PPT-Sketching and Embedding are Equivalent for Norms

Author : giovanna-bartolotta | Published Date : 2016-04-04

Alexandr Andoni Simons Institute Robert Krauthgamer Weizmann Institute Ilya Razenshteyn CSAIL MIT 1 Sketching Compress a massive object to a small sketch

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Sketching and Embedding are Equivalent for Norms: Transcript

Alexandr Andoni Simons Institute Robert Krauthgamer Weizmann Institute Ilya Razenshteyn CSAIL MIT 1 Sketching Compress a massive object to a small sketch Rich theories . Non-normed spaces. Alexandr. . Andoni. (MSR). Embedding / Sketching. Definition. : an embedding . is a map . f:M. . H. . of a metric . (M, . d. M. ). into a host metric . (H, . . H. ). such that for any . Alexandr. . Andoni. (MSR). Definition by example. Problem. : Compute the diameter of a set . S. , of size . n. , living in . d. -dimensional . ℓ. 1. d. Trivial solution: . O(d * n. 2. ) . time. Will see solution in . are Equivalent for Norms. Alexandr Andoni . (Simons Inst. / Columbia). Robert . Krauthgamer. . (Weizmann. . Inst.). Ilya . Razenshteyn . (MIT, now at IBM . Almaden. ). 1. Sketching. n. d. When is sketching possible?. Sublinear. Algorithms:. Euclidean space: . dimension reduction and NNS. Alex Andoni. (MSR SVC). A Sketching Problem. 2. Sketching:. :objects . short bit-strings. given . . and . . should be able to deduce if . Purposes of Sketching. Think through a design. Convey your ideas. Uses lines and symbols to describe a design. Common Uses of Sketching . Brainstorm. Communicate. Document Measurements. Advantages of Sketching. Sketching. for streaming. Alexandr. . Andoni. (MSR). Application: Streaming. IP. Frequency. 131.107.65.14. 3. 18.0.1.12. 2. 80.97.56.20. 2. 131.107.65.14. 131.107.65.14. 131.107.65.14. 18.0.1.12. 18.0.1.12. © 2012 Project Lead The Way, Inc.. Introduction to Engineering Design. Sketching an Isometric Circle. Circular features and cylindrical forms are common in engineering designs, and appear as . ellipses. Design and Modeling. Common Uses of Sketching . Brainstorm. Communicate. Document. Advantages of Hand Sketching. Convenient. Inexpensive. Sketching Techniques. Lines. Vertical Line. Horizontal Line. English II. What is embedding? . Embedding involves selecting only the most important words in your text evidence. In other words, you will never use an entire sentence from the text verbatim (that means word-for- word). . Ilya Razenshteyn . (MIT CSAIL). j. oint with. Alexandr Andoni . (Columbia University). Aleksandar Nikolov . (University of Toronto). Erik Waingarten . (Columbia University). arXiv:1611.06222. Motivation. 2. Alex Andoni. Plan. 2. Dimension reduction. Application: Numerical Linear Algebra. Sketching. Application: Streaming. Application: Nearest Neighbor Search. and more…. Dimension reduction: . linear . © 2012 Project Lead The Way, Inc.. Introduction to Engineering Design. Sketching an Isometric Circle. Circular features and cylindrical forms are common in engineering designs, and appear as . ellipses. by: R. Yang. ,. . J. Shi. ,. . X. Xiao. ,. . Y. Yang. ,. . J. Liu. ,. . and . S. . Bhowmick. Basic data analytics is easy.. Stock. Profit. Revenue. Market share. Overvalued?. Buy?. TSLA. $721m. $31B. Robert Krauthgamer, . Weizmann Institute of Science. Bertinoro. . workshop, May . 2014. Joint work with . Alexandr. . Andoni. and David Woodruff. TexPoint. fonts used in EMF. . Read the . TexPoint.

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