
| string
| cell
CollusiveDisplacement
— Collusive displacement calculation method
"maximal"
(default) | "average"
Collusive displacement calculation method, specified as
"maximal"
or "average"
.
The rrcforest
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. For details, see Anomaly Scores.
Example: CollusiveDisplacement="average"
Data Types: char
| string
ContaminationFraction
— Fraction of anomalies in training data
0 (default) | numeric scalar in the range [0,1]
Fraction of anomalies in the training data, specified as a numeric scalar in the range [0,1].
If the
ContaminationFraction
value is 0 (default), thenrrcforest
treats all training observations as normal observations, and sets the score threshold (ScoreThreshold
property value offorest
) to the maximum value ofscores
.If the
ContaminationFraction
value is in the range (0,1], thenrrcforest
determines the threshold value so that the function detects the specified fraction of training observations as anomalies.
Example: ContaminationFraction=0.1
Data Types: single
| double
NumLearners
— Number of robust random cut trees
100 (default) | positive integer scalar
Number of robust random cut trees (trees in the robust random cut forest model), specified as a positive integer scalar.
Example: NumLearners=50
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
Number of observations to draw from the training data without replacement for each robust random cut tree (tree in the robust random cut forest model), specified as a positive integer scalar greater than or equal to 3.
Example: NumObservationsPerLearner=100
Data Types: single
| double
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 usePredictorNames
to specify which predictor variables to use. That is,rrcforest
uses only the predictor variables inPredictorNames
.PredictorNames
must be a subset ofTbl.Properties.VariableNames
.By default,
PredictorNames
contains the names of all predictor variables inTbl
.
If you supply
X
, then you can usePredictorNames
to assign names to the predictor variables inX
.The order of the names in
PredictorNames
must correspond to the column order ofX
. That is,PredictorNames{1}
is the name ofX(:,1)
,PredictorNames{2}
is the name ofX(:,2)
, and so on. Also,size(X,2)
andnumel(PredictorNames)
must be equal.By default,
PredictorNames
is{"x1","x2",...}
.
Data Types: string
| cell
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 rrcforest
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
UseParallel
— Flag to run in parallel
false
or 0
(default) | true
or 1
Flag to run in parallel, specified as a numeric or logical 1
(true
) or 0 (false
). If you specify
UseParallel=true
, the rrcforest
function executes
for
-loop iterations by using parfor
. The loop runs in parallel when you have Parallel Computing Toolbox™.
Example: UseParallel=true
Data Types: logical
Output Arguments
forest
— Trained robust random cut forest model
RobustRandomCutForest
model object
Trained robust random cut forest model, returned as a RobustRandomCutForest
model object.
You can use the object function isanomaly
with forest
to find anomalies in new data.
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
.
rrcforest
identifies observations with
scores
above the threshold (ScoreThreshold
property value of forest
) as
anomalies. The function determines the threshold value to detect the specified fraction
(ContaminationFraction
name-value argument) of training
observations as anomalies.
scores
— Anomaly scores
numeric column vector in the range [0,Inf
)
Anomaly scores, returned as a numeric column vector with values 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
. A small
positive value indicates a normal observation, and a large positive value indicates an
anomaly.
More About
Robust Random Cut Forest
The robust random cut forest algorithm [1] classifies a point as a normal point or an anomaly based on the change in model complexity introduced by the point. Similar to the Isolation Forest algorithm, the robust random cut forest algorithm builds an ensemble of trees. The two algorithms differ in how they choose a split variable in the trees and how they define anomaly scores.
The rrcforest
function creates a robust random cut forest model (ensemble
of robust random cut trees) for training observations and detects outliers (anomalies in the
training data). Each tree is trained for a subset of training observations as follows:
rrcforest
draws samples without replacement from the training observations for each tree.rrcforest
grows a tree by choosing a split variable in proportion to the ranges of variables, and choosing the split position uniformly at random. The function continues until every sample reaches a separate leaf node for each tree.
Using the range information in to choose a split variable makes the algorithm robust to irrelevant variables.
Anomalies are easy to describe, but make describing the remainder of the data more
difficult. Therefore, adding an anomaly to a model increases the model complexity of a
forest model [1]. The rrcforest
function identifies outliers using anomaly scores that are defined
based on the change in model complexity.
The isanomaly
function uses a trained robust random cut forest model to
detect anomalies in the data. For novelty detection (detecting anomalies in new data with
uncontaminated training data), you can train a robust random cut forest model with
uncontaminated training data (data with no outliers) and use it to detect anomalies in new
data. For each observation of the new data, the function finds the corresponding leaf node
in each tree, computes the change in model complexity introduced by the leaf nodes, and
returns an anomaly indicator and score.
Anomaly Scores
The robust random cut forest algorithm uses collusive displacement as an anomaly score. The collusive displacement of a point x indicates the contribution of x to the model complexity of a forest model. A small positive anomaly score value indicates a normal observation, and a large positive value indicates an anomaly.
As defined in [1], the model complexity |M(T)| of a tree T is the sum of path lengths (the distance from the root node to the leaf nodes) over all points in the training data Z.
where f(y,Z,T) is the depth of y in tree T. The displacement of x is defined to indicate the expected changes in the model complexity introduced by x.
where T' is a tree over Z – {x}. Disp
(x,Z) is the expected number of points in the sibling node of the leaf node
containing x. This definition is not robust to duplicates or
near-duplicates, and can cause outlier masking. To avoid outlier masking, the robust random
cut forest algorithm uses the collusive displacement CoDisp
, where a set
C includes x and the colluders of
x.
where T" is a tree over Z – C, and |C| is the number of points in the subtree of T for C.
The default value for the CollusiveDisplacement
name-value argument of rrcforest
is "maximal"
. For each tree, by default, the software finds the set
C that maximizes the ratio Disp
(x,C)/|C| by traversing from the leaf node of x to the root node,
as described in [2]. If you specify
, the
software computes the average of the ratios for each tree, and uses the averaged values to
compute the collusive displacement value.CollusiveDisplacement
="average"
Algorithms
rrcforest
considers NaN
, ''
(empty character vector), ""
(empty string), <missing>
, and <undefined>
values in Tbl
and NaN
values in X
to be missing values.
rrcforest
uses observations with missing values to find splits on
variables for which these observations have valid values. The function might place these
observations in a branch node, not a leaf node. Then rrcforest
computes the ratio (Disp
(x,C)/|C|) by traversing from the branch node to the root node for each tree. The
function places an observation with all missing values in the root node. Therefore, the
ratio and the anomaly score become the number of training observations for each tree, which
is the maximum possible anomaly score for the trained robust random cut forest model. You
can specify the number of training observations for each tree by using the NumObservationsPerLearner
name-value argument.
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, set the UseParallel
name-value argument to
true
in the call to this function.
For more general information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).
Version History
Introduced in R2023a
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