Explaining neighborhood preservation for multidimensional projections

Dimensionality reduction techniques are the tools of choice for exploring high-dimensional datasets by means of low-dimensional projections. However, even state-of-the-art projection methods fail, up to various degrees, in perfectly preserving the structure of the data, expressed in terms of inter-point distances and point neighborhoods. To support better interpretation of a projection, we propose several metrics for quantifying errors related to neighborhood preservation. Next, we propose a number of visualizations that allow users to explore and explain the quality of neighborhood preservation at different scales, captured by the aforementioned error metrics. We demonstrate our exploratory views on three real-world datasets and two state-of-the-art multidimensional projection techniques.