Bagging the Peaks: Matrix and Tensor Factorization with Unimodal Constraints

We consider matrix and tensor factorization problems where there are unimodal constraints. Such methods find application in a variety of problems such as target localization, environmental monitoring, epidemic detection, and medical diagnosis. We presume that we have incomplete (sparse) and noisy samples of a particular field or image and that our objects of interest have spatial extent and can be modeled as unimodal: there is a single strong signal peak and this signal decays as one moves away from the strong signal peak. By exploiting modern signal processing techniques such as matrix completion and active search methods, we develop a high performance, moderate complexity algorithm for peak detection. This method is extended to the case of multiple targets via novel matrix factorization and isotonic projection methods. We further extend the approach to handle multimodal sensor data by exploiting tensor completion methods. Finally, we show how we can exploit our methods to solve a data clustering problem which is motivated by the application of radio map building. Radio signals in urban environments can be described by multiple propagation models. We can transform and compress location-labeled wireless channel measurements into a low-dimensional feature matrix. By analyzing the local peaks of the feature matrix, we can identify the regional propagation laws, which enable the clustering of the data. Theoretical performance bounds derived and properties of key matrices are proven. The methods are compared against the state of the art on both synthetic and real data sets and shown to offer superior performance with moderate complexity.

Biography
Urbashi Mitra received the B.S. and the M.S. degrees from the University of California at Berkeley and her Ph.D. from Princeton University. Dr. Mitra is currently the Gordon S. Marshall Professor in Engineering at the University of Southern California with appointments in Electrical Engineering and Computer Science. She was the inaugural Editor-in-Chief for the IEEE Transactions on Molecular, Biological and Multi-scale Communications. She has been a member of the IEEE Information Theory Society’s Board of Governors (2002-2007, 2012-2017), the IEEE Signal Processing Society’s Technical Committee on Signal Processing for Communications and Networks (2012-2016), the IEEE Signal Processing Society’s Awards Board (2017-2018), and the Chair/Vice-Chair of the IEEE Communication Theory Technical Committee (2017-2020). Dr. Mitra is a Fellow of the IEEE. She is the recipient of: the 2017 IEEE Women in Communications Engineering Technical Achievement Award, a 2015 UK Royal Academy of Engineering Distinguished Visiting Professorship, a 2015 US Fulbright Scholar Award, a 2015-2016 UK Leverhulme Trust Visiting Professorship, IEEE Communications Society Distinguished Lecturer, 2012 Globecom Signal Processing for Communications Symposium Best Paper Award, 2012 US National Academy of Engineering Lillian Gilbreth Lectureship, the 2009 DCOSS Applications & Systems Best Paper Award, Texas Instruments Visiting Professorship (Fall 2002, Rice University), 2001 Okawa Foundation Award, 2000 Ohio State University’s College of Engineering Lumley Award for Research, 1997 Ohio State University’s College of Engineering MacQuigg Award for Teaching, and a 1996 National Science Foundation CAREER Award. She has been an Associate Editor for the following IEEE publications: Transactions on Signal Processing, Transactions on Information Theory, Journal of Oceanic Engineering, and Transactions on Communications. Dr. Mitra has held visiting appointments at: King’s College, London, Imperial College, the Delft University of Technology, Stanford University, Rice University, and the Eurecom Institute. Her research interests are in: wireless communications, communication and sensor networks, biological communication systems, detection and estimation and the interface of communication, sensing and control.