Class IsoMap
 All Implemented Interfaces:
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.
 See Also:

Field Summary
Modifier and TypeFieldDescriptionfinal double[][]
The coordinate matrix in embedding space.final AdjacencyList
The nearest neighbor graph.final int[]
The original sample index. 
Constructor Summary
ConstructorDescriptionIsoMap
(int[] index, double[][] coordinates, AdjacencyList graph) Constructor. 
Method Summary
Modifier and TypeMethodDescriptionstatic 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
Runs the CIsomap algorithm.static <T> IsoMap
Runs the Isomap algorithm.

Field Details

index
public final int[] indexThe original sample index. 
coordinates
public final double[][] coordinatesThe coordinate matrix in embedding space. 
graph
The nearest neighbor graph.


Constructor Details

IsoMap
Constructor. Parameters:
index
 the original sample index.coordinates
 the coordinates.graph
 the nearest neighbor graph.


Method Details

of
Runs the CIsomap algorithm with Euclidean distance. Parameters:
data
 the input data.k
 knearest neighbor. Returns:
 the model.

of
Runs the Isomap algorithm. Parameters:
data
 the input data.k
 knearest neighbor.d
 the dimension of the manifold.conformal
 CIsomap algorithm if true, otherwise standard algorithm. Returns:
 the model.

of
Runs the CIsomap algorithm. Type Parameters:
T
 the data type of points. Parameters:
data
 the input data.distance
 the distance function.k
 knearest neighbor. Returns:
 the model.

of
Runs the Isomap algorithm. Type Parameters:
T
 the data type of points. Parameters:
data
 the input data.distance
 the distance function.k
 knearest neighbor.d
 the dimension of the manifold.conformal
 CIsomap algorithm if true, otherwise standard algorithm. Returns:
 the model.
