Package smile.manifold

Class UMAP

java.lang.Object

smile.manifold.UMAP

public class UMAP
extends Object

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

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	UMAP.Options	The UMAP hyperparameters.

Method Summary

Modifier and Type	Method	Description
static double[][]	fit(double[][] data, UMAP.Options options)	Runs the UMAP algorithm with Euclidean distance.
static <T> double[][]	fit(T[] data, NearestNeighborGraph nng, UMAP.Options options)	Runs the UMAP algorithm.
static <T> double[][]	fit(T[] data, Metric<T> distance, UMAP.Options options)	Runs the UMAP algorithm.

Methods inherited from class java.lang.Object

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

Method Details

fit

public static double[][] fit(double[][] data,
 UMAP.Options options)

Runs the UMAP algorithm with Euclidean distance.

Parameters:

data - the input data.

options - the hyperparameters.

Returns:

The embedding coordinates.

fit

public static <T> double[][] fit(T[] data,
 Metric<T> distance,
 UMAP.Options options)

Runs the UMAP algorithm.

Type Parameters:

T - The data type of points.

Parameters:

data - the input data.

distance - the distance function.

options - the hyperparameters.

Returns:

The embedding coordinates.

fit

public static <T> double[][] fit(T[] data,
 NearestNeighborGraph nng,
 UMAP.Options options)

Runs the UMAP algorithm.

Type Parameters:

T - the data type of points.

Parameters:

data - the input data.

nng - the k-nearest neighbor graph.

options - the hyperparameters.

Returns:

the embedding coordinates.