edu.stanford.math.plex4.streams.impl

Class FlexibleVietorisRipsStream<T>

java.lang.Object

edu.stanford.math.plex4.streams.interfaces.PrimitiveStream<Simplex>

edu.stanford.math.plex4.streams.impl.FlagComplexStream

edu.stanford.math.plex4.streams.impl.FlexibleVietorisRipsStream<T>

Type Parameters:

T - the base type of the underlying metric space

All Implemented Interfaces:

AbstractFilteredStream<Simplex>, java.lang.Iterable<Simplex>

Direct Known Subclasses:

VietorisRipsStream

public class FlexibleVietorisRipsStream<T>
extends FlagComplexStream

This class implements the Vietoris-Rips filtered simplicial complex. A simplex [v_0, ..., v_k] is in VR(r) if and only if the pairwise distances d(v_i, v_j) are less than r for all 0 <= i, j <= k. Thus a Vietoris-Rips complex is fully defined by its 1-skeleton, in that it is the maximal simplicial complex given such a 1-skeleton. For this reason, we simply derive from the FlagComplexStream abstract class, and implement the pairwise thresholding in order to generate the 1-skeleton.

Author:

Andrew Tausz, Mikael Vejdemo-Johansson

Field Summary

Fields

Modifier and Type	Field and Description
protected double	maxDistance The maximum distance allowed between two connected vertices.
protected AbstractSearchableMetricSpace<T>	metricSpace This is the metric space upon which the stream is built from.

Fields inherited from class edu.stanford.math.plex4.streams.impl.FlagComplexStream

converter, indices, maxAllowableDimension, neighborhoodGraph

Fields inherited from class edu.stanford.math.plex4.streams.interfaces.PrimitiveStream

storageStructure

Constructor Summary

Constructors

Constructor and Description
FlexibleVietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace, double maxDistance, int maxDimension, FiltrationConverter converter) Constructor which initializes the complex with a metric space.
FlexibleVietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace, double maxDistance, int maxDimension, FiltrationConverter converter, int[] indices)
FlexibleVietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace, double maxDistance, int maxDimension, FiltrationConverter converter, StreamStorageStructure<Simplex> storageStructure)

Method Summary

Methods

Modifier and Type	Method and Description
protected UndirectedWeightedListGraph	constructEdges() This function implements the construction of the 1-skeleton.

Methods inherited from class edu.stanford.math.plex4.streams.impl.FlagComplexStream

addCofaces, constructComplex, getConverter, getFiltrationValue, getNeighborhoodGraph, incrementalExpansion, transform

Methods inherited from class edu.stanford.math.plex4.streams.interfaces.PrimitiveStream

containsElement, finalizeStream, getBasisComparator, getBoundary, getBoundaryCoefficients, getDimension, getFiltrationIndex, getMaximumFiltrationIndex, getMinimumFiltrationIndex, getSize, isFinalized, iterator, validate, validateVerbose

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

metricSpace

protected final AbstractSearchableMetricSpace<T> metricSpace

This is the metric space upon which the stream is built from.

maxDistance

protected final double maxDistance

The maximum distance allowed between two connected vertices.

Constructor Detail

FlexibleVietorisRipsStream

public FlexibleVietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace,
                          double maxDistance,
                          int maxDimension,
                          FiltrationConverter converter)

Constructor which initializes the complex with a metric space.

Parameters:

metricSpace - the metric space to use in the construction of the complex

maxDistance - the maximum allowable distance

maxDimension - the maximum dimension of the complex

converter - the Filtration Converter to be used

FlexibleVietorisRipsStream

public FlexibleVietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace,
                          double maxDistance,
                          int maxDimension,
                          FiltrationConverter converter,
                          StreamStorageStructure<Simplex> storageStructure)

FlexibleVietorisRipsStream

public FlexibleVietorisRipsStream(AbstractSearchableMetricSpace<T> metricSpace,
                          double maxDistance,
                          int maxDimension,
                          FiltrationConverter converter,
                          int[] indices)

Method Detail

constructEdges

protected UndirectedWeightedListGraph constructEdges()

Description copied from class: FlagComplexStream

This function implements the construction of the 1-skeleton. It must output a list containing pairs of filtration values and 1-simplices. The filtration value of an edge is the threshold value at which the edge appears in the filtered sequence of simplicial complexes.

Specified by:

constructEdges in class FlagComplexStream

Returns:

the 1-skeleton of the complex along with its filtration values