smile.manifold

Class TSNE

java.lang.Object

smile.manifold.TSNE

public class TSNE
extends java.lang.Object

The t-distributed stochastic neighbor embedding (t-SNE) is a nonlinear dimensionality reduction technique that is particularly well suited for embedding high-dimensional data into a space of two or three dimensions, which can then be visualized in a scatter plot. Specifically, it models each high-dimensional object by a two- or three-dimensional point in such a way that similar objects are modeled by nearby points and dissimilar objects are modeled by distant points.

The t-SNE algorithm comprises two main stages. First, t-SNE constructs a probability distribution over pairs of high-dimensional objects in such a way that similar objects have a high probability of being picked, whilst dissimilar points have an infinitesimal probability of being picked. Second, t-SNE defines a similar probability distribution over the points in the low-dimensional map, and it minimizes the Kullback–Leibler divergence between the two distributions with respect to the locations of the points in the map. Note that while the original algorithm uses the Euclidean distance between objects as the base of its similarity metric, this should be changed as appropriate.

References

1. L.J.P. van der Maaten. Accelerating t-SNE using Tree-Based Algorithms. Journal of Machine Learning Research 15(Oct):3221-3245, 2014.
2. L.J.P. van der Maaten and G.E. Hinton. Visualizing Non-Metric Similarities in Multiple Maps. Machine Learning 87(1):33-55, 2012.
3. L.J.P. van der Maaten. Learning a Parametric Embedding by Preserving Local Structure. In Proceedings of the Twelfth International Conference on Artificial Intelligence & Statistics (AI-STATS), JMLR W&CP 5:384-391, 2009.
4. L.J.P. van der Maaten and G.E. Hinton. Visualizing High-Dimensional Data Using t-SNE. Journal of Machine Learning Research 9(Nov):2579-2605, 2008.

Field Summary

Fields

Modifier and Type	Field and Description
double[][]	coordinates Coordinate matrix.

Constructor Summary

Constructors

Constructor and Description
TSNE(double[][] X, int d) Constructor.
TSNE(double[][] X, int d, double perplexity, double eta, int iterations) Constructor.

Method Summary

Modifier and Type	Method and Description
void	update(int iterations) Performs additional iterations.

Methods inherited from class java.lang.Object

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

Field Detail

coordinates

public final double[][] coordinates

Coordinate matrix.

Constructor Detail

TSNE

public TSNE(double[][] X,
            int d)

Constructor. Train t-SNE for 1000 iterations, perplexity = 20 and learning rate = 200.

Parameters:

X - input data. If X is a square matrix, it is assumed to be the squared distance/dissimilarity matrix.

d - the dimension of embedding space.

TSNE

public TSNE(double[][] X,
            int d,
            double perplexity,
            double eta,
            int iterations)

Constructor. Train t-SNE for given number of iterations.

Parameters:

X - input data. If X is a square matrix, it is assumed to be the squared distance/dissimilarity matrix.

d - the dimension of embedding space.

perplexity - the perplexity of the conditional distribution.

eta - the learning rate.

iterations - the number of iterations.

Method Detail

update

public void update(int iterations)

Performs additional iterations.