Dimensionality Reduction (DR) is a technique used to project high-dimensional points to lower-dimensional spaces. A common application is to project the dataset to a 2D plane, so it can be visualized as a scatterplot.

However, we know that this process is not perfect, and it tends to create some distortions of the data, that we need to take into account when we analyze the projections [1]. But these distortions can be complex and hard to understand, since we cannot visualize the original data. To complicate matters, there are many DR methods, each with its set of hyperparameters to adjust, that will produce very different projections. Which one to choose? How much can we trust it? What parts of the projection are good or bad?

Over the years, the DR community has come up with many quality metrics that automatically compute "how good" the projection is. Again, we have the problem of a multitude of metrics (with their own hyperparameters) that measure different things. But they all have a common issue: they only measure how close structurally the projected points are to the original ones, disregarding the visual aspect of it [2].

In this project we want to develop new DR quality metrics that are focused on the visual perception of the projection. How much can the user trust the clusters, holes and other structures of points that can be seen in a 2D scatterplot? Is it really in the data, or an artifact created by DR?

[1] https://doi.org/10.1111/j.1467-8659.2010.01835.x

[2] https://doi.org/10.1111/cgf.70101