The dimensional reduction and visualization project.

Here we give an example of the dimensional reduction techniques using jupyter notebooks. We have 3 different methods we try in this notebook:

1. PCA
2. Laplacian Eigenmaps
3. TSNE (and Barnes-Hut TSNE as well)

With these three we hope to visualize distributions of avalanches of stars. In particular, we want to visualize the space of such distributions. Since this space is approximately 500-dimensional, we use the three different dimensional reduction techniques to visualize our results.

In order to understand the background behind this project, please see this blog post: https://publish.illinois.edu/mohammedsheikh/2017/09/23/hello-world-2/

In order to look at the LEM algorithm, please take a look at this blog post: https://publish.illinois.edu/mohammedsheikh/2017/11/30/manifold-learning/

To see the mathematical intuition behind manifold learning, see this blog post: https://publish.illinois.edu/mohammedsheikh/2017/11/30/the-geometry-behind-manifold-learning/

Finally, to see comparison of TSNE and LEM, take a look at this blog post: https://publish.illinois.edu/mohammedsheikh/2017/12/04/evaluation-of-lem-and-t-sne/