Package elki.distance

Distance functions for use within ELKI.

Distance functions

There are three basic types of distance functions:

• Primitive Distance Functions that can be computed for any two objects.
• DBID Distance Functions, that are only defined for object IDs, e.g., an external distance matrix
• Index-Based Distance Functions, that require an indexing/preprocessing step, and are then valid for existing database objects.

These types differ significantly in both implementation and use.

Using distance functions

As a 'consumer' of distances, you usually do not care about the type of distance function you want to use. To facilitate this, a distance function can be bound to a database by calling the 'instantiate' method to obtain a DistanceQuery object. A distance query is a best-effort adapter for the given distance function. Usually, you pass it two DBIDs and get the distance value back. When required, the adapter will get the appropriate records from the database needed to compute the distance.

Note: instantiating a preprocessor based distance will invoke the preprocessing step. It is recommended to do this as soon as possible, and only instantiate the query once, then pass the query object through the various methods.

Code example

DistanceQuery<V> distanceQuery = database.getDistanceQuery(EuclideanDistance.STATIC);

Interface Summary

Interface	Description
DBIDDistance	Distance functions valid in a database context only (i.e. for DBIDs)
DBIDRangeDistance	Distance functions valid in a static database context only (i.e. for DBIDRanges) For any "distance" that cannot be computed for arbitrary objects, only those that exist in the database and referenced by their ID.
Distance<O>	Base interface for any kind of distances.
IndexBasedDistance<O>	Distance function relying on an index (such as preprocessed neighborhoods).
IndexBasedDistance.Instance<T,I extends Index>	Instance interface for Index based distance functions.
Norm<O>	Abstract interface for a mathematical norm.
NumberVectorDistance<O>	Base interface for the common case of distance functions defined on numerical vectors.
PrimitiveDistance<O>	Primitive distance function that is defined on some kind of object.
SpatialPrimitiveDistance<V extends SpatialComparable>	API for a spatial primitive distance function.
WeightedNumberVectorDistance<V>	Distance functions where each dimension is assigned a weight.

Class Summary

Class	Description
AbstractDatabaseDistance<O>	Abstract super class for distance functions needing a database context.
AbstractDatabaseDistance.Instance<O>	The actual instance bound to a particular database.
AbstractDBIDRangeDistance	Abstract base class for distance functions that rely on integer offsets within a consecutive range.
AbstractIndexBasedDistance<O,F extends IndexFactory<O>>	Abstract super class for distance functions needing a database index.
AbstractIndexBasedDistance.Instance<O,I extends Index,F extends Distance<? super O>>	The actual instance bound to a particular database.
AbstractNumberVectorDistance	Abstract base class for the most common family of distance functions: defined on number vectors and returning double values.
ArcCosineDistance	Arcus cosine distance function for feature vectors.
ArcCosineDistance.Par	Parameterization class.
ArcCosineUnitlengthDistance	Arcus cosine distance function for feature vectors.
ArcCosineUnitlengthDistance.Par	Parameterization class.
BrayCurtisDistance	Bray-Curtis distance function / Sørensen–Dice coefficient for continuous vector spaces (not only binary data).
BrayCurtisDistance.Par	Parameterization class.
CanberraDistance	Canberra distance function, a variation of Manhattan distance.
CanberraDistance.Par	Parameterization class.
ClarkDistance	Clark distance function for vector spaces.
ClarkDistance.Par	Parameterization class.
CosineDistance	Cosine distance function for feature vectors.
CosineDistance.Par	Parameterization class.
CosineUnitlengthDistance	Cosine distance function for unit length feature vectors.
CosineUnitlengthDistance.Par	Parameterization class.
MahalanobisDistance	Mahalanobis quadratic form distance for feature vectors.
MatrixWeightedQuadraticDistance	Matrix weighted quadratic distance, the squared form of MahalanobisDistance.
RandomStableDistance	This is a dummy distance providing random values (obviously not metrical), useful mostly for unit tests and baseline evaluations: obviously this distance provides no benefit whatsoever.
RandomStableDistance.Par	Parameterization class.
SharedNearestNeighborJaccardDistance<O>	SharedNearestNeighborJaccardDistance computes the Jaccard coefficient, which is a proper distance metric.
SharedNearestNeighborJaccardDistance.Instance<T>	Actual instance for a dataset.
SharedNearestNeighborJaccardDistance.Par<O>	Parameterization class.
SqrtCosineDistance	Cosine distance function for feature vectors using the square root.
SqrtCosineDistance.Par	Parameterization class.
SqrtCosineUnitlengthDistance	Cosine distance function for unit length feature vectors using the square root.
SqrtCosineUnitlengthDistance.Par	Parameterization class.
WeightedCanberraDistance	Weighted Canberra distance function, a variation of Manhattan distance.
WeightedCanberraDistance.Par	Parameterization class.