Similarity between planetary systems and dimensionality reduction using T-SNE
Planetary systems are physical objects characterised by many features. Assuming N planets in a system, each of them characterised by its mass, distance to its central star, and radius, the dimensionality of a planetary system is 3N. Comparing results of simulations with observations is not easily done using Euclidean metric in a 3N dimension vector space, as demonstrated in our paper.
Instead, we developed a new metric to compare planetary systems, based on mixture of Gaussian, and L2 distance between the resulting distributions. Our new metric can be used for dimensionality reduction calculations, and we demonstrate, using T-SNE, that the properties of planetary systems are linked to the properties in circum-stellar disks in which they formed.
This video illustrates the use of T-SNE to demonstrate that similar protoplanetary disks lead to the formation of similar planetary systems. At the beginning of the video, each point represents a planetary system: points located close one to the other representing most similar planetary systems. The color is a uniform gradient, therefore similar systems are represented with a similar color. During the video, new locations of points are computed using T-SNE, but now considering the similarity between circum-stellar disks. At the end of the video, it is clear that the gradient of colours is somewhat preserved, meaning that two points located close one to each other (representing therefore similar disks) have similar color (therefore representing similar planetary systems). More details can be found in our paper.