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Perplexity-free t-SNE and twice Student tt-SNE

In dimensionality reduction and data visualisation, t-SNE has become a popular method. In this paper, we propose two variants to the Gaussian similarities used to characterise the neighbourhoods around each high-dimensional datum in t-SNE. A first alternative is to use t distributions like already used in the low-dimensional embedding space; a variable degree of freedom accounts for the intrinsic dimensionality of data. The second variant relies on compounds of Gaussian neighbourhoods with growing widths, thereby suppressing the need for the user to adjust a single size or perplexity. In both cases, heavy-tailed distributions thus characterise the neighbourhood relationships in the data space. Experiments show that both variants are competitive with t-SNE, at no extra cost.