Y = tsne (X) embeds the $N\; \times \; P$ data matrix X (rows are observations) into a low-dimensional space and returns the $N\; \times$NumDimensions matrix Y of embedded points, whose pairwise (Student-t) affinities approximate the Gaussian affinities of the rows of X.

[Y, loss] = tsne (…) also returns the Kullback-Leibler divergence loss between the two affinity distributions at the returned embedding.

Name/Value pairs:

'Algorithm'

'exact' (default) forms the affinities and the gradient over every pair of points, which costs $O(N^2)$ in time and memory at each iteration. 'barneshut' approximates both: the high-dimensional affinities are kept only over each point’s $3\; \times \; Perplexity$ nearest neighbours, and the repulsive part of the gradient is summed over a space-partitioning tree of the embedding, giving $O(N\; log\; N)$. Use it when $N$ is large enough that the exact algorithm is slow or cannot allocate; on this machine the two cost the same at about $N\; =\; 500$ and 'barneshut' is eight times faster at $N\; =\; 2000$.

The two do not return the same embedding, and their loss values are not comparable either: the divergence is summed over the pairs that carry an affinity, and 'barneshut' keeps far fewer of them.

'Theta'

The tree opening criterion for 'barneshut', a non-negative scalar (default 0.5). A cell of the tree is collapsed to its centre of mass when its width is smaller than Theta times its distance from the point being pushed, so a larger value is faster and coarser. 0 collapses nothing and makes the repulsion exact, at $O(N^2)$; note that this still leaves the affinities sparse, so it does not reproduce 'exact'. Ignored by 'exact'.

'Distance'

The distance metric used for the high-dimensional affinities, as accepted by pdist (default 'euclidean').

'NumDimensions'

The dimension of the embedding Y (default min (P, 2)).

'NumPCAComponents'

If positive, reduce X to this many principal components before embedding (default 0, no reduction).

'Standardize'

Logical; center and scale each column of X before embedding (default false).

'Perplexity'

The effective number of local neighbors (default 30). It must be smaller than $N$.

'Exaggeration'

Tightness factor applied to the high-dimensional affinities for the first 100 iterations (default 4, no less than 1).

'LearnRate'

The learning rate of the optimization (default 500).

'InitialY'

An $N\; \times$NumDimensions initial embedding (default 1e-4 * randn).

'Options'

A structure (as returned by statset) whose MaxIter (default 1000) and TolFun (default 1e-10) fields control the optimization.

The embedding is not unique: it depends on the initial configuration and the random state. Set 'InitialY' (or the random seed) for a reproducible result.

See also: pca, pdist, statset

Source Code: tsne