DIEM

Dimension Insensitive Euclidean Metric

This repository contains the Matlab functions to correctly compute the Dimension Insensitive Euclidean Metric.

The repository contains 3 files:

• DIEM_Stat.m --> This function computes the statistical parameters of the DIEM distribution given a dimension N and variables range (minV,maxV).
• getDIEM.m --> This function computes the DIEM between any pairs of vectors or matrices.
• Example_DIEM.m --> This script provides a simple example on how to run and use the DIEM_Stat.m and getDIEM.m functions.
• getCosineSimilarity.m --> This function computes the Cosine Similarity between any pairs of vectors or matrices.
• randu_sphere.m --> This function allows the generation of uniformly distributed random points on a shpere.
• DIEM_paper_results.m --> Run this script to reproduce the results of the the paper on arXiv.
  • In order to run this code you should also download two additional .csv files containing the vector embeddings for the LLM case-study. You can download such files from this link: https://drive.google.com/drive/folders/1LvvYO7YfgsR0jJ3Je3wIkUsl1sdKRcoe?usp=sharing
  • Place the 2 .csv files in the TextEmbeddings folder.

Python code

You need to install the following libraries to run the python implementation:

pip install numpy
pip install matplotlib
pip install scipy
pip install seaborn

After that, you can run the example with:

python diem_functions.py

Then, if you want to replicate the results of the paper, you need to first download the .csv files containing the vector embeddings for the LLM case-study, as explained before. Then, you can simply run:

python diem_analysis.py