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      Electrical & Computer Engineering Fall Seminar Series in Georgetown

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      October 1, 2020

      Thursday  11:15 AM

      16483 County Seat Highway
      Georgetown, Delaware 19947

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      Electrical & Computer Engineering Fall Seminar Series

      SPC Speaker, Dimitris A. Pados, Florida Atlantic University

      Title: Data Analytics and Machine Learning with L1-norm Principal Components


      Principal-component analysis (L2-norm-based), frequently called (eigen-)feature extraction in machine learning literature, has been lifeblood of data/signal processing with defining applications in classification and estimation in the past hundred years. In this talk, we ask questions on L1-norm principal-component analysis (L1-PCA). The answers that we can provide at this time feed optimism that a new line of L1-PCA data/signal processing is possible that can revolutionize modern outlier-resistant machine learning principles.

      Along these lines, we first describe ways to define and calculate L1-norm principal components (data/signal subspaces) which are less sensitive to outlying data (faulty measurements) than L2-calculated components. We start with the computation of the L1 maximum-projection principal component of a data matrix containing N signal samples of dimension D. We show that while the general problem is formally NP-hard in jointly asymptotically large N, D, surprisingly the case of practical interest of fixed dimension D and asymptotically large sample size N is not. For the case where the sample size is less than the fixed dimension (N < D), we present in explicit form an optimal algorithm that computes the L1-norm principal component with computational cost 2^N. For the case N >= D, we present an optimal algorithm of complexity O(N^D). We generalize to multiple components and present an explicit optimal L1-subspace calculation algorithm of complexity O(N^DK) where K is the desired number of L1 principal components/features (subspace rank). A near-optimal calculator of L1-norm principal components with computational complexity similar to conventional singular-value decomposition is also presented. We conclude with illustrations of optimal L1-PCA data processing in the fields of data conditioning and dimensionality reduction, direction-of-arrival estimation, and image restoration. The findings show that L1-PCA is about the same/as great as L2-PCA on clean training data. When the data set is corrupted, the superiority of L1-PCA is unequivocal at all corruption levels. Does this mean that L2-PCA is to be replaced by L1-PCA in the future?


      Dimitris A. Pados received the Ph.D. degree in electrical engineering with minors in mathematics and computer science from the University of Virginia. From 1997 to 2017, he was with the Department of Electrical Engineering, The State University of New York at Buffalo, holding in sequence the titles of Assistant Prof., Associate Prof., Professor, and Clifford C. Furnas Endowed Chair Professor. He served the Department as Associate Chair in 2009-2010 and was appointed Chair in June 2017. Dr. Pados was elected four times University Faculty Senator and served on the University Budget Priorities Committee and the Faculty Senate Executive Committee. In Aug. 2017, he joined Florida Atlantic University in Boca Raton, FL as the Schmidt Eminent Chair Professor of Engineering and Computer Science and Fellow of the I-SENSE Institute. Dr. Pados is the Founding Director of the FAU Center for Connected Autonomy and Artificial Intelligence. His research interests are in the general areas of communications theory and systems, artificial intelligence, machine learning and data analytics with applications to connected AI and autonomous systems, training dataset curation and operational data screening. He served as an Associate Editor for the IEEE Transactions on Neural Networks and the IEEE Signal Processing Letters and has published more than 220 journal and conference proceedings articles in predominantly IEEE venues. Articles that he co-authored with his students received distinctions that include the IEEE Intern. Conf. on Telecomm. best paper award, IEEE Transactions on Neural Networks Outstanding Paper Award, IEEE ICC Best Paper Award, Intern. Symposium on Wireless Comm. Systems Best Paper Award, Best of IEEEE GLOBECOM - Top 50 Papers Special Presentation, Best Paper Selection IEEE Intern. Conf. on Multimedia Big Data (IEEE BigMM) and others. Professor Pados has been a recipient of the SUNY-system-wide Chancellor's Award for Excellence in Teaching and the University at Buffalo Exceptional Scholar – Sustained Achievement Award. His academic research work has been supported cumulatively over the past twenty years by federal sources (NSF and DoD) with grants of about $17M.

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