## Linear Algebra at Work with MATLAB

On Thursday, September 21, Mike Michailidis, Academic Discipline Manager for MathWorks, gave a hybrid seminar in HPE DSI’s Data Visualization Laboratory, discussing two innovative applications of linear algebra: machine learning and cybersecurity.

Linear algebra stands as the foundation for many fields of work, such as mathematics, statistics, and computer science. MathWorks, the developers of MATLAB, is on a mission to modernize the way linear algebra is taught in today’s world, as well as introduce practical applications in the classroom.

In the first half of the seminar, Mike presented a linear algebra-based algorithm that can classify handwritten digits, which can be used in the classroom to enhance student learning. Inspired by the honors thesis of Zecheng Kuang, an undergraduate student at the University of California San Diego, this process utilizes the Gram Schmidt algorithm or the singular value decomposition to calculate the “digit spaces” of a MNIST training dataset, obtaining a framework that can be used as a recognition system. The unfolded vector from an unknown digit image is then projected onto every known digit space for classification.

Mike walked through the algorithm in an interactive MATLAB demo, where he showcased two modules: “Recognizing Handwritten Digits”, which contains the overview of the algorithm, exercises, training, and testing components for classroom application, and “Read My Writing”, which students can use to test the algorithm on their own handwriting.

In the second half of the seminar, Mike centered on matrix/meta-factorization and its role in unlocking state-of-the-art cybersecurity research, focused specifically on Distributed Denial of Service (DDoS) attacks. He talked about the FLDX, an adaptive DDoS protection system that detects and mitigates malicious traffic, and how it uses MATLAB to compute and control incoming attacks. The technology, originally developed by Polish national research institute NASK, is reportedly able to suppress network traffic anomalies in just 15 seconds. To track down an attack’s sources, the interface samples network traffic and then calculates a mixing matrix, which can be used to identify dominant signals for the sampled matrix-based representation of traffic flow. Mike ended the seminar by providing a quick overview of the FLDX’s DDoS attack detection and mitigation workflow.