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AWDS-2015 - Mini Courses

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Mini Courses

Dr. Ali Sekmen , Professor of Computer Science
Tennessee State University

Title: Fundamentals from Real Analysis ( slides pptx )

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Abstract: This mini course will introduce various spaces that include normed vector, inner product, metric, topological, Banach, and Hilbert spaces. The subspaces and manifolds concepts will be briefly introduced. Some properties of subspaces will be explained (e.g. disjoint, independent subspaces, angles and distances between subspaces). The notion of infinite dimensional spaces will be discussed with some examples.

Title: Subspace Segmentation, PCA, and Spectral Clustering ( slides pptx )

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Abstract: Principle Component Analysis (PCA) will be introduced for clustering of data that comes from a single space. Then, the subspace segmentation problem will be introduced for data that comes from a union of subspaces. The mathematical proof will be provided to show that the motion segmentation problem can be cast as a subspace segmentation problem. Most of the state-of-the-art subspace clustering algorithms utilizes some variants of the Spectral Clustering algorithm. Therefore, the Spectral Clustering algorithm will also be introduced.

Biography
Dr. Ali Sekmen is a Professor of Computer Science and the Chair of the Computer Science Department at Tennessee State University, Nashville, TN. He holds PhD degrees in Electrical Engineering and also in Mathematics, both from Vanderbilt University. Dr. Sekmen is the director of the Robotics and Intelligent Systems Laboratory (RISL) at Tennessee State University. He has published over 50 research papers in approximation theory, robotics, and artificial intelligence. He has been involved in funded research activities in the areas of approximation theory, robotics, control systems, signal processing, and computer vision funded by various agencies and companies including NSF, NASA, and AFRL.

Dr. Ghan S. Bhatt, Associate Professor of Mathematics
Tennessee State University

Title: Fundamentals from Linear Algebra ( slides pptx )

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Abstract: This mini course will introduce fundamental linear algebra concepts including eigenvalues, eigenvectors, matrix decompositions, and different matrix norms. It will also explain Singular Value Decomposition (SVD) and its geometric interpretation. Closest k-rank approximation via SVD will also be discussed.

Biography
Dr. Bhatt is an associate professor in the department of Mathematical Sciences, Tennessee State University. He did his Masters degree in Mathematics from Tribhuvan University, Kathmandu, Nepal. He did diploma in Mathematics from The Abdus Salam International Center for Theoretical Physics (ICTP), Trieste, Italy. He did his Ph.D. from Iowa State University in Applied Mathematics. He has been working in application and construction of wavelets and frames.