(AI Studio Core)

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.