xSNE Stochastic Neighbor Embedding methods with novel neighborhood probabilitieshttp://mloss.orgUpdates and additions to xSNE Stochastic Neighbor Embedding methods with novel neighborhood probabilitiesenTue, 20 Aug 2013 11:02:21 -0000xSNE Stochastic Neighbor Embedding methods with novel neighborhood probabilities 1.2<html><p>Stochastic neighbor embedding originally aims at the reconstruction of given distance 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 also allows for handling dissimilarity or score-induced neighborhood topologies and makes use of quasi 2nd order gradient-based (l-)BFGS optimization. </p> <p>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'. </p> <p>The functionality is {SNE, t-SNE} x {symmetric, asymmetric} where SNE is ordinary (yet well-working) stochastic neighbor embedding, and t-SNE tries to avoid the 'crowding' problem by using Student-t rather than Gaussian neighborhood density assumption on the output space. </p> <p>Symmetric refers to forcing symmetric neighborhood relationships (as originally proposed for t-SNE) for visually appealing plots, else asymmetric relationship reconstruction might be preferred for better representation qualities of the embedded point cloud. </p> <p>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. </p> <p>Acknowledgements: </p> <ul> <li><p>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. </p> </li> <li><p>The great (l-)BFGS optimizer (fminlbfgs.m) of Dirk-Jan Kroon found at included here is STRONGLY acknowledged. </p> </li> </ul></html>marc strickertTue, 20 Aug 2013 11:02:21 -0000 reductionmdsmultidimensional scalingsnestochastic neighbor embeddingneighborhood probability estimation