rmoutliers
Detect and remove outliers in data
Syntax
Description
detects and removes outliers from the data in B
= rmoutliers(A
)A
.
If
A
is a matrix, thenrmoutliers
detects outliers in each column ofA
separately and removes the entire row.If
A
is a table or timetable, thenrmoutliers
detects outliers in each variable ofA
separately and removes the entire row.
By default, an outlier is a value that is more than three scaled median absolute deviations (MAD) from the median.
specifies additional parameters for detecting and removing outliers using one or more
namevalue arguments. For example, B
= rmoutliers(___,Name,Value
)rmoutliers(A,"SamplePoints",t)
detects outliers in A
relative to the corresponding elements of a time
vector t
.
Examples
Remove Outliers from Vector
Create a vector containing two outliers and remove them.
A = [57 59 60 100 59 58 57 58 300 61 62 60 62 58 57]; B = rmoutliers(A)
B = 1×13
57 59 60 59 58 57 58 61 62 60 62 58 57
Use Mean Detection Method
Identify potential outliers in a timetable of data using the mean detection method, remove any outliers, and visualize the cleaned data.
Create a timetable of data, and visualize the data to detect potential outliers.
T = hours(1:15); V = [57 59 60 100 59 58 57 58 300 61 62 60 62 58 57]; A = timetable(T',V'); plot(A.Time,A.Var1)
Remove outliers in the data, where an outlier is defined as a point more than three standard deviations from the mean.
B = rmoutliers(A,"mean")
B=14×1 timetable
Time Var1
_____ ____
1 hr 57
2 hr 59
3 hr 60
4 hr 100
5 hr 59
6 hr 58
7 hr 57
8 hr 58
10 hr 61
11 hr 62
12 hr 60
13 hr 62
14 hr 58
15 hr 57
In the same graph, plot the original data and the data with the outlier removed.
hold on plot(B.Time,B.Var1,"o") legend("Original Data","Cleaned Data")
Use Moving Detection Method
Use a moving median to detect and remove local outliers from a sine wave that corresponds to a time vector.
Create a vector of data containing a local outlier.
x = 2*pi:0.1:2*pi; A = sin(x); A(47) = 0;
Create a time vector that corresponds to the data in A
.
t = datetime(2017,1,1,0,0,0) + hours(0:length(x)1);
Define outliers as points more than three local scaled MAD from the local median within a sliding window. Find the locations of the outliers in A
relative to the points in t
with a window size of 5 hours, and remove them.
[B,TFrm] = rmoutliers(A,"movmedian",hours(5),"SamplePoints",t);
Plot the original data and the data with the outlier removed.
plot(t,A) hold on plot(t(~TFrm),B,"o") legend("Original Data","Cleaned Data")
Remove Columns Containing Outliers
Remove the outliers from a matrix of data, and examine the removed columns and outliers.
Create a matrix containing two outliers.
A = magic(5); A(4,4) = 200; A(5,5) = 300; A
A = 5×5
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 200 3
11 18 25 2 300
Remove the columns containing outliers by specifying the dimension for removal as 2. Return a logical output vector TFrm
to identify which columns of A
were removed, and return a logical output array TFoutlier
to identify the locations of the outliers in A
.
[B,TFrm,TFoutlier] = rmoutliers(A,2)
B = 5×3
17 24 1
23 5 7
4 6 13
10 12 19
11 18 25
TFrm = 1x5 logical array
0 0 0 1 1
TFoutlier = 5x5 logical array
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 1 0
0 0 0 0 1
Find the values in the removed columns of A
.
rmCol = A(:,TFrm)
rmCol = 5×2
8 15
14 16
20 22
200 3
2 300
Find the values of the outliers in A
.
rmVal = A(TFoutlier)
rmVal = 2×1
200
300
Specify Outlier Locations
Create a vector containing two outliers and detect their locations.
A = [57 59 60 100 59 58 57 58 300 61 62 60 62 58 57]; detect = isoutlier(A)
detect = 1x15 logical array
0 0 0 1 0 0 0 0 1 0 0 0 0 0 0
Remove the outliers. Instead of using a detection method, provide the outlier locations detected by isoutlier
.
B = rmoutliers(A,"OutlierLocations",detect)
B = 1×13
57 59 60 59 58 57 58 61 62 60 62 58 57
Visualize Outlier Thresholds
Remove an outlier from a vector of data and visualize the cleaned data.
Create a vector of data containing an outlier.
A = [60 59 49 49 58 100 61 57 48 58];
Remove the outlier using the default detection method "median"
.
[B,TFrm,TFoutlier,L,U,C] = rmoutliers(A);
Plot the original data, the data with outliers removed, and the thresholds and center value determined by the detection method. The center value is the median of the data, and the upper and lower thresholds are three scaled MAD above and below the median.
plot(A) hold on plot(find(~TFrm),B,"o") yline([L U C],":",["Lower Threshold","Upper Threshold","Center Value"]) legend("Original Data","Cleaned Data")
Input Arguments
A
— Input data
vector  matrix  table  timetable
Input data, specified as a vector, matrix, table, or timetable.
If
A
is a table, then its variables must be of typedouble
orsingle
, or you can use theDataVariables
argument to listdouble
orsingle
variables explicitly. Specifying variables is useful when you are working with a table that contains variables with data types other thandouble
orsingle
.If
A
is a timetable, thenrmoutliers
operates only on the table elements. If row times are used as sample points, then they must be unique and listed in ascending order.
Data Types: double
 single
 table
 timetable
method
— Method for detecting outliers
"median"
(default)  "mean"
 "quartiles"
 "grubbs"
 "gesd"
Method for detecting outliers, specified as one of these values.
Method  Description 

"median"  Outliers are defined as elements more than three scaled MAD from the
median. The scaled MAD is defined as
c*median(abs(Amedian(A))) , where
c=1/(sqrt(2)*erfcinv(3/2)) . 
"mean"  Outliers are defined as elements more than three standard deviations from
the mean. This method is faster but less robust than
"median" . 
"quartiles"  Outliers are defined as elements more than 1.5 interquartile ranges above
the upper quartile (75 percent) or below the lower quartile (25 percent). This
method is useful when the data in A is not normally
distributed. 
"grubbs"  Outliers are detected using Grubbs’ test for outliers, which removes one
outlier per iteration based on hypothesis testing. This method assumes that
the data in A is normally distributed. 
"gesd"  Outliers are detected using the generalized extreme Studentized deviate
test for outliers. This iterative method is similar to
"grubbs" but can perform better when there are multiple
outliers masking each other. 
threshold
— Percentile thresholds
twoelement row vector
Percentile thresholds, specified as a twoelement row vector whose elements are in
the interval [0, 100]. The first element indicates the lower percentile threshold, and
the second element indicates the upper percentile threshold. The first element of
threshold
must be less than the second element.
For example, a threshold of [10 90]
defines outliers as points
below the 10th percentile and above the 90th percentile.
movmethod
— Moving method
"movmedian"
 "movmean"
Moving method for detecting outliers, specified as one of these values.
Method  Description 

"movmedian"  Outliers are defined as elements more than three local scaled MAD from
the local median over a window length specified by window .
This method is also known as a Hampel filter. 
"movmean"  Outliers are defined as elements more than three local standard
deviations from the local mean over a window length specified by
window . 
window
— Window length
positive integer scalar  twoelement vector of positive integers  positive duration scalar  twoelement vector of positive durations
Window length, specified as a positive integer scalar, a twoelement vector of positive integers, a positive duration scalar, or a twoelement vector of positive durations.
When window
is a positive integer scalar, the window is centered
about the current element and contains window1
neighboring elements.
If window
is even, then the window is centered about the current and
previous elements.
When window
is a twoelement vector of positive integers
[b f]
, the window contains the current element,
b
elements backward, and f
elements
forward.
When A
is a timetable or SamplePoints
is
specified as a datetime
or duration
vector,
window
must be of type duration
, and the windows
are computed relative to the sample points.
dim
— Dimension for removal
1 (default)  2
Dimension for removal, specified as 1 or 2. By default,
rmoutliers
removes each row with a detected outlier. To remove each
matrix column or table variable with a detected outlier, specify a dimension of
2.
NameValue Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Namevalue arguments must appear after other arguments, but the order of the
pairs does not matter.
Example: rmoutliers(A,ThresholdFactor=4)
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: rmoutliers(A,"ThresholdFactor",4)
SamplePoints
— Sample points
vector  table variable name  scalar  function handle  table vartype
subscript
Sample points, specified as either a vector of sample point values or one of the
options in the following table when the input data is a table. The sample points
represent the xaxis locations of the data, and must be sorted and
contain unique elements. Sample points do not need to be uniformly sampled. The vector
[1 2 3 ...]
is the default.
When the input data is a table, you can specify the sample points as a table variable using one of these options.
Option for Table Input  Description  Examples 

Variable name  A character vector or scalar string specifying a single table variable name 

Scalar variable index  A scalar table variable index 

Logical vector  A logical vector whose elements each correspond to a table variable, where


Function handle  A function handle that takes a table variable as input and returns a logical scalar,
which must be 

vartype subscript  A table subscript generated by the 

Note
This namevalue argument is not supported when the input data is a
timetable
. Timetables use the vector of row times as the sample
points. To use different sample points, you must edit the timetable so that the row times
contain the desired sample points.
Moving windows are defined relative to the sample points. For example, if
t
is a vector of times corresponding to the input data, then
rmoutliers(rand(1,10),"movmean",3,"SamplePoints",t)
has a window
that represents the time interval between t(i)1.5
and
t(i)+1.5
.
When the sample points vector has data type datetime
or
duration
, then the moving window length must have type
duration
.
Example: rmoutliers(A,"SamplePoints",0:0.1:10)
Example: rmoutliers(T,"SamplePoints","Var1")
Data Types: single
 double
 datetime
 duration
DataVariables
— Table variables to operate on
table variable name  scalar  vector  cell array  function handle  table vartype
subscript
Table variables to operate on, specified as one of the options in this table. The
DataVariables
value indicates which variables of the input table
to examine for outliers. The data type associated with the indicated variables must be
double
or single
.
Other variables in the table not specified by DataVariables
pass through to the output without being examined for outliers.
When operating on the rows of A
, rmoutliers
removes any row that has outliers in the columns corresponding to the variables
specified. When operating on the columns of A
,
rmoutliers
removes the specified variables from the table.
Option  Description  Examples 

Variable name  A character vector or string scalar specifying a single table variable name 

Vector of variable names  A cell array of character vectors or string array, where each element is a table variable name 

Scalar or vector of variable indices  A scalar or vector of table variable indices 

Logical vector  A logical vector whose elements each correspond to a table variable, where


Function handle  A function handle that takes a table variable as input and returns a logical scalar 

vartype subscript  A table subscript generated by the 

Example: rmoutliers(T,"DataVariables",["Var1" "Var2"
"Var4"])
ThresholdFactor
— Detection threshold factor
nonnegative scalar
Detection threshold factor, specified as a nonnegative scalar.
For methods "median"
and "movmedian"
, the
detection threshold factor replaces the number of scaled MAD, which is 3 by
default.
For methods "mean"
and "movmean"
, the
detection threshold factor replaces the number of standard deviations from the mean,
which is 3 by default.
For methods "grubbs"
and "gesd"
, the
detection threshold factor is a scalar ranging from 0 to 1. Values close to 0 result
in a smaller number of outliers, and values close to 1 result in a larger number of
outliers. The default detection threshold factor is 0.05.
For the "quartiles"
method, the detection threshold factor
replaces the number of interquartile ranges, which is 1.5 by default.
This namevalue pair is not supported when the specified method is
"percentiles"
.
OutlierLocations
— Known outlier indicator
vector  matrix
Known outlier indicator, specified as a logical vector or matrix of the same size
as A
. The known outlier indicator elements can be a numeric or
logical 1 (true
) to indicate an outlier in the corresponding
location of A
or 0 (false
) to indicate a
nonoutlier. When you specify OutlierLocations
,
rmoutliers
does not use an outlier detection method. Instead,
it uses the elements of the known outlier indicator to define outliers. The output
TFoutlier
contains the same logical vector or matrix.
You cannot specify the OutlierLocations
namevalue argument if
you specify method
.
Data Types: logical
MaxNumOutliers
— Maximum outliers detected by GESD
positive integer scalar
Maximum outliers detected by GESD, specified as a positive integer scalar. The
MaxNumOutliers
value specifies the maximum number of outliers
that are detected by the "gesd"
method. For example,
rmoutliers(A,"gesd","MaxNumOutliers",5)
detects no more than five
outliers.
The default value for MaxNumOutliers
is the integer nearest to
10 percent of the number of elements in A
. Setting a larger value
for the maximum number of outliers makes it more likely that all outliers are detected
but at the cost of reduced computational efficiency.
The "gesd"
method assumes the nonoutlier input data is sampled
from an approximate normal distribution. When the data is not sampled in this way, the
number of detected outliers might exceed the MaxNumOutliers
value.
MinNumOutliers
— Minimum outliers required for removal
1 (default)  positive integer scalar
Minimum outliers required for removal, specified as a positive integer scalar. The
MinNumOutliers
value specifies the minimum number of outliers
required to remove a row or column. For example,
rmoutliers(A,"MinNumOutliers",3)
removes a row of a matrix
A
when there are 3 or more outliers detected in that row.
Output Arguments
B
— Data with outliers removed
vector  matrix  table  timetable
Data with outliers removed, returned as a vector, matrix, table, or timetable. The
size of B
depends on the number of removed rows or columns.
TFrm
— Removed data indicator
vector
Removed data indicator, returned as a logical vector. Elements with a value of 1
(true
) correspond to rows or columns of A
that
were removed. Elements with a value of 0 (false
) correspond to
unchanged rows or columns. The orientation and size of TFrm
depend on
A
and the dimension of operation.
Data Types: logical
TFoutlier
— Outlier indicator
vector  matrix
Outlier indicator, returned as a logical vector or matrix. Elements with a value of
1 (true
) correspond to the location of outliers in
A
. Elements with a value of 0 (false
) correspond
to nonoutliers.
TFoutlier
is the same size as A
.
Data Types: logical
L
— Lower threshold
scalar  vector  matrix  table  timetable
Lower threshold used by the outlier detection method, returned as a scalar, vector, matrix, table, or timetable. For example, the lower threshold value of the default outlier detection method is three scaled MAD below the median of the input data.
If method
is used for outlier detection, then
L
has the same size as A
in all dimensions
except for the operating dimension where the length is 1. If
movmethod
is used, then L
has the same size as
A
.
U
— Upper threshold
scalar  vector  matrix  table  timetable
Upper threshold used by the outlier detection method, returned as a scalar, vector, matrix, table, or timetable. For example, the upper threshold value of the default outlier detection method is three scaled MAD above the median of the input data.
If method
is used for outlier detection, then
U
has the same size as A
in all dimensions
except for the operating dimension where the length is 1. If
movmethod
is used, then U
has the same size as
A
.
C
— Center value
scalar  vector  matrix  table  timetable
Center value used by the outlier detection method, returned as a scalar, vector, matrix, table, or timetable. For example, the center value of the default outlier detection method is the median of the input data.
If method
is used for outlier detection, then
C
has the same size as A
in all dimensions
except for the operating dimension where the length is 1. If
movmethod
is used, then C
has the same size as
A
.
Extended Capabilities
Tall Arrays
Calculate with arrays that have more rows than fit in memory.
Usage notes and limitations:
The
"percentiles"
,"grubbs"
, and"gesd"
methods are not supported.The
"movmedian"
and"movmean"
methods do not support tall timetables.The
SamplePoints
andMaxNumOutliers
namevalue arguments are not supported.The value of
DataVariables
cannot be a function handle.Computation of
rmoutliers(A)
,rmoutliers(A,"median",...)
, orrmoutliers(A,"quartiles",...)
along the first dimension is supported only whenA
is a tall column vector.rmoutliers(A,2)
is not supported for tall tables.
For more information, see Tall Arrays.
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Usage notes and limitations:
The
"movmean"
and"movmedian"
methods for detecting outliers do not support timetable input data, datetimeSamplePoints
values, or durationSamplePoints
values.For table input data,
dim
must equal1
.
ThreadBased Environment
Run code in the background using MATLAB® backgroundPool
or accelerate code with Parallel Computing Toolbox™ ThreadPool
.
This function fully supports threadbased environments. For more information, see Run MATLAB Functions in ThreadBased Environment.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Usage notes and limitations:
The
"movmedian"
moving method is not supported.The
SamplePoints
andDataVariables
namevalue arguments are not supported.
For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).
Version History
Introduced in R2018bR2022b: Return outlier indicator, lower threshold, upper threshold, and center value
You can optionally return a logical outlier indicator that corresponds to the locations of outliers in the input data. You can also return the lower threshold value, upper threshold value, and center value used by the outlier detection method.
R2022b: Define outlier locations
Define the location of outliers in the input data with a known outlier indicator. You
can define outlier locations, rather than using an outlier detection method, by setting the
OutlierLocations
namevalue argument to a logical array the same size
as the input data.
You cannot specify the OutlierLocations
namevalue argument if you
specify method
.
R2021b: Specify sample points as table variable
For table input data, specify the sample points as a table variable using the
SamplePoints
namevalue argument.
See Also
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