HNSW-Discrete-Project-

This repo contains the code for our implementation of the HNSW algorithm (Hierarchical Navigable Small Worlds) for our CS 2051 Math paper.

I, Ankith, will eventually create a python file that measures the performance of a specific hnsw algorithm in querying a vector database for the nearest neighbours.

Logarithmic Regression

Using the logarithmic function $y = a \log_{2}(x) + b$ I calculate the parameters that best fit each of the graphs created by the varying distance metrics. The graphs are in the figures folder.

Cosine

a: 1.9052

b: -8.46

Inner Product

a: 1.90521

b: -7.31

L2

a: 2.3636

b: -13.8 The logarthmic regression functions are seen here.