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Abstract

The paper investigates the acceleration of t-SNE-an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots-using two tree-based algorithms. In particular, the paper develops variants of the Barnes-Hut algorithm and of the dual-tree algorithm that approximate the gradient used for learning t-SNE embeddings in O(N*logN). Our experiments show that the resulting algorithms substantially accelerate t-SNE, and that they make it possible to learn embeddings of data sets with millions of objects. Somewhat counterintuitively, the Barnes-Hut variant of t-SNE appears to outperform the dual-tree variant.

Source

Journal of machine learning research. 15(2014), S.3221-3245

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Abstract

Techniques for multidimensional scaling visualize objects as points in a low-dimensional metric map. As a result, the visualizations are subject to the fundamental limitations of metric spaces. These limitations prevent multidimensional scaling from faithfully representing non-metric similarity data such as word associations or event co-occurrences. In particular, multidimensional scaling cannot faithfully represent intransitive pairwise similarities in a visualization, and it cannot faithfully visualize "central" objects. In this paper, we present an extension of a recently proposed multidimensional scaling technique called t-SNE. The extension aims to address the problems of traditional multidimensional scaling techniques when these techniques are used to visualize non-metric similarities. The new technique, called multiple maps t-SNE, alleviates these problems by constructing a collection of maps that reveal complementary structure in the similarity data. We apply multiple maps t-SNE to a large data set of word association data and to a data set of NIPS co-authorships, demonstrating its ability to successfully visualize non-metric similarities.