For the final project of Matrices and Linear Algebra (21-241), my partner and I implemented spectral clustering on both the k-nearest neighbor and e-neighborhood similarity graphs.
In short, for the k-nearest-neighbor similarity graph, vertices are connected with weighted edges based on how close they were. Meanwhile, the e-neighborhood graph has vertices connected by an edge if the distance between them is less than a specified e.
After creating these two graphs, we clustered data points into groups using linear algebra concepts. In particular, we derived a Laplachian matrix, essentially a matrix representation of a graph, and then decomposed it into eigenvalues and eigenvectors.
This algorithm for spectral clustering was applied on real world data of earthquake locations from 1000 seismic events of MB > 4.0 near Fiji since 1964. The results uncovered the coordinates of earthquake hotspots.
Note: all code is written in Julia
A complete write-up can be found here: 21241_Final_Project.pdf