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 (matrices) 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 is a sophisticated algorithm that 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.
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.
- Working together to compute the code and understand the theory. Communicating with each other to accurately translate the theory into code
- reading the professor's notes and making sure we understand our code by doing a lot of reading and understanding what the computer is giving us
- adding many comments so we know exactly what everything does and anyone reading the code can also understand it
- 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
- 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
- Project Guide: A guide for anyone wanting to catch up with the project or understand the entire process. Can be used as a guide or a resource to refresh
last update by Karim at 3:03 AM May 16th 2024