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isoutlier

Find outliers in data

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Syntax

TF = isoutlier(A)
TF = isoutlier(A,method)
TF = isoutlier(A,'percentiles',threshold)
TF = isoutlier(A,movmethod,window)
TF = isoutlier(___,dim)
TF = isoutlier(___,Name,Value)
[TF,L,U,C] = isoutlier(___)

Description

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TF= isoutlier(A)returns a logical array whose elements aretruewhen an outlier is detected in the corresponding element ofA。By default, an outlier is a value that is more than three scaled我dian absolute deviations (MAD)away from the median. IfAis a matrix or table, thenisoutlieroperates on each column separately. IfAis a multidimensional array, thenisoutlieroperates along the first dimension whose size does not equal 1.

example

TF= isoutlier(A,我thod)specifies a method for detecting outliers. For example,isoutlier(A,'mean')returnstruefor all elements more than three standard deviations from the mean.

TF= isoutlier(A,'percentiles',threshold)defines outliers as points outside of the percentiles specified inthreshold。Thethresholdargument is a two-element row vector containing the lower and upper percentile thresholds, such as[10 90]。

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TF= isoutlier(A,movmethod,window)specifies a moving method for detecting local outliers according to a window length defined bywindow。For example,isoutlier(A,'movmedian',5)returnstruefor all elements more than three local scaled MAD from the local median within a sliding window containing five elements.

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TF= isoutlier(___,dim)operates along dimensiondimofAfor any of the previous syntaxes. For example,isoutlier(A,2)operates on each row of a matrixA。

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TF= isoutlier(___,Name,Value)specifies additional parameters for detecting outliers using one or more name-value pair arguments. For example,isoutlier(A,'SamplePoints',t)detects outliers inArelative to the corresponding elements of a time vectort。

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[TF,L,U,C] = isoutlier(___)also returns the lower and upper thresholds and the center value used by the outlier detection method.

Examples

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Open Live Script

Find the outliers in a vector of data. A logical 1 in the output indicates the location of an outlier.

A = [57 59 60 100 59 58 57 58 300 61 62 60 62 58 57]; TF = isoutlier(A)
TF =1x15 logical array0 0 0 1 0 0 0 0 1 0 0 0 0 0 0
Open Live Script

Define outliers as points more than three standard deviations from the mean, and find the locations of outliers in a vector.

A = [57 59 60 100 59 58 57 58 300 61 62 60 62 58 57]; TF = isoutlier(A,'mean')
TF =1x15 logical array0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
Open Live Script

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 inA。

t = datetime(2017,1,1,0,0,0) + hours(0:length(x)-1);

Define outliers as points more than three local scaled MAD away from the local median within a sliding window. Find the locations of the outliers inArelative to the points intwith a window size of 5 hours. Plot the data and detected outliers.

TF = isoutlier(A,'movmedian',hours(5),'SamplePoints',t); plot(t,A,t(TF),A(TF),'x') legend('Data','Outlier')

Figure contains an axes object. The axes object contains 2 objects of type line. These objects represent Data, Outlier.

Open Live Script

Find outliers for each row of a matrix.

Create a matrix of data containing outliers along the diagonal.

A = magic(5) + diag(200*ones(1,5))
A =5×5217 24 1 8 15 23 205 7 14 16 4 6 213 20 22 10 12 19 221 3 11 18 25 2 209

Find the locations of outliers based on the data in each row.

TF = isoutlier(A,2)
TF =5x5 logical array1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
Open Live Script

Create a vector of data containing an outlier. Find and plot the location of the outlier, and the thresholds and center value determined by the outlier 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.

x = 1:10; A = [60 59 49 49 58 100 61 57 48 58]; [TF,L,U,C] = isoutlier(A); plot(x,A,x(TF),A(TF),'x',x,L*ones(1,10),x,U*ones(1,10),x,C*ones(1,10)) legend('Original Data','Outlier','Lower Threshold','Upper Threshold','Center Value')

Figure contains an axes object. The axes object contains 5 objects of type line. These objects represent Original Data, Outlier, Lower Threshold, Upper Threshold, Center Value.

Input Arguments

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Input data, specified as a vector, matrix, multidimensional array, table, or timetable.

IfAis a table, then its variables must be of typedoubleorsingle, or you can use the'DataVariables'name-value pair to listdoubleorsinglevariables explicitly. Specifying variables is useful when you are working with a table that contains variables with data types other thandoubleorsingle。

IfAis a timetable, thenisoutlieroperates only on the table elements. Row times must be unique and listed in ascending order.

Data Types:double|single|table|timetable

Method for detecting outliers, specified as one of the following:

Method Description
'median' Returnstruefor elements more than three scaled MAD from the median. The scaled MAD is defined asc*median(abs(A-median(A))), wherec=-1/(sqrt(2)*erfcinv(3/2))。
'mean' Returnstruefor elements more than three standard deviations from the mean. This method is faster but less robust than'median'。
'quartiles' Returnstruefor elements more than 1.5 interquartile ranges above the upper quartile or below the lower quartile. This method is useful when the data inAis not normally distributed.
'grubbs' Applies Grubbs’s test for outliers, which removes one outlier per iteration based on hypothesis testing. This method assumes that the data inAis normally distributed.
'gesd' Applies 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.

Percentile thresholds, specified as a two-element 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. For example, a threshold of[10 90]defines outliers as points below the 10th percentile and above the 90th percentile. The first element ofthresholdmust be less than the second element.

Moving method for detecting outliers, specified as one of the following:

Method Description
'movmedian' Returnstruefor elements more than three local scaled MAD from the local median over a window length specified bywindow。This method is also known as aHampel filter。
'movmean' Returnstruefor elements more than three local standard deviations from the local mean over a window length specified bywindow。

Window length, specified as a positive integer scalar, a two-element vector of positive integers, a positive duration scalar, or a two-element vector of positive durations.

Whenwindowis a positive integer scalar, the window is centered about the current element and containswindow-1neighboring elements. Ifwindowis even, then the window is centered about the current and previous elements.

Whenwindowis a two-element vector of positive integers[b f], the window contains the current element,belements backward, andfelements forward.

WhenAis a timetable or'SamplePoints'is specified as adatetimeordurationvector, thenwindowmust be of typeduration, and the windows are computed relative to the sample points.

Data Types:double|single|int8|int16|int32|int64|uint8|uint16|uint32|uint64|duration

Dimension to operate along, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 1.

Consider a matrixA。

isoutlier(A,1)detects outliers based on the data in each column ofA。

isoutlier(A,2)detects outliers based on the data in each row ofA。

WhenAis a table or timetable,dimis not supported.isoutlieroperates along each table or timetable variable separately.

Data Types:double|single|int8|int16|int32|int64|uint8|uint16|uint32|uint64

Name-Value Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Namemust appear inside quotes. You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN。

Example:isoutlier(A,'mean','ThresholdFactor',4)
Data Options

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Sample points, specified as the comma-separated pair consisting of'SamplePoints'and 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 thex-axis 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 the following options.

Option for Table Input Description Examples
Variable name

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

'Var1'

"Var1"
Scalar variable index

A scalar table variable index

3
Logical vector

A logical vector whose elements each correspond to a table variable, wheretruespecifies the corresponding variable as the sample points, and all other elements arefalse

[true false false]
Function handle

A function handle that takes a table variable as input and returns a logical scalar, which must betruefor only one table variable

@isnumeric
vartypesubscript

A table subscript generated by thevartypefunction that returns a subscript for only one variable

vartype('numeric')

Note

This name-value pair is not supported when the input data is atimetable。Timetables always 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, iftis a vector of times corresponding to the input data, thenisoutlier(rand(1,10),'movmean',3,'SamplePoints',t)has a window that represents the time interval betweent(i)-1.5andt(i)+1.5。

When the sample points vector has data typedatetimeorduration, then the moving window length must have typeduration。

Example:isoutlier(A,'SamplePoints',0:0.1:10)

Example:isoutlier(T,'SamplePoints',"Var1")

Data Types:single|double|datetime|duration

Table variables to operate on, specified as the comma-separated pair consisting of'DataVariables'and 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 bedoubleorsingle。没有指定表中的其他变量'DataVariables'are not operated on, so the output containsfalsevalues for those variables.

Option Description Examples
Variable name

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

'Var1'

"Var1"
Vector of variable names

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

{'Var1' 'Var2'}

["Var1" "Var2"]
Scalar or vector of variable indices

A scalar or vector of table variable indices

1

[1 3 5]
Logical vector

A logical vector whose elements each correspond to a table variable, wheretrueincludes the corresponding variable andfalseexcludes it

[true false true]
Function handle

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

@isnumeric
vartypesubscript

A table subscript generated by thevartypefunction

vartype('numeric')

Example:isoutlier(T,'DataVariables',["Var1" "Var2" "Var4"])

Outlier Detection Options

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Detection threshold factor, specified as the comma-separated pair consisting of'ThresholdFactor'and 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'检测阈值的因素是一个标量让依ng 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'方法,检测阈值因子代替the number of interquartile ranges, which is 1.5 by default.

This name-value pair is not supported when the specified method is'percentiles'。

Data Types:double|single|int8|int16|int32|int64|uint8|uint16|uint32|uint64

Maximum outlier count, for the'gesd'我thod only, specified as the comma-separated pair consisting of'MaxNumOutliers'and a positive integer. The'MaxNumOutliers'value specifies the maximum number of outliers returned by the'gesd'我thod. For example,isoutlier(A,'gesd','MaxNumOutliers',5)returns no more than five outliers.

The default value for'MaxNumOutliers'is the integer nearest to 10 percent of the number of elements inA。Setting a larger value for the maximum number of outliers can ensure that all outliers are detected, but at the cost of reduced computational efficiency.

The'gesd'我thod assumes the non-outlier input data is sampled from an approximate normal distribution. When the data is not sampled in this way, the number of returned outliers might exceed the'MaxNumOutliers'value.

Data Types:double|single|int8|int16|int32|int64|uint8|uint16|uint32|uint64

Output Arguments

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Outlier indicator, returned as a vector, matrix, or multidimensional array. An element ofTFistruewhen the corresponding element ofAis an outlier andfalseotherwise.TFis the same size asA。

Data Types:logical

Lower threshold used by the outlier detection method, returned as a scalar, vector, matrix, multidimensional array, table, or timetable. For example, the lower value of the default outlier detection method is three scaled MAD below the median of the input data.Lhas the same size asAin all dimensions except for the operating dimension where the length is 1.

Data Types:double|single|table|timetable

Upper threshold used by the outlier detection method, returned as a scalar, vector, matrix, multidimensional array, table, or timetable. For example, the upper value of the default outlier detection method is three scaled MAD above the median of the input data.Uhas the same size asAin all dimensions except for the operating dimension where the length is 1.

Data Types:double|single|table|timetable

Center value used by the outlier detection method, returned as a scalar, vector, matrix, multidimensional array, table, or timetable. For example, the center value of the default outlier detection method is the median of the input data.Chas the same size asAin all dimensions except for the operating dimension where the length is 1.

Data Types:double|single|table|timetable

More About

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Median Absolute Deviation

For a random variable vectorAmade up ofNscalar observations, the median absolute deviation (MAD) is defined as

MAD = median ( | A i − 我dian ( A ) | )

fori = 1,2,...,N。

The scaled MAD is defined asc*median(abs(A-median(A)))wherec=-1/(sqrt(2)*erfcinv(3/2))。

Extended Capabilities

See Also

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Topics

Introduced in R2017a

MATLAB Documentation

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Introducing Deep Learning with MATLAB

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