Understanding_Sectral_Inference

This is a workflow to recreate and understand Doran et al 2024's method called Spectral Inference.

(https://doi.org/10.1101/2023.12.04.569969)

This contains the following:

1. Construction of Dataset

Some random mutation of a sequence at random spots in the "genes" creates different "species. Of course, all of this can be done with a real dataset

2. Singular Value Decomposition

SVD decomposition is performed and we show that it is lossless (This we know to be true, this is just a demonstration). We can reconstruct the original dataset using the U, S, and V matrices.

3. Partition of singular values:

This is done with respect to the median drop in subsequent singular values

4. Distance calculation within each partition and final distance summation:

This gives us a distance matrix between the species.

5. Phylogenetic Tree Construction

Finally, a Phylogenetic tree based on this distance matric is created:

6. Then we verify this against Doran et al's code.

(Link to the paper: https://doi.org/10.1101/2023.12.04.569969)