# Explaining Multidimensional Projections

Multidimensional projections, also known as *embeddings* or dimensionality reduction methods, are techniques that take a high-dimensional dataset at input (say, tens..hundreds of dimensions) and produce a low-dimensional dataset with the same number of data points (say, 2D..3D). The key idea behind is that we can visualize a low-dimensional dataset easily, e.g. by a scatterplot. No equivalent method exists for a high-dimensional dataset.

## Explaining projections

We can surely create projections, but, what do the patterns that we see in them *mean*? The aim of this project is to provide interactive *explanatory tools* that tell us what point-clusters in a projection mean.

## Correlation and dimensionality

We can explain point clusters in a projection in different ways:

- we can explain which dimension makes points cluster together. We explored this in this paper;
- we can explain which dimensions are strongly correlated in a cluster of points;
- we can explain what is the local intrinsic dimensionality of a cluster of points in high-dimensional space.

In this project, we explore the latter two aspects. We propose visual techniques for showing, on a projection, which are the locally strongest correlated dimensions; and also what is the local intrinsic dimensionality of a cluster.

## References

A full description of the proposed techniques is given in the BSc thesis of D. van Driel (2017)

## Software

An implementation of the above techniques, including test datasets, is provided here.