Gradient-based explanation for non-linear non-parametric dimensionality reduction

Dimensionality reduction (DR) is a popular technique that shows great results to analyze high-dimensional data. Generally, DR is used to produce visualizations in 2 or 3 dimensions. While it can help understanding correlations between data, embeddings generated by DR are hard to grasp. The position of instances in low-dimension may be difficult to interpret, especially for non-linear, non-parametric DR techniques. Because most of the techniques are said to be neighborhood preserving (which means that explaining long distances is not relevant), some approaches try explaining them locally. These methods use simpler interpretable models to approximate the decision frontier locally. This can lead to misleading explanations. In this paper a novel approach to locally explain non-linear, non-parametric DR embeddings like t-SNE is introduced. It is the first gradient-based method for explaining these DR algorithms. The technique presented in this paper is applied on t-SNE, but is theoretically suitable for any DR method that is a minimization or maximization problem. The approach uses the analytical derivative of a t-SNE embedding to explain the position of an instance in the visualization.