public class IsoMap
extends java.lang.Object
implements java.io.Serializable
To be specific, the classical MDS performs lowdimensional embedding based on the pairwise distance between data points, which is generally measured using straightline Euclidean distance. Isomap is distinguished by its use of the geodesic distance induced by a neighborhood graph embedded in the classical scaling. This is done to incorporate manifold structure in the resulting embedding. Isomap defines the geodesic distance to be the sum of edge weights along the shortest path between two nodes. The top n eigenvectors of the geodesic distance matrix, represent the coordinates in the new ndimensional Euclidean space.
The connectivity of each data point in the neighborhood graph is defined as its nearest k Euclidean neighbors in the highdimensional space. This step is vulnerable to "shortcircuit errors" if k is too large with respect to the manifold structure or if noise in the data moves the points slightly off the manifold. Even a single shortcircuit error can alter many entries in the geodesic distance matrix, which in turn can lead to a drastically different (and incorrect) lowdimensional embedding. Conversely, if k is too small, the neighborhood graph may become too sparse to approximate geodesic paths accurately.
This class implements CIsomap that involves magnifying the regions of high density and shrink the regions of low density of data points in the manifold. Edge weights that are maximized in MultiDimensional Scaling(MDS) are modified, with everything else remaining unaffected.
Modifier and Type  Field and Description 

double[][] 
coordinates
The coordinate matrix in embedding space.

AdjacencyList 
graph
The nearest neighbor graph.

int[] 
index
The original sample index.

Constructor and Description 

IsoMap(int[] index,
double[][] coordinates,
AdjacencyList graph)
Constructor.

Modifier and Type  Method and Description 

static IsoMap 
of(double[][] data,
int k)
Runs the CIsomap algorithm with Euclidean distance.

static IsoMap 
of(double[][] data,
int k,
int d,
boolean conformal)
Runs the Isomap algorithm.

static <T> IsoMap 
of(T[] data,
Distance<T> distance,
int k)
Runs the CIsomap algorithm.

static <T> IsoMap 
of(T[] data,
Distance<T> distance,
int k,
int d,
boolean conformal)
Runs the Isomap algorithm.

public final int[] index
public final double[][] coordinates
public final AdjacencyList graph
public IsoMap(int[] index, double[][] coordinates, AdjacencyList graph)
index
 the original sample index.coordinates
 the coordinates.graph
 the nearest neighbor graph.public static IsoMap of(double[][] data, int k)
data
 the input data.k
 knearest neighbor.public static IsoMap of(double[][] data, int k, int d, boolean conformal)
data
 the input data.d
 the dimension of the manifold.k
 knearest neighbor.conformal
 CIsomap algorithm if true, otherwise standard algorithm.public static <T> IsoMap of(T[] data, Distance<T> distance, int k)
data
 the input data.k
 knearest neighbor.public static <T> IsoMap of(T[] data, Distance<T> distance, int k, int d, boolean conformal)
data
 the input data.distance
 the distance measure.k
 knearest neighbor.d
 the dimension of the manifold.conformal
 CIsomap algorithm if true, otherwise standard algorithm.