Dimensionality Reduction

Dimensionality reduction is a topic that permeates many of our interests. An important application for dimensionality reduction is visualisation: “compressing” data to two dimensions allows us a visual appreciation of the dataset at hand possibly revealing relationships of data similarity. This compression of data is often done in ad hoc way that disregards the particular nature of the data. One can easily imagine that different types of data are amenable only to different kinds of compression. Hence, the compression mechanism needs to incorporate certain domain knowledge in order to be able to distinguish between salient information that is worth keeping and should be visible in the visualisation, and information that can be neglected without suppressing the structure present in the data.

The plot here shows a visualisation of eclipsing binary stars constructed by an algorithm akin to the popular Self-Organising Map algorithm. An important point in this visualisation is the adoption of a basic physical model that describes how light curves of binary stars are generated.