Smoothing Affinity Matrix Impacts t-SNE Neighborhood Preservation

Researchers have explored the impact of modifying the affinity matrix within t-SNE, a widely used dimensionality reduction technique, on its ability to preserve neighborhood structures. The affinity matrix, which represents pairwise similarities as symmetrized probabilities, is central to t-SNE's optimization. The study introduces a row-wise power transform, governed by a parameter 'gamma', to either smooth or sharpen each row of this matrix while maintaining sparsity and rank order. This transform is shown to be equivalent to adjusting the Gaussian bandwidth, and thus perplexity, but with a key distinction: a fixed 'gamma' results in point-dependent effective perplexities, making it different from a global perplexity change. The empirical findings reveal that sharpening the probability distribution improves the preservation of the very nearest neighbors. Conversely, smoothing the distribution enhances the preservation of broader local neighborhoods. Notably, this smoothing technique was found to outperform alternative affinity constructions, including existing multiscale methods, specifically within the mid-local range of neighborhood preservation.