# Univariate Outlier Detection

A univariate outlier is an occurrence of an abnormal value within a single observation point.

## Details

Given a set

*of*X

*feature vectors of dimension*n

*, the problem is to identify the vectors that do not belong to the underlying distribution (see [Ben2005] for exact definitions of an outlier).*p

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.

## 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 0.0 |

scatter | A set of 1.0 |

threshold | A set of 3.0 |

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 i -th feature.j 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*

Python*

Batch Processing: