Description:

Stochastic neighbor embedding aims at the reconstruction of given distance, dissimilarity, or score neighborhood relations in a low-dimensional Euclidean space. This can be regarded as general approach to multi-dimensional scaling, but the reconstruction is based on the definition of input (and output) neighborhood probability alone. The present implementation makes use of quasi 2nd order gradient-based (l-)BFGS optimization.

Neighbor relationships in the embedding space ('scatter plots') are estimated as probabilities of Gaussian or Student-t distributions; probabilities can be derived from from Gaussians over pairwise Euclidean input distances, or, as in the present case, by novel score neighborhood probabilities that do not require extra settings such as 'Gaussian width' or 'perplexity'. The estimate of neighborhood probabilities is realized as probabilities of input score exceedance for reconstructing probabilities of distances in the embedding by minimizing KL-divergence. In an experimental version soft ranks are used for numerical optimization.

The functionality is SNE, t-SNE and soft-rank-based KL minimization where SNE is ordinary (yet well-working) stochastic neighbor embedding, t-SNE tries to avoid the 'crowding' problem by using Student-t rather than Gaussian neighborhood density assumption on the output space. That original assumption of input relationship symmetry is no longer used in this package, because point-wise reconstruction is supposed to be more specific than for general neighborhood probability distributions in the input and output space.

As additional feature, the embedding quality of data points is assessed by the contributions of embedding point placement to the cost function, i.e. the sum of absolute KL-divergence gradients caused by individual points.

Acknowledgements:

• The work on SNE and t-SNE I is highly appreciated "Visualizing Data using t-SNE", JMLR 9, pp. 2579-2605, 2008, and the freely available implementations by Laurens van der Maaten.

• The great (l-)BFGS optimizer (fminlbfgs.m) of Dirk-Jan Kroon found at http://www.mathworks.de/matlabcentral/fileexchange/23245 included here is STRONGLY acknowledged.

Changes to previous version:

• scoretoprob.m replaced by d2p.m

• protein score data set added

• trank.m computes (mid/max -tied) ranks along columns of matrix

• local P- neighborhood probability estimation added

• experimental soft_rank_SNE added for minimizing KL between probabilities of exceedance in source and embedding space

• symmetry option removed, because this was strange in previous version

BibTeX Entry: Download

Supported Operating Systems: Platform Independent

Data Formats: Matlab

Tags: Dimension Reduction, Mds, Multidimensional Scaling, Sne, Stochastic Neighbor Embedding, Neighborhood Probability Estimation

Archive: download here

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