Class UMAP

java.lang.Object

smile.manifold.UMAP

public class UMAP
extends Object

Uniform Manifold Approximation and Projection (UMAP).

UMAP is a nonlinear dimensionality reduction method designed for manifold visualization and unsupervised representation learning. It rests upon three key assumptions:

• The data manifold is locally Riemannian.
• The local metric is approximately constant in local neighborhoods.
• The manifold is locally connected.

From these topological assumptions, high-dimensional data is represented as a weighted fuzzy simplicial set, and embedded into low dimensions by minimizing cross-entropy via stochastic gradient descent.

References

• L. McInnes, J. Healy, and J. Melville. UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction. arXiv:1802.03426, 2018.
• How UMAP Works

See Also:

• TSNE

Nested Class Summary

Nested Classes

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

Method Summary

Modifier and Type	Method	Description
static double[][]	fit(double[][] data, UMAP.Options options)	Executes UMAP on coordinate observations using Euclidean distance.
static <T> double[][]	fit(T[] data, NearestNeighborGraph nng, UMAP.Options options)	Executes UMAP using a precomputed nearest neighbor graph.
static <T> double[][]	fit(T[] data, Metric<T> distance, UMAP.Options options)	Executes UMAP with a custom metric distance function.

Methods inherited from class Object

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

Method Details

fit

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

Executes UMAP on coordinate observations using Euclidean distance.

Parameters:

data - input observations.

options - algorithm hyperparameters.

Returns:

low-dimensional coordinates matrix.

fit

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

Executes UMAP with a custom metric distance function.

Type Parameters:

T - point data type.

Parameters:

data - input observations.

distance - distance metric.

options - algorithm hyperparameters.

Returns:

low-dimensional coordinates matrix.

fit

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

Executes UMAP using a precomputed nearest neighbor graph.

Type Parameters:

T - point data type.

Parameters:

data - input observations.

nng - nearest neighbor graph.

options - algorithm hyperparameters.

Returns:

low-dimensional coordinates matrix.