# Detect Outlier (LOF) (RapidMiner Studio Core)

## Synopsis

This operator identifies outliers in the given ExampleSet based on local outlier factors (LOF). The LOF is based on a concept of a local density, where locality is given by the*k*nearest neighbors, whose distance is used to estimate the density. By comparing the local density of an object to the local densities of its neighbors, one can identify regions of similar density, and points that have a substantially lower density than their neighbors. These are considered to be outliers

## Description

This operator performs a LOF outlier search. LOF outliers or outliers with a local outlier factor per object are density based outliers according to Breunig, Kriegel, et al. As indicated by the name, the local outlier factor is based on a concept of a local density, where locality is given by *k* nearest neighbors, whose distance is used to estimate the density. By comparing the local density of an object to the local densities of its neighbors, one can identify regions of similar density, and points that have a substantially lower density than their neighbors. These are considered to be outliers. The local density is estimated by the typical distance at which a point can be 'reached' from its neighbors. The definition of 'reachability distance' used in LOF is an additional measure to produce more stable results within clusters.

The approach to find the outliers is based on measuring the density of objects and its relation to each other (referred to as local reachability density). Based on the average ratio of the local reachability density of an object and its k-nearest neighbors (i.e. the objects in its k-distance neighborhood), a local outlier factor (LOF) is computed. The approach takes a parameter *MinPts* (actually specifying the 'k') and it uses the maximum LOFs for objects in a *MinPts* range (lower bound and upper bound to *MinPts*).

This operator supports cosine, inverted cosine, angle and squared distance in addition to the usual euclidian distance which can be specified by the *distance function* parameter. In the first step, the objects are grouped into containers. For each object, using a radius screening of all other objects, all the available distances between that object and another object (or group of objects) on the same radius given by the distance are associated with a container. That container then has the distance information as well as the list of objects within that distance (usually only a few) and the information about how many objects are in the container.

In the second step, three things are done:
The containers for each object are counted in ascending order according to the cardinality of the object list within the container (= that distance) to find the k-distances for each object and the objects in that k-distance (all objects in all the subsequent containers with a smaller distance).
Using this information, the local reachability densities are computed by using the maximum of the actual distance and the k-distance for each object pair (object and objects in k-distance) and averaging it by the cardinality of the k-neighborhood and then taking the reciprocal value.
The LOF is computed for each *MinPts* value in the range (actually for all up to upper bound) by averaging the ratio between the MinPts-local reachability-density of all objects in the k-neighborhood and the object itself. The maximum LOF in the *MinPts* range is passed as final LOF to each object.
Afterwards LOFs are added as values for a special real-valued outlier attribute in the ExampleSet which the operator will return.

An outlier is an example that is numerically distant from the rest of the examples of the ExampleSet. An outlying example is one that appears to deviate markedly from other examples of the ExampleSet. Outliers are often (not always) indicative of measurement error. In this case such examples should be discarded.

## Input

- example set input (Data Table)
This input port expects an ExampleSet. It is the output of the Generate Data operator in the attached Example Process. The output of other operators can also be used as input.

## Output

- example set output (Data Table)
A new attribute 'outlier' is added to the given ExampleSet which is then delivered through this output port.

- original (Data Table)
The ExampleSet that was given as input is passed without changing to the output through this port. This is usually used to reuse the same ExampleSet in further operators or to view the ExampleSet in the Results Workspace.

## Parameters

- minimal_points_lower_boundThis parameter specifies the lower bound for
*MinPts*for the Outlier test. Range: integer - minimal_points_upper_boundThis parameter specifies the upper bound for
*MinPts*for the Outlier test. Range: integer - distance_functionThis parameter specifies the distance function that will be used for calculating the distance between two objects. Range: selection

## Tutorial Processes

### Detecting outliers from an ExampleSet

The Generate Data operator is used for generating an ExampleSet. The target function parameter is set to 'gaussian mixture clusters'. The number examples and number of attributes parameters are set to 200 and 2 respectively. A breakpoint is inserted here so that you can view the ExampleSet in the Results Workspace. A good plot of the ExampleSet can be seen by switching to the 'Plot View' tab. Set Plotter to 'Scatter', x-Axis to 'att1' and y-Axis to 'att2' to view the scatter plot of the ExampleSet.

The Detect Outlier (LOF) operator is applied on this ExampleSet with default values for all parameters. The minimal points lower bound and minimal points upper bound parameters are set to 10 and 20 respectively. The resultant ExampleSet can be seen in the Results Workspace. For better understanding switch to the 'Plot View' tab. Set Plotter to 'Scatter', x-Axis to 'att1', y-Axis to 'att2' and Color Column to 'outlier' to view the scatter plot of the ExampleSet.