PPT-We saw last the notion of a subspace

W of a vector space V Recall Definition The examples we have seen so far originated from considering the span of the column vectors of a matrix A or the solution set of the equation. Moritz . Hardt. , David P. Woodruff. IBM Research . Almaden. Two Aspects of Coping with Big Data. Efficiency. Handle. enormous inputs. Robustness. Handle . adverse conditions. Big Question: Can we have both?. . Mardani. , Gonzalo . Mateos. and . Georgios. . Giannakis. ECE Department, University of Minnesota. Acknowledgment. : . AFOSR MURI grant no. FA9550-10-1-0567. Vancouver, Canada. May 18, 2013. Rank Minimization for Subspace Tracking from Incomplete Data. T y = In the plane, the space containing only the zero vector and any line through the origin ar n 12 5 into two perpendicular subspaces. For A = 2 4 10 , the row space has 1 dimension 1 and basi M. Soltanolkotabi E.Elhamifar E.J. Candes. 报告. 人：万晟、元玉慧. 、. 张. 驰. 昱. 信息科学与技术学院. 智. 能科学系. 1. Main Contribution. Existing work. Subspace Clustering. Real Vector Spaces. Subspaces. Linear Independence. Basis and Dimension. Row Space, Column Space, and Nullspace. Rank and Nullity. 2. 5-2 Subspaces. A . subset. . W. of a vector space . V. is called a . Asymptotics. Yining Wang. , Jun . zhu. Carnegie Mellon University. Tsinghua University. 1. Subspace Clustering. 2. Subspace Clustering Applications. Motion Trajectories tracking. 1. 1 . (. Elhamifar. Zeev . Dvir. (Princeton). Shachar. Lovett (IAS). STOC 2012. Subspace evasive sets. is . (. k,c. ) subspace evasive. if for any k-dimensional linear subspace V, . Motivation. is . Yining Wang. , Yu-Xiang Wang, . Aarti. Singh. Machine Learning Department. Carnegie . mellon. university. 1. Subspace Clustering. 2. Subspace Clustering Applications. Motion Trajectories tracking. 1. René Vidal. Center for Imaging Science. Institute for Computational Medicine. Johns Hopkins University. Data segmentation and clustering. Given a set of points, separate them into multiple groups. Discriminative methods: learn boundary. A Deterministic Result. 1. st. Annual Workshop on Data Science @. Tennessee . State University. 1. Problem Definition . (. Robust Subspace Clustering). input. output. white noise. outliers. m. issing entries. Venkat. . Guruswami. , Nicolas Resch and . Chaoping. Xing. Algebraic . Pseudorandomness. Traditional pseudorandom objects (e.g., . expander graphs. , . randomness extractors. , . pseudorandom generators. It’s no secret that this world we live in can be pretty stressful sometimes. If you find yourself feeling out-of-sorts, pick up a book.According to a recent study, reading can significantly reduce stress levels. In as little as six minutes, you can reduce your stress levels by 68%. The Benefits of Reading Books,Most people read to read and the benefits of reading are surplus. But what are the benefits of reading. Keep reading to find out how reading will help you and may even add years to your life!.The Benefits of Reading Books,What are the benefits of reading you ask? Down below we have listed some of the most common benefits and ones that you will definitely enjoy along with the new adventures provided by the novel you choose to read.,Exercise the Brain by Reading .When you read, your brain gets a workout. You have to remember the various characters, settings, plots and retain that information throughout the book. Your brain is doing a lot of work and you don’t even realize it. Which makes it the perfect exercise! . H. HABEEB RANI. Assistant professor of Mathematics. Department of mathematics. Hajee. . Karutha. . Rowther. . Howdia. College. VECTOR SPACES. Definition. Examples. THEOREM. Subspaces.