Week 1
Lecture 01: Introduction, 1/9/2018
Course logistics, overview.
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Lecture 02: HD, 1/11/2018
Visualization pipeline, dimensionality reduction and vis: PCA
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Mandatory Reading and Tasks:
- Scikit-learn tutorial.
- Install and read the documentation of kepler-mapper.
Recommended Reading:
- Interactive Data Visualization for the Web, 2nd Ed. Scott Murray, 2017.
- [LiuMaljovecWang2017]: Visualizing High-Dimensional Data: Advances in the Past Decade.
Shusen Liu, Dan Maljovec, Bei Wang, Peer-Timo Bremer and Valerio Pascucci, IEEE Transactions on Visualization and Computer Graphics (TVCG), 2017.
- [JeongZiemkiewiczFisher2009]: iPCA: An Interactive System for PCA-based Visual Analytics.
Dong Hyun Jeong, Caroline Ziemkiewicz, Brian Fisher, William Ribarsky and Remco Chang, Computer Graphics Forum, 2009.
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Week 2
Lecture 03: HD, 1/16/2018
Dimensionality reduction and vis: t-SNE.
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Project 1 has been posted!
Lecture 04: HD+TOPO, 1/18/2018
Mapper, clustering and beyond.
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Mandatory Reading and Tasks:
- [SinghMemoliCarlsson2007]: Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition. Gurjeet Singh, Facundo Mémoli,
and Gunnar Carlsson, Eurographics Symposium on Point-Based Graphics, 2007
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[LumSinghLehman2013]: Extracting insights from the shape of complex data using topology.
P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Vejdemo-Johansson, M. Alagappan, J. Carlsson, and G. Carlsson, Scientific Reports, 2013.
- [vanderMaatenHinton2008]:
Visualizing Data using t-SNE. Laurens van der Maaten and Geoffrey Hinton, Journal of Machine Learning Research, 9, pages 2579-2605, 2008.
Recommended Reading:
-
[BrunoRomanoMazaika2017]: Longitudinal identification of clinically distinct
neurophenotypes in young children with
fragile X syndrome.
Jennifer L. Bruno, David Romano, Paul Mazaika, Amy A. Lightbody, Heather Cody Hazlett, Joseph Piven,
and Allan L. Reiss, PNAS, 114(40), pages 10767-10772, 2017.
- [Carlsson2009]: Topology and data.
Bulletin of the American Mathematical Society, 46, pages 255-308, 2009.
- [DeyMemoliWang2016]:
Multiscale Mapper: Topological Summarization via Codomain Covers.
Tamal K. Dey, Facundo Memoli, and Yusu Wang, Proceedings of the 27th annual ACM-SIAM symposium on Discrete algorithms, pages 997-1013, 2016.
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[DeyMemoliWang2017]:Topological Analysis of Nerves, Reeb Spaces, Mappers, and Multiscale Mappers. Tamal K. Dey, Facundo Memoli, and Yusu Wang, arXiv:1703.07387, 2017.
- [NicolauLevineCarlsson2011]:
Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and
excellent survival.
Monica Nicolau, Arnold J. Levine, and Gunnar Carlsson,
PNAS, 2011.
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Week 3
Lecture 05: HD, 1/23/2018
More DR, clustering and visualization.
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Lecture 06: HD, 1/25/2018
Subspace clustering, regression and vis.
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Mandatory Reading and Tasks:
- [LeeVerleysen2009]: Quality assessment of dimensionality reduction: Rank-based criteria. John A. Lee and Michel Verleysen, Neurocomputing, 72, pages 1431-1443 2009.
- Section 3.2 of [LiuMaljovecWang2017]: Visualizing High-Dimensional Data: Advances in the Past Decade.
Shusen Liu, Dan Maljovec, Bei Wang, Peer-Timo Bremer and Valerio Pascucci, IEEE Transactions on Visualization and Computer Graphics (TVCG), 2017.
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[GerberBremerPascucci2010]: Visual Exploration of High Dimensional Scalar Functions.
Samuel Gerber, Peer-Timo Bremer, Valerio Pascucci and Ross Whitaker,
IEEE Transactions on Visualization and Computer Graphics, 16(6), pages 1271 - 1280, 2010.
Recommended Reading:
-
[BrownLiuBrodley2012]:
Dis-Function: Learning Distance Functions Interactively.
Eli T. Brown, Jingjing Liu, Carla E. Brodley, and Remco Chang,
IEEE Conference on Visual Analytics Science and Technology, pages 83-92,
2012.
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[YuanRenWang2013]:
Dimension Projection Matrix/Tree: Interactive Subspace Visual Exploration and Analysis of High Dimensional Data.
Xiaoru Yuan, Donghao Ren, Zuchao Wang, and Cong Guo,
IEEE Transactions on Visualization and Computer Graphics (TVCG), 19(12), pages 2625 - 2633, 2013.
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[TurkayLundervoldLundervold2012]:
Representative factor generation for the interactive visual analysis of high-dimensional data.
Cagatay Turkay, Arvid Lundervold, Astri Johansen Lundervold, and Helwig Hauser,
IEEE Transactions on Visualization and Computer Graphics, 18(12), pages 2621 - 2630, 2012.
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[TurkayFilzmoserHauser2011]:
Brushing Dimensions -
A Dual Visual Analysis Model for High-Dimensional Data.
Cagatay Turkay, Peter Filzmoser, and Helwig Hauser,
IEEE Transactions on Visualization and Computer Graphics (TVCG),
17(12), pages 2591 - 2599, 2011.
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[PaulovichSilvaNonato2010]:
Two-Phase Mapping for Projecting Massive Data Sets.
Fernando V. Paulovich, Claudio T. Silva, and Luis G. Nonato,
IEEE Transactions on Visualization and Computer Graphics, 16(6), pages 1281 - 1290, 2010.
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[MokbelLueksGirbrecht2013]:
Visualizing the quality of dimensionality reduction.
Bassam Mokbel, Wouter Lueks, Andrej Gisbrecht, and Barbara Hammer.
Neurocomputing, 112 (18), pages 109-123, 2012.
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[AnandWilkinsonDang2012]: Visual Pattern Discovery using Random Projections.
Anushka Anand, Leland Wilkinson, and Tuan Nhon Dang,
IEEE Conference on Visual Analytics Science and Technology (VAST), 2012.
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[ChengFuZhang1999]: Entropy-based Subspace Clustering for Mining Numerical Data.
Chun-Hung Cheng,
Ada Waichee Fu, and Yi Zhang.
Proceedings of the 5th ACM SIGKDD international conference on Knowledge discovery and data mining (KDD), pages 84-93, 1999.
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[LiuWangThiagarajan2015]:
Visual Exploration of High-Dimensional Data through Subspace Analysis and Dynamic Projections.
Shusen Liu, Bei Wang, Jayaraman J. Thiagarajan, Peer-Timo Bremer and Valerio Pascucci,
Computer Graphics Forum (CGF), 34(3), pages 271-280, 2015.
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[PiringerBergerKrasser2010]: HyperMoVal: Interactive Visual Validation of Regression Models for Real-Time Simulation.
H. Piringer, W. Berger, and J. Krasser,
Computer Graphics Forum (CGF), 29(3), pages 983-992, 2010.
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[Rodriguez-MartinezGoulermasMu2010]: Automatic Induction of Projection Pursuit Indices.
E. Rodriguez-Martinez, John Yannis Goulermas, Tingting Mu, and Jason F. Ralph,
IEEE Transactions on Neural Networks, 21(8), 2010.
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Week 4
Lecture 07: HD, 1/30/2018
Visual mapping for high-dimensional data.
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Lecture 08: HD, 2/1/2018
Visual mapping for high-dimensional data continued.
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Project 1 Due!
Project 2 Posted! (Download via Canvas)
Mandatory Reading and Tasks:
- Section 4 of [LiuMaljovecWang2017]: Visualizing High-Dimensional Data: Advances in the Past Decade.
Shusen Liu, Dan Maljovec, Bei Wang, Peer-Timo Bremer and Valerio Pascucci, IEEE Transactions on Visualization and Computer Graphics (TVCG), 2017.
Recommended Reading:
-
[SachaZhangSedlmair2016]: Visual Interaction with Dimensionality Reduction: A Structured Literature Analysis.
Dominik Sacha, Leishi Zhang, Michael Sedlmair, John A. Lee, Jaakko Peltonen,
Daniel Weiskopf, Stephen C. North, Daniel A. Keim,
IEEE Transactions on Visualization and Computer Graphics (TVCG), 23 (1), pages 241 - 250, 2016.
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[WenskovitchCrandell Ramakrishnan2018]: Towards a Systematic Combination of Dimension Reduction and Clustering in Visual Analytics.
John Wenskovitch, Ian Crandell, Naren Ramakrishnan, Leanna House, Scotland Leman, Chris North,
IEEE Transactions on Visualization and Computer Graphics (TVCG), 24(1), pages 131 - 141, 2018.
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[PiringerBergerKrasser2010]: HyperMoVal: Interactive Visual Validation of Regression Models for Real-Time Simulation.
H. Piringer, W. Berger, J. Krasser, Computer Graphics Forum, 2010.
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[ChanCorreaMa2013]:The Generalized Sensitivity Scatterplot.
Yu-Hsuan Chan, Carlos D. Correa, and
Kwan-Liu Ma,
IEEE Transactions on Visualization and Computer Graphics (TVCG), 19(10), 2013.
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[CaoGotzSun2011]: DICON: Interactive Visual Analysis of Multidimensional Clusters.
Nan Cao, David Gotz, Jimeng Sun, and Huamin Qu,
IEEE Transactions on Visualization and Computer Graphics (TVCG), 17(12), 2011.
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[Chernoff1973]: The Use of Faces to Represent Points in K-Dimensional Space Graphically.
Herman Chernoff, Journal of the American Statistical Association,
68(342), 1973.
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[ElmqvistDragicevicFekete2008]: Rolling the Dice: Multidimensional Visual Exploration
using Scatterplot Matrix Navigation.
Niklas Elmqvist, Pierre Dragicevic, and Jean-Daniel Fekete.
IEEE Transactions on Visualization and Computer Graphics (TVCG), 14(6), 2008.
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[EtemadpourMottaPaiva2015]: Perception-Based Evaluation of Projection Methods for Multidimensional Data Visualization.
Ronak Etemadpour, Robson Motta, Jose Gustavo de Souza Paiva, Rosane Minghim, Maria Cristina Ferreira de Oliveira, and Lars Linsen,
IEEE Transactions on Visualization and Computer Graphics (TVCG), 21, 1, 2015.
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[HoltenWijk2010]: Evaluation of Cluster Identification Performance for Different PCP Variants.
Danny Holten and Jarke J. van Wijk,
Computer Graphics Forum,
2010.
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[KeimHaoLadisch2001]: Pixel Bar Charts: A New Technique for Visualizing Large Multi-Attribute Data Sets without Aggregation.
Daniel Keim, Ming C. Hao, Julian Ladisch, Meichun Hsu, Umeshwar Dayal,
IEEE Symposium on Information Visualization, 2001.
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[SedlmairMunznerTory2013]: Empirical Guidance on Scatterplot and Dimension Reduction Technique Choices.
Michael Sedlmair, Tamara Munzner, and Melanie Tory,
IEEE Transactions on Visualization and Computer Graphics (TVCG), 19(12), 2013.
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[GerberBremerPacucci2010]: Visual exploration of high dimensional scalar functions.
S. Gerber, P. Bremer, V. Pascucci, and R. Whitaker, IEEE Transactions on Visualization and Computer Graphics, 16(6), pages 1271-1280, 2010.
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Week 5
Lecture 09: HD, 2/6/2018
View transformation and user interactions, decision trees.
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Lecture 10: HD, 2/8/2018
Deep learning and vis.
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Mandatory Reading and Tasks:
- Section 5 and 6 of [LiuMaljovecWang2017]: Visualizing High-Dimensional Data: Advances in the Past Decade.
Shusen Liu, Dan Maljovec, Bei Wang, Peer-Timo Bremer and Valerio Pascucci, IEEE Transactions on Visualization and Computer Graphics (TVCG), 2017.
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[Moore Lecture: Information Gain]: Andrew Moore's lecture on Information Gain.
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[Moore Lecture: Decision Trees]: Andrew Moore's lecture on Decision Trees.
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[TensorFlow Playground]: Tinker With a Neural Network Right Here in Your Browser.
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[TensorFlow: ML Beginners]: TensorFlow: Getting Started for ML Beginners.
Recommended Reading:
-
[TensorFlow: Getting Started]: TensorFlow: Getting Started with TensorFlow.
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[Deep Learning Tutorial 1]: Deep Learning Tutorial at Stanford University.
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[Deep Learning Tutorial 2]: Neural Networks and Deep Learning by Michael Nielsen.
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[Deep Learning Book]: Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville.
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Week 6
Lecture 11: Guest Lecture, 2/13/2018
An Overview of Design Studies.
Given by Prof. Miriah Meyer.
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Lecture 12: Guest Lecture, 2/15/2018
Current Research on Multivariate Network
Visualization.
Given by Prof. Alex Lex.
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Mandatory Reading and Tasks:
-
[SedlmairMeyerMunzner2012]: Design Study Methodology: Reflections from the Trenches and the Stacks. Michael Sedlmair, Miriah Meyer, Tamara Munzner, IEEE Transactions on Visualization and Computer Graphics (Proceedings of InfoVis 2012), 18(12): 2431-2440, 2012.
Recommended Reading:
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[McCurdyLeinColes2016]: Poemage: Visualizing the Sonic Topology of a Poem. Nina McCurdy, Julie Lein, Katharine Coles, Miriah Meyer. IEEE Transactions on Visualization and Computer Graphics (Proceedings of InfoVis 2015), 22(1):439-448, 2016.
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[FerstayNielsenMunzner2013]:Variant View: Visualizing Sequence Variants in their Gene Context.
Joel A. Ferstay, Cydney B Nielsen and Tamara Munzner.
IEEE Trans. Visualization and Computer Graphics (Proc. InfoVis), 19(12):2546-2555, 2013.
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[NielsenJackmanBirol2009]:ABySS-Explorer: Visualizing genome sequence assemblies. Nielsen CB, Jackman SD, Birol I, Jones SJM. IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization / Information Visualization 2009). 2009. 15(6):881-8.
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[Munzner2008]: Process and Pitfalls in Writing Information Visualization Research Papers.
Tamara Munzner.
Information Visualization: Human-Centered Issues and Perspectives. Andreas Kerren, John T. Stasko, Jean-Daniel Fekete, Chris North, eds. Springer LNCS Volume 4950, p 134-153, 2008.
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Week 7
Lecture 13: TOPO, 2/20/2018
Topological abstraction for scalar field data.
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Lecture 14: TOPO, 2/22/2018
Introduction to Topology ToolKit (TTK).
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Project 2 Due!
Project 3 Posted! (Download via Canvas)
Mandatory Reading and Tasks:
-
Read the documentation of TTK; follow the instructions to install TTK on your own computer.
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Lecture Notes on Morse-Smale Complex by Prof. Guoning Chen.
Recommended Reading:
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[CarrSnoeyinkAxen2003]: Computing contour trees in all dimensions.
Hamish Carr, Jack Snoeyink,Ulrike Axen.
Computational Geometry, 24(2), pages 75-94, 2003.
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[TiernyFavelierLevine2018]: The Topology ToolKit.
Julien Tierny, Guillaume Favelier, Joshua A. Levine,Charles Gueunet, Michael Michaux.
IEEE Transactions on Visualization and Computer Graphics, 24(1), pages 1077-2626, 2018.
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[EdelsbrunnerHarerZomorodian2003]:
Hierarchical Morse-Smale Complexes for Piecewise Linear 2-Manifolds.
Herbert Edelsbrunner, John Harer, Afra Zomorodian.
Discrete & Computational Geometry, 30(1), pages 87-107, 2003.
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Week 8
Lecture 15: TOPO, 2/27/2018
Contour tree and Morse-Smale complex for visualization.
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Lecture 16: TOPO, 3/1/2018
Discrete Morse theory (DMT) for discrete data.
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Mandatory Reading and Tasks:
-
[Forman2002]: A User's Guide To Discrete Morse Theory.
Robin Forman.
Séminare Lotharinen de Combinatore 48, 2002.
Recommended Reading:
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[CarraSnoeyinkPanne2010]: Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree.
Hamish Carr, Jack Snoeyink, Michiel van de Panne.
Computational Geometry: Theory and Applications, 43, pages 42-58, 2010.
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[GuntherReininghausWagner2012]:
Efficient computation of 3D Morse-Smale complexes and persistent homology using discrete Morse theory.
David Günther, Jan Reininghaus, Hubert Wagner, Ingrid Hotz.
The Visual Computer, 28(10), pages 959-969, 2012.
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[KingKnudsonMramor2005]: Generating Discrete Morse Functions from Point Data.
Henry King, Kevin Knudson, and Neza Mramor.
Experimental Mathematics, 14(4), page 435, 2005.
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[GuntherReininghausSeidel2014]: Notes on the Simplification of the Morse-Smale Complex.
D Günther, J Reininghaus, HP Seidel, T Weinkauf.
Topological Methods in Data Analysis and Visualization III, pages 135-150, 2014.
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Week 9
Lecture 17: HD + TOPO, 3/6/2018
Structural inference for high-dimensional data, Part 1
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Final project proposal requirement!
Lecture 18: HD + TOPO, 3/8/2018
Structural inference for high-dimensional data, Part 2
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Final project proposal due.
Mandatory Reading and Tasks:
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[CarlssonnIshkhanovSilva2008]: On the Local Behavior of Spaces of Natural Images.
Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva, Afra Zomorodian.
International Journal of Computer Vision, 76(1), pages 1 - 12, 2008.
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[ChazalGuibasOudot2011]: Scalar Field Analysis over Point Cloud Data.
Frédéric Chazal, Leonidas J. Guibas, Steve Y. Oudot, Primoz Skraba.
Discrete & Computational Geometry, 2011.
Recommended Reading:
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[PereaCarlsson2014]: A Klein-bottle-based Dictionary for Texture Representation.
J. A. Perea and G. Carlsson.
International Journal of Computer Vision, 107(1), pages 75-97, 2014.
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[Cohen-SteinerEdelsbrunnerHarer2007]: Stability of Persistence Diagrams.
David Cohen-Steiner, Herbert Edelsbrunner, John Harer.
Discrete & Computational Geometry, 37(1), pages103-120, 2007.
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Week 10
Lecture 19: HD + TOPO, 3/13/2018
Robust structural inference
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Lecture 20: PV, 3/15/2018
Physical visualization and personalized visualization.
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Project 3 Due!
Project 4 has been posted!
Project 4 Bonus has been posted!
Mandatory Reading and Tasks:
-
Think about what personal data you might want to work with for Project 4.
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Play with KDE and Kernel distance implementation from TDA-R.
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Explore various physical visualization examples at http://dataphys.org/.
Recommended Reading:
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[PhillipsWnagZheng2015]: Geometric Inference on Kernel Density Estimates.
Jeff M. Phillips, Bei Wang, and Yan Zheng.
International Symposium on Computational Geometry (SOCG), 2015.
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[BuchetChazalOudot2016]: Efficient and robust persistent homology for measures.
Mickaël Buchet, Frederic Chazal, Steve Y. Oudot, Donald R. Sheehy. Computational Geometry: Theory and Applications, 58:70?96, 2016.
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[VandeMoerePatel2009]: The Physical Visualization of Information: Designing Data Sculptures in an Educational Context.
Andrew Vande Moere and Stephanie Patel,
International Conference on Digital Interactive Media in Entertainment and Arts (DIMEA'08), ACM International Conference Proceeding Series Vol.349, Athens, Greece, pp. 343-350, 2009.
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Week 11
Spring Break! No classes on 3/20/18 and 3/22/18.
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Week 12
Lecture 21: PV, 3/27/2018
Data sculptures and constructive visualization.
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Lecture 22: NV, 3/29/2018
Foundations for network visualization
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Mandatory Reading and Tasks:
Recommended Reading:
-
[MoerePatel2009]:
The Physical Visualization of Information: Designing Data Sculptures in an Educational Context. Andrew Vande Moere and Stephanie Patel.
Visual Information Communication, 2009.
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[HuronJansenCarpendale]: Constructing Visual Representations: Investigating the Use of Tangible Tokens. Samuel Huron, Yvonne Jansen, Sheelagh Carpendale, IEEE Transactions on Visualization and Computer Graphics, 20(12), 2014.
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Week 13
Lecture 23: NV, 4/3/2018
Beyond Force-Directed Layout.
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Lecture 24: NV, 4/5/2018
More on Graph Layout.
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Mandatory Reading and Tasks:
-
[FruchtermanReingold1991]: Graph drawing by force-directed
placement. T. M. Fruchterman and E. M. Reingold. Software: Practice and experience, 21(11):1129?1164, 1991.
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[TarawnehKellerEbert2011]: A General Introduction To Graph Visualization Techniques.
Raga'ad M. Tarawneh, Patric Keller, and Achim Ebert.
Proceedings of IRTG 1131 - Visualization of Large and Unstructured Data Sets Workshop 2011.
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[ArchambaultMunznerAuber2007]:
TopoLayout: Multi-Level Graph Layout by Topological Features.
Daniel Archambault, Tamara Munzner and David Auber.
IEEE Transactions on Visualization and Computer Graphics, 13(2), 2007.
Recommended Reading:
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[GajerGoodrichKobourov2004]:
A multi-dimensional approach to force-directed layouts
of large graphs. Pawel Gajer, Michael T. Goodrich, Stephen G. Kobourov.
Computational Geometry, 29, 3-18, 2004.
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[ArleoDidimoLiotta2016]:
A Distributed Multilevel Force-directed Algorithm
Alessio Arleo, Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani.
Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD), 2016.
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Week 14
Lecture 25: NV, 4/10/2018
Graph Layout and Edge Bundling.
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Project 5 (bonus) posted!
Lecture 26: NV, 4/12/2018
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Mandatory Reading and Tasks:
-
[Holten2006]: Hierarchical Edge Bundles: Visualization of Adjacency Relations in Hierarchical Data.
Danny Holten.
IEEE Transactions on Visualization and Computer Graphics, 12(5), pages 741-748, 2006.
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Brain Connectivity Toolbox: List of network measures.
Recommended Reading:
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[ZhouXuYuan2013]: Edge Bundling in Information Visualization.
Hong Zhou, Panpan Xu, Xiaoru Yuan, Huamin Qu.
Tsinghua Science and Technology, 18(2), pages 145-156, 2013.
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[Zhou2017]: A Survey of Edge Bundling Methods for Graph Visualization.
Chaofeng Zhou, 2017.
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Week 15
Lecture 27: NV, 4/17/2018
Machine learning on graphs.
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Lecture 28: HD+TOPO+NV+PV, 4/19/2018
The future of data visualization. What's the next cool startup?
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Mandatory Reading and Tasks:
-
Semi-Supervised Learning Tutorial: Xiaojin Zhu, ICML 2007.
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[KwonCrnovrsaninMa2018]:What Would a Graph Look Like in This Layout?
A Machine Learning Approach to Large Graph Visualization.
Oh-Hyun Kwon, Tarik Crnovrsanin, and Kwan-Liu Ma.
IEEE Transactions on Visualization and Computer Graphics, 24(1), 2018.
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[PientaAbelloKahng2015]: Scalable Graph Exploration and Visualization: Sensemaking Challenges and Opportunities. Robert Pienta, James Abello, Minsuk Kahng, Duen Horng Chau, International Conference on Big Data and Smart Computing (BigComp), 2015 .
Recommended Reading:
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Graph-Based Semi-Supervised Learning Tutorial: Zoubin Ghahramani, 2012.
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[EadesHongKlein2017]: Shape-Based Quality Metrics for Large Graph
Visualization. Peter Eades, Seok-Hee Hong, An Nguyen, Karsten Klein.
Journal of Graph Algorithms and Applications, 21(1):29-53, 2017.
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[VieiraNascimentoSilva2015]:The Application of Machine Learning to Problems in Graph Drawing
A Literature Review.
R. dos Santos Vieira, H. A. D. do Nascimento, and W. B. da Silva.
Proc. International Conference on Information, Process,
and Knowledge Management, pages 112-118, 2015.
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[Masui1994]: Evolutionary Learning of Graph Layout Constraints
from Examples. Toshiyuki Masui, Proc. ACM Symposium on User Interface Software and
Technology, pages 103-108, 1994.
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[OstingPalandeWang2017]: Towards Spectral Sparsification of Simplicial Complexes Based on Generalized Effective Resistance.
Braxton Osting, Sourabh Palande, Bei Wang, 2017.
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Week 16
Final Project Presentation: 4/24/2018 (9:10 a.m. - 10:30 a.m.)
Final Project Presentation: 4/27/2018 (Friday, 8:00 a.m. - 10:00 a.m.)
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