PPT-The Sketching Complexity of Graph Cuts

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. Michael Tao and Patrick Virtue. Agenda. History of the problem. Graph cut background. Compute graph cut. Extensions. State . of the art. Continued Work. Agenda. History of the problem. Graph cut background. Why graph clustering is useful?. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. Xiaoming. Sun and David P. Woodruff. Chinese Academy of Sciences and IBM Research-. Almaden. Streaming Models. Long sequence of items appear one-by-one. numbers, points, edges, …. (usually) . adversarially. Simon Prince. s.prince@cs.ucl.ac.uk. Plan of Talk. Denoising. problem. Markov random fields (MRFs). Max-flow / min-cut. Binary MRFs (exact solution). Binary . Denoising. Before. After. Image represented as binary discrete variables. Some proportion of pixels randomly changed polarity.. Why graph clustering is useful?. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. . . July 2008. Optimization of surface functionals . using . graph . cut algorithms. Yuri Boykov. presenting joint work with. V. .. Kolmogorov. ,. . O.Veksler, . D. .. Cremers. Many slides drawn from presentations by Simon Prince/UCL and Kevin Wayne/Princeton. Image . Denoising. Foreground Extraction. Stereo Disparity. Why study MRFs?. Image . denoising. is based on modeling what kinds of images are more probable. 25. . Rational Functions. Rational Functions. A function of the form. . f. (. x. ) = . N. (. x. )/. D. (. x. ). ,. where . N. . and . D . are both polynomials. . Examples:. What we will be doing. Finding some characteristics of rational functions that will help us to be able to graph the function. Robert Krauthgamer, . Weizmann Institute of Science. WorKer. 2015, . Nordfjordeid. TexPoint. fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. Graph . Sparsification. Why graph clustering is useful?. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. Xiaoming. Sun and David P. Woodruff. Chinese Academy of Sciences and IBM Research-. Almaden. Streaming Models. Long sequence of items appear one-by-one. numbers, points, edges, …. (usually) . adversarially. Agenda. History of the problem. Graph cut background. Compute graph cut. Extensions. State . of the art. Continued Work. Agenda. History of the problem. Graph cut background. Compute graph cut. Extensions. Distance matrices are graphs .  as useful as any other clustering. Identification of communities in social networks. Webpage clustering for better data management of web data. Outline. Min s-t cut problem. Segmentation . with Graph Cuts. Computer Vision. Jia-Bin Huang, Virginia Tech. Many slides from D. Hoiem. Administrative stuffs. Final project . Proposal due . Oct 27 (Thursday. ). HW 4 is out. Due 11:59pm .