**Invited Talks to RSL-CV 2017**

**Title: **Dynamic Mode Decomposition for Background Modeling

**Abstract:**

The dynamic mode decomposition (DMD) is a spatio-temporal matrix decomposition method that has recently been introduced for background modeling in video streams. DMD is a regression technique that integrates two of the leading data analysis methods in use today: Fourier transforms and singular value decomposition. Innovations in compressed sensing and matrix sketching allow for a scalable and rapid decomposition of video streams that scales with the intrinsic rank of the matrix, rather than the size of the actual video (data) matrix. Moreover, the temporal decomposition can leverage concepts from wavelet analysis in order to produce a hierarchy of multi-resolution time-scaled components, thus allowing for separation of different foreground components in a video. Our results show that the quality of the resulting background model is competitive, quantified by the F-measure, recall and precision. A GPU (graphics processing unit) accelerated implementation is also possible which further boosts the computational performance of the algorithm. The GPU algorithm can also be parallelized using the streaming method of snapshots singular value decomposition. This allows the algorithm to operate efficiently on streaming data by avoiding redundant inner-products as new data becomes available. In addition, it is possible to leverage the native compressed format of many data streams, such as HD video and computational physics codes that are represented sparsely in the Fourier domain, to massively reduce data transfer from CPU to GPU and to enable sparse matrix multiplications. Taken together, these algorithms facilitate real-time streaming DMD on high-dimensional data streams.

**Biography:** Professor Nathan Kutz was awarded the B.S. in Physics and Mathematics from the University of Washington in 1990 and the PhD in Applied Mathematics from Northwestern University in 1994. Following postdoctoral fellowships at the Institute for Mathematics and its Applications (University of Minnesota, 1994-1995) and Princeton University (1995-1997), he joined the faculty of applied mathematics and served as Chair from 2007-2015. He is interested combining data-driven methods and machine learning with dynamical systems and partial differential equations.

**Title: Incremental Robust Principal Component Analysis for Video Background Modeling via projections onto the L1-ball**

**Abstract:**

**Biography:** Professor Paul Rodriguez received the BSc degree in electrical engineering from the « Pontificia Universidad Católica del Perú » (PUCP), Lima, Peru, in 1997, and the MSc and PhD degrees in electrical engineering from the University of New Mexico, USA, in 2003 and 2005 respectively. He spent two years (2005-2007) as a postdoctoral researcher at Los Alamos National Laboratory, and is currently a Full Professor with the Department of Electrical Engineering at PUCP. His research interests include AM-FM models, parallel algorithms, adaptive signal decompositions, and inverse problems in signal and image processing.

**Title: Dynamic Robust PCA and Applications in Video Analytics **

**Abstract:**

While PCA is a classical well studied problem, PCA techniques fail if the data is corrupted by anything other than small noise. However, modern datasets are usually corrupted by sparse outliers which may have large magnitudes. Moreover, for long sequences, the subspace in which the data lies also changes with time, albeit gradually. This problem of tracking the low dimensional subspace in which a given dataset lies, in the presence of sparse outliers, is referred to as dynamic robust PCA. While the static robust PCA problem has received a lot of attention in recent literature, the dynamic problem is largely open. In a recent body of work that starting in 2010, we introduced the first provably correct and practically usable solution framework for dynamic robust PCA called Recursive Projected Compressive Sensing (ReProCS). Because it exploits slow subspace change, we can both prove and demonstrate that ReProCS is able to tolerate a much larger fraction of outliers than the existing static robust PCA solutions, while enjoying the extra advantages of being fast, online and memory-efficient. One important application domain where the above problem arises is in computer vision and video analytics in trying to separate a given video into a sparse foreground layer (consisting of one or more moving objects) and a slowly changing but dense background layer on-the-fly. This video layering problem is often the first important step in solving many high-level computer vision problems. We will show experimental comparisons for video layering and for video enhancement and denoising. In both cases, we demonstrate that ReProCS outperforms existing techniques for videos involving slow moving and occasionally static or large-sized foreground objects.

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**Biography:** Professor Namrata Vaswani received a B.Tech. from the Indian Institute of Technology (IIT-Delhi), in 1999, and a Ph.D. from the University of Maryland, College Park, in 2004, both in Electrical Engineering. During 2004-05, she was a postdoctoral fellow and research scientist at Georgia Tech. Since Fall 2005, she has been with the Iowa State University where she is currently a Professor of Electrical and Computer Engineering and (by courtesy) of Mathematics. Her research interests lie at the intersection of data science and machine learning for high dimensional problems, signal and information processing, and computer vision and bio-imaging. Her most recent work has focused on provably correct and practically useful algorithms for dynamic robust PCA, dynamic compressive sensing, correlated-PCA, and low rank phase retrieval. Prof. Vaswani has served one term as an Associate Editor for the IEEE Transactions on Signal Processing (2009-2012) and is currently serving her second term. She is a recipient of the Harpole-Pentair Assistant Professorship at Iowa State (2008-09), the Iowa State Early Career Engineering Faculty Research Award (2014) and the IEEE Signal Processing Society Best Paper Award (2014) for her Modified-CS paper (that appeared in IEEE Trans. Sig. Proc. in Sept. 2010).

**Title: Innovation pursuit: A new geometrical approach for subspace clustering**

**Abstract**: In subspace clustering, a group of data points belonging to a union of subspaces are assigned membership to their respective subspaces. In our recently released research work, we presented a new approach dubbed Innovation Pursuit to the problem of subspace clustering using a new geometrical idea whereby subspaces are successively identified based on their relative novelties. The proposed approach finds the subspaces by solving a series of simple linear optimization problems, each searching for some direction of innovation in the span of the data that is potentially orthogonal to all subspaces except for the one to be identified in one step of the algorithm. We provided a detailed mathematical analysis establishing sufficient conditions for the proposed approach to correctly cluster the data points. The proposed approach can provably yield exact clustering even when the subspaces have significant intersections under mild conditions on the distribution of the data points in the subspaces. The numerical simulations with both real and synthetic data demonstrated that Innovation pursuit often outperforms the state-of-the-art subspace clustering algorithms, more so for subspaces with significant intersections. The proposed idea for direction search underlying Innovation pursuit is also integrated with spectral clustering to yield a new variant of spectral clustering based algorithms. The integration of proposed approach with spectral clustering yields the state-of-the-art results for the problem of face clustering using subspace segmentation.

**Bio**: Professor George K. Atia received the B.Sc. and M.Sc. degrees from Alexandria University, Egypt, in 2000 and 2003, respectively, and the Ph.D. degree from Boston University, MA, in 2009, all in electrical and computer engineering. He joined the University of Central Florida in Fall 2012, where he is currently an assistant professor in the Department of Electrical and Computer Engineering. From Fall 2009 to 2012, he was a postdoctoral research associate at the Coordinated Science Laboratory (CSL) at the University of Illinois at Urbana-Champaign (UIUC). Dr. Atia is the recipient of many awards, including the NSF CAREER Award in 2016, the Inaugural UCF Luminary Award and the Dean’s Advisory Board Fellowship Award in 2017, the Charles N. Millican Faculty Fellowship Award in 2015, and the best paper award at the International Conference on Distributed Computing in Sensor Systems (DCOSS) in 2008. His research interests include statistical signal processing, machine learning, stochastic control, wireless communications, detection and estimation theory, and information theory.