Package smile.manifold

Class UMAP

java.lang.Object

smile.manifold.UMAP

All Implemented Interfaces:

Serializable

public class UMAP
extends Object
implements Serializable

Uniform Manifold Approximation and Projection. UMAP is a dimension reduction technique that can be used for visualization similarly to t-SNE, but also for general non-linear dimension reduction. The algorithm is founded on three assumptions about the data:

• The data is uniformly distributed on a Riemannian manifold;
• The Riemannian metric is locally constant (or can be approximated as such);
• The manifold is locally connected.

From these assumptions it is possible to model the manifold with a fuzzy topological structure. The embedding is found by searching for a low dimensional projection of the data that has the closest possible equivalent fuzzy topological structure.

References

1. McInnes, L, Healy, J, UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction, ArXiv e-prints 1802.03426, 2018
2. How UMAP Works

See Also:

• TSNE
• Serialized Form

Field Summary

Fields

Modifier and Type	Field	Description
final double[][]	coordinates	The coordinate matrix in embedding space.
final AdjacencyList	graph	The nearest neighbor graph.
final int[]	index	The original sample index.

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
static UMAP	of(double[][] data)	Runs the UMAP algorithm.
static UMAP	of(double[][] data, int k)	Runs the UMAP algorithm.
static UMAP	of(double[][] data, int k, int d, int iterations, double learningRate, double minDist, double spread, int negativeSamples, double repulsionStrength)	Runs the UMAP algorithm.
static <T> UMAP	of(T[] data, Distance<T> distance)	Runs the UMAP algorithm.
static <T> UMAP	of(T[] data, Distance<T> distance, int k)	Runs the UMAP algorithm.
static <T> UMAP	of(T[] data, Distance<T> distance, int k, int d, int iterations, double learningRate, double minDist, double spread, int negativeSamples, double repulsionStrength)	Runs the UMAP algorithm.

Methods inherited from class java.lang.Object

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

Field Details

coordinates

public final double[][] coordinates

The coordinate matrix in embedding space.

index

public final int[] index

The original sample index.

graph

public final AdjacencyList graph

The nearest neighbor graph.

Constructor Details

UMAP

public UMAP(int[] index,
 double[][] coordinates,
 AdjacencyList graph)

Constructor.

Parameters:

index - the original sample index.

coordinates - the coordinates.

graph - the nearest neighbor graph.

Method Details

of

public static UMAP of(double[][] data)

Runs the UMAP algorithm.

Parameters:

data - the input data.

Returns:

the model.

of

public static <T> UMAP of(T[] data,
 Distance<T> distance)

Runs the UMAP algorithm.

Type Parameters:

T - the data type of points.

Parameters:

data - the input data.

distance - the distance function.

Returns:

the model.

of

public static UMAP of(double[][] data,
 int k)

Runs the UMAP algorithm.

Parameters:

data - the input data.

k - k-nearest neighbors. Larger values result in more global views of the manifold, while smaller values result in more local data being preserved. Generally in the range 2 to 100.

Returns:

the model.

of

public static <T> UMAP of(T[] data,
 Distance<T> distance,
 int k)

Runs the UMAP algorithm.

Type Parameters:

T - the data type of points.

Parameters:

data - the input data.

distance - the distance function.

k - k-nearest neighbor. Larger values result in more global views of the manifold, while smaller values result in more local data being preserved. Generally in the range 2 to 100.

Returns:

the model.

of

public static UMAP of(double[][] data,
 int k,
 int d,
 int iterations,
 double learningRate,
 double minDist,
 double spread,
 int negativeSamples,
 double repulsionStrength)

Runs the UMAP algorithm.

Parameters:

data - the input data.

k - k-nearest neighbors. Larger values result in more global views of the manifold, while smaller values result in more local data being preserved. Generally in the range 2 to 100.

d - The target embedding dimensions. defaults to 2 to provide easy visualization, but can reasonably be set to any integer value in the range 2 to 100.

iterations - The number of iterations to optimize the low-dimensional representation. Larger values result in more accurate embedding. Muse be at least 10. Choose wise value based on the size of the input data, e.g, 200 for large data (10000+ samples), 500 for small.

learningRate - The initial learning rate for the embedding optimization, default 1.

minDist - The desired separation between close points in the embedding space. Smaller values will result in a more clustered/clumped embedding where nearby points on the manifold are drawn closer together, while larger values will result on a more even disperse of points. The value should be set no-greater than and relative to the spread value, which determines the scale at which embedded points will be spread out. default 0.1.

spread - The effective scale of embedded points. In combination with minDist, this determines how clustered/clumped the embedded points are. default 1.0.

negativeSamples - The number of negative samples to select per positive sample in the optimization process. Increasing this value will result in greater repulsive force being applied, greater optimization cost, but slightly more accuracy, default 5.

repulsionStrength - Weighting applied to negative samples in low dimensional embedding optimization. Values higher than one will result in greater weight being given to negative samples, default 1.0.

Returns:

the model.

of

public static <T> UMAP of(T[] data,
 Distance<T> distance,
 int k,
 int d,
 int iterations,
 double learningRate,
 double minDist,
 double spread,
 int negativeSamples,
 double repulsionStrength)

Runs the UMAP algorithm.

Type Parameters:

T - the data type of points.

Parameters:

data - the input data.

distance - the distance function.

k - k-nearest neighbor. Larger values result in more global views of the manifold, while smaller values result in more local data being preserved. Generally in the range 2 to 100.

d - The target embedding dimensions. defaults to 2 to provide easy visualization, but can reasonably be set to any integer value in the range 2 to 100.

iterations - The number of iterations to optimize the low-dimensional representation. Larger values result in more accurate embedding. Muse be at least 10. Choose wise value based on the size of the input data, e.g, 200 for large data (1000+ samples), 500 for small.

learningRate - The initial learning rate for the embedding optimization, default 1.

minDist - The desired separation between close points in the embedding space. Smaller values will result in a more clustered/clumped embedding where nearby points on the manifold are drawn closer together, while larger values will result on a more even disperse of points. The value should be set no-greater than and relative to the spread value, which determines the scale at which embedded points will be spread out. default 0.1.

spread - The effective scale of embedded points. In combination with minDist, this determines how clustered/clumped the embedded points are. default 1.0.

negativeSamples - The number of negative samples to select per positive sample in the optimization process. Increasing this value will result in greater repulsive force being applied, greater optimization cost, but slightly more accuracy, default 5.

repulsionStrength - Weighting applied to negative samples in low dimensional embedding optimization. Values higher than one will result in greater weight being given to negative samples, default 1.0.

Returns:

the model.