This project is supervised by Professor Thomas Sinclair of Purdue Mathematics. Contributors of this project are Darshini Rajamani, Abbas Dohadwala, Luke Luschwitz, and Karim El-Sharkawy of Purdue University.

Our research focuses on analyzing positive mappings and their extendibility, involving the development of an intricate code to evaluate specific matrix properties and visualize their cones. We're using Python with NumPy, SciPy (specifically linprog), and sklearn libraries. The code itself classifies and validates matrices based on mathematical criteria such as extendibility. It draws on a blend of disciplines including linear algebra, optimization, linear programming, Euclidean distance geometry, and machine learning, particularly SVM. Please read our papers for more information on the theory of positive mappings and their extensions.

Our main goal is to find patterns within extendable matrices. In other words, we want to know what differentiates extendable and nonextendable matrices. This would decrease the amount of time and effort needed to identify if a matrix extends or not. Currently, we're investigating colinearity and if the matrices are coplanar, to determine if that's the key.

1. Creating_Extendable_and_Nonextendable_Maps.ipynb: Finds a large number of mappings, some extendable and others not, then uses ML (sklearn.logisticregression) to get closer to our goal
2. pattern_recognition_and_visualization.ipynb: finding all aptterns and testing theories
3. Data Sets Folder

• (Non)ExtendableMappings: two files of extendable and non-extendable mappings (100k total) generated by the first file.
• farthestBsMORE: lists the farthest nonextendable mappings from the extendable mappings
• trueClassifiersGood: lists the best classifiers

1. Python 3.10.12
2. NumPy 1.26.4
3. Scikit-learn 1.3.2
4. SciPy 1.13.1
5. Matplotlib 3.7.1

last update by Karim on July 31st, 2024