Univariate Outlier Detection
A univariate outlier is an occurrence of an abnormal value within a single observation point.
Details
Given a set 
of 
feature vectors
of dimension 
,
the problem is to identify the vectors that do not belong to the underlying distribution
(see [Ben2005] for exact definitions of an outlier).
of feature vectors
of dimension ,
the problem is to identify the vectors that do not belong to the underlying distribution
(see [Ben2005] for exact definitions of an outlier).The algorithm for univariate outlier detection considers each feature independently.
The univariate outlier detection method can be parametric, assumes a known underlying distribution for the data set,
and defines an outlier region such that if an observation belongs to the region, it is marked as an outlier.
Definition of the outlier region is connected to the assumed underlying data distribution.
The following is an example of an outlier region for the univariate outlier detection:
where 
and 
are (robust) estimates of the mean and standard deviation
computed for a given data set, 
is the confidence coefficient,
and 
defines the limits of the region and should be adjusted to the number of observations.
and are (robust) estimates of the mean and standard deviation
computed for a given data set, is the confidence coefficient,
and defines the limits of the region and should be adjusted to the number of observations.Batch Processing
Algorithm Input
The univariate outlier detection algorithm accepts the input described below.
Pass the
Input ID
as a parameter to the methods that provide input for your algorithm.
For more details, see Algorithms.Input ID | Input |
|---|---|
data | Pointer to the  numeric table with the data for outlier detection.The input can be an object of any class derived from the NumericTable class. |
location | Pointer to the  numeric table with the vector of means.The input can be an object of any class derived from NumericTable except PackedSymmetricMatrix and PackedTriangularMatrix . |
scatter | Pointer to the numeric table with the vector of standard deviations.The input can be an object of any class derived from NumericTable except PackedSymmetricMatrix and PackedTriangularMatrix . |
threshold | Pointer to the numeric table with non-negative numbers that define the outlier region.The input can be an object of any class derived from NumericTable except PackedSymmetricMatrix and PackedTriangularMatrix . |
If you do not provide at least one of the
location
, scatter
, threshold
inputs,
the library will initialize all of them with the following default values:location | A set of  |
scatter | A set of  |
threshold | A set of  |
Algorithm Parameters
The univariate outlier detection algorithm has the following parameters:
Parameter | Default Value | Description |
|---|---|---|
algorithmFPType | float | The floating-point type that the algorithm uses for intermediate computations. Can be float or double . |
method | defaultDense | Performance-oriented computation method, the only method supported by the algorithm. |
Algorithm Output
The univariate outlier detection algorithm calculates the result described below.
Pass the
Result ID
as a parameter to the methods that access the results of your algorithm.
For more details, see Algorithms.Result ID | Result |
|---|---|
weights | Pointer to the numeric table of zeros and ones.
Zero in the position  indicates an outlier in the  -th observation of the  -th feature.By default, the result is an object of the HomogenNumericTable class,
but you can define the result as an object of any class derived from NumericTable
except PackedSymmetricMatrix , PackedTriangularMatrix , and СSRNumericTable . |
Examples
C++ (CPU)
Batch Processing:
Java*
There is no support for Java on GPU.
Batch Processing:
Python*
Batch Processing: