Clustering

AbstractClusteringMethod{P}

Abstract supertype for all clustering types, with partition of type P.

Notes

A clustering method defines a function which maps reach-sets to one or several reach-sets. The mapping can possibly be over-approximative, i.e. such that the set union of the input reach-sets is included in the set union of the output reach-sets.

By taking the convex hull of the input reach-sets one can reduce the number of outputs sets to a single one, overapproximately. This is the method that corresponds to the LazyClustering type. However, in some cases it is convenient to do other types of transformations, such as:

• Return several reach-sets that are obtained by grouping the input in a way defined by a partition. For example, a vector of ten input sets can be clustered in two groups of five sets each, or five groups of two sets each, etc.
• Use different set representations such as boxes or zonotopes.
• Further post-process the output of the convexification by splitting into smaller sets, eg. box splitting.

Each concrete subtype of AbstractClusteringMethod has a parameter P that defines what type of clustering strategy is applied. The method should be accessed with the partition getter function.

The following strategies are implemented at the interface level:

• If P is of type Missing: no partition is applied
• If P is of type integer: the partition corresponds to grouping the into the given integer number of sets (or as close as possible)
• If P is of type vector of vectors: the given partition is applied

Examples

LazyClustering([1:2, 3:10]) groups the first two reach-sets in one cluster and the third to tenth reach-sets in another cluster.

NoClustering{P} <: AbstractClusteringMethod{P}

No-op clustering method.

LazyClustering{P} <: AbstractClusteringMethod{P}

Cluster according to the given partition by applying a lazy representation of the convex hull.

BoxClustering{PI, PO} <: AbstractClusteringMethod{P}

Notes

This method first takes a lazy convex hull for the given partition, then computes a tight hyperrectangular approximation for each element in the partition.

ZonotopeClustering{P} <: AbstractClusteringMethod{P}

Notes

This method first takes a lazy convex hull for the given partition, then computes a zonotope overapproximation of the convex hull.

UnionClustering{P} <: AbstractClusteringMethod{P}

Cluster according to the given partition by applying a lazy representation of the set union.