PPT-Lossless Dimension Expanders via Linearized Polynomials and Subspace Designs

Venkat Guruswami Nicolas Resch and Chaoping Xing Algebraic Pseudorandomness Traditional pseudorandom objects eg expander graphs randomness extractors pseudorandom generators. 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?. Tali Kaufman. Joint work with Irit Dinur. Codes as CSPs . A constraint satisfaction problem (CSP) is a sequence of constraints over variables:. f. 1 . (x. 1. ,x. 2. ,x. 5. ), f. 2 . (x. 5. ,x. 1. ,x. 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. Goal: To simplify polynomial expressions by adding or subtracting. Standard: . 9.2.3.2 – Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.. Guiding Question: How do I simplify polynomials expressions? AND how do I add or subtract polynomials expressions?. Tali Kaufman. Joint work with Irit Dinur. Codes as CSPs . A constraint satisfaction problem (CSP) is a sequence of constraints over variables:. f. 1 . (x. 1. ,x. 2. ,x. 5. ), f. 2 . (x. 5. ,x. 1. ,x. Asymptotics. Yining Wang. , Jun . zhu. Carnegie Mellon University. Tsinghua University. 1. Subspace Clustering. 2. Subspace Clustering Applications. Motion Trajectories tracking. 1. 1 . (. Elhamifar. 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. Yining Wang. , Yu-Xiang Wang, . Aarti. Singh. Machine Learning Department. Carnegie . mellon. university. 1. Subspace Clustering. 2. Subspace Clustering Applications. Motion Trajectories tracking. 1. 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?. 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. Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems. Students will know the terms for polynomials.. Students will know how to arrange polynomials in ascending and descending order.. 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. Metric . Embeddings. COMS E6998-9. . F15. Administrivia. , Plan. PS2:. Pick up after class. 120->144 auto extension. Plan:. Least Squares Regression (finish). Metric . Embeddings. “reductions for distances”.