CS 6965: Advanced Data Visualization

Combine Data Analysis and Machine Learning with Visualization

Fall 2019

Schedule at a Glance (subject to change, guest lectures marked with a *)

Mutually Inclusive Modules
HD: High-dimensional data visualization
TOPO: Topological abstraction and summarization
NV: Network visualization
PV: Personalized visualization


Week
Date
Modules
Topic
Lecture
Comments & Due Dates
1 8/20 Course logistics, overview Lecture 01
8/22 HD Vis pipeline, dim reduction and vis: PCA Lecture 02
2 8/27 HD dim reduction and vis: t-SNE Lecture 03 Project 01 Posted.
8/29 HD+TOPO Mapper, clustering and beyond Lecture 04
3 9/3 HD More DR, clustering and vis Lecture 05
9/5 HD Subspace clustering, regression & vis Lecture 06
4 9/10 HD Visual mapping for high-dim data Lecture 07
9/12 HD Visual mapping for high-dim data Lecture 08 Final project team creation due.
5 9/17 PV Physical and personalized visualization Lecture 09 Project 01 due.
9/19 PV Data sculptures and constructive visualization Lecture 10 Project 02 Posted.
6 9/24 HD View transformation, decision trees Lecture 11
9/26 HD Decision tree continued Lecture 12
7 10/1 NV Visualize multi-layer network Lecture 13
10/3 PV Physical visualization: presentations Lecture 14 Project 02 Due. Project 03 Posted.
8 10/8 Fall Break!
10/10 Fall Break!
9 10/15 HD Deep Learning and Vis I Lecture 15 Final project proposal due.
10/17 HD Deep Learning and Vis II Lecture 16
10 10/22* HD Visualization of internal neurons in a neural net
By Prof. Aditya Bhaskara 		Lecture 17
10/24* HD Embedding tensor factorization domains in ML
By Prof. Shandian Zhe 		Lecture 18
11 10/29 NV Foundations for network visualization Lecture 19
10/31 NV Graph layout and edge bundling I Lecture 20
12 11/5 NV Graph layout and edge bundling II Lecture 21
11/7 NV Graph layout and edge bundling III Lecture 22
13 11/12 NV Emerging techniques in network visualization with ML Lecture 23
11/14 TOPO Topological structures in visualization I Lecture 24 Project 04 Posted.
14 11/19 TOPO Topological structures in visualization II Lecture 25 Project 03 Due.
Final project progress report due.
11/21 TOPO Structural Inference Lecture 26
15 11/26 TOPO Discrete Morse theory for discrete data Lecture 27
11/28 Thanksgiving Day!
16 12/3 The future of data visualization.
What's the next cool startup? 		Lecture 28 Project 04 due.
12/5 Final project presentation
(Thursday, 9:10 a.m. - 10:30 a.m.)
17 12/9 (Monday) Final project presentation
(Monday, 8:00 a.m. - 10:00 a.m.)
17 12/10 Final project report due (9:10 a.m. MDT).

Weekly Schedule (subject to change)

Week 1

Lecture 01: Introduction, 8/20/2019
Course logistics, overview.
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Lecture 02: HD, 8/22/2019
Visualization pipeline, dimensionality reduction and vis: PCA
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Mandatory Reading and Tasks:
  1. Scikit-learn tutorial.

Recommended Reading:
  1. Interactive Data Visualization for the Web, 2nd Ed. Scott Murray, 2017.
  2. [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.
  3. [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.

Week 2

Lecture 03: HD, 8/27/2019
Dimensionality reduction and vis: t-SNE.
Download slides
Project 01

Lecture 04: HD+TOPO, 8/29/2019
Mapper, clustering and beyond.
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Mandatory Reading and Tasks:
  1. [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
  2. [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.
  3. [vanderMaatenHinton2008]: Visualizing Data using t-SNE. Laurens van der Maaten and Geoffrey Hinton, Journal of Machine Learning Research, 9, pages 2579-2605, 2008.
  4. [McInnesHealyMelville2018]: UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction, arXiv:1802.03426, 2018.

Recommended Reading:
  1. [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.
  2. [Carlsson2009]: Topology and data. Bulletin of the American Mathematical Society, 46, pages 255-308, 2009.
  3. [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.
  4. [DeyMemoliWang2017]:Topological Analysis of Nerves, Reeb Spaces, Mappers, and Multiscale Mappers. Tamal K. Dey, Facundo Memoli, and Yusu Wang, arXiv:1703.07387, 2017.
  5. [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.

Week 3

Lecture 05: HD, 9/3/2019
More DR, clustering and visualization.
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Lecture 06: HD, 9/5/2019
Subspace clustering, regression and vis.
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Mandatory Reading and Tasks:
  1. [LeeVerleysen2009]: Quality assessment of dimensionality reduction: Rank-based criteria. John A. Lee and Michel Verleysen, Neurocomputing, 72, pages 1431-1443 2009.
  2. 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.
  3. [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:
  1. [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.
  2. [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.
  3. [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.
  4. [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.
  5. [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.
  6. [MokbelLueksGirbrecht2013]: Visualizing the quality of dimensionality reduction. Bassam Mokbel, Wouter Lueks, Andrej Gisbrecht, and Barbara Hammer. Neurocomputing, 112 (18), pages 109-123, 2012.
  7. [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.
  8. [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.
  9. [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.
  10. [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.
  11. [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.

Week 4

Lecture 07: HD, 9/10/2019
Visual mapping for high-dimensional data.
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Lecture 08: HD, 9/12/2019
Visual mapping for high-dimensional data continued.
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Final project team creation due!

Mandatory Reading and Tasks:
  1. 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:
  1. [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.
  2. [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.
  3. [PiringerBergerKrasser2010]: HyperMoVal: Interactive Visual Validation of Regression Models for Real-Time Simulation. H. Piringer, W. Berger, J. Krasser, Computer Graphics Forum, 2010.
  4. [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.
  5. [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.
  6. [Chernoff1973]: The Use of Faces to Represent Points in K-Dimensional Space Graphically. Herman Chernoff, Journal of the American Statistical Association, 68(342), 1973.
  7. [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.
  8. [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.
  9. [HoltenWijk2010]: Evaluation of Cluster Identification Performance for Different PCP Variants. Danny Holten and Jarke J. van Wijk, Computer Graphics Forum, 2010.
  10. [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.
  11. [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.
  12. [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.

Week 5

Lecture 9: PV, 9/17/2019
Physical visualization and personalized visualization.
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Lecture 10: PV, 9/19/2019
Data sculptures and constructive visualization.
Download slides
Project 02



Mandatory Reading and Tasks:
  1. Think about what personal data you might want to work with for Project 4.
  2. Play with KDE and Kernel distance implementation from TDA-R.
  3. Explore various physical visualization examples at http://dataphys.org/.

Recommended Reading:
  1. [PhillipsWnagZheng2015]: Geometric Inference on Kernel Density Estimates. Jeff M. Phillips, Bei Wang, and Yan Zheng. International Symposium on Computational Geometry (SOCG), 2015.
  2. [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.
  3. [MoerePatel2009]: The Physical Visualization of Information: Designing Data Sculptures in an Educational Context. Andrew Vande Moere and Stephanie Patel. Visual Information Communication, 2009.
  4. [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.

Week 6

Lecture 11: HD, 9/24/2019
View transformation and user interactions, decision trees.
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Lecture 12: HD, 9/26/2019
Decision tree continued, deep learning and vis.
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Additional materials on decision trees: Decision Trees (by Andrew W. Moore), Information Gain (by Linda Shapiro)

Mandatory Reading and Tasks:
  1. 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.
  2. [Moore Lecture: Information Gain]: Andrew Moore's lecture on Information Gain.
  3. [Moore Lecture: Decision Trees]: Andrew Moore's lecture on Decision Trees.
  4. [TensorFlow Playground]: Tinker With a Neural Network Right Here in Your Browser.
  5. [TensorFlow: ML Beginners]: TensorFlow: Getting Started for ML Beginners.

Recommended Reading:
  1. [TensorFlow: Getting Started]: TensorFlow: Getting Started with TensorFlow.
  2. [Deep Learning Tutorial 1]: Deep Learning Tutorial at Stanford University.
  3. [Deep Learning Tutorial 2]: Neural Networks and Deep Learning by Michael Nielsen.
  4. [Deep Learning Book]: Deep Learning by Ian Goodfellow, Yoshua Bengio, and Aaron Courville.

Week 7

Lecture 13: NV, 10/1/2019
Visualize multi-layer network.
Presentation by domain scientists on visualizing multilayer infrastructure network.
See Canvas: Project 03 for details.

Lecture 14: PV, 10/3/2019
Physical visualization: presentations.
Presentations by students on Project 02: physical visualization of personal data.
Project 03

Week 8

Fall Break! No classes.

Week 9

Lecture 15: HD, 10/15/2019
Deep Learning and Vis I.
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Lecture 16: HD, 10/17/2019
Deep Learning and Vis II.
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Mandatory Reading and Tasks:
  1. [HohmanKahngPienta2018]: Visual Analytics in Deep Learning: An Interrogative Survey for the Next Frontiers.
  2. [CarterArmstrongSchubert2019]: Activation Atlas: Exploring Neural Networks with Activation Atlases.

Recommended Reading:
  1. [HohmanParkRobinson2019]: SUMMIT: Scaling Deep Learning Interpretability by Visualizing Activation and Attribution Summarizations.
  2. [ZahavyBaramMannor2017]: Graying the black box: Understanding DQNs.
  3. [TensorFlow Playground]: Tinker With a Neural Network Right Here in Your Browser.

Week 10

Lecture 17: HD, 10/22/2019
Visualization of internal neurons in a neural net
Guest Lecture By Prof. Aditya Bhaskara

Lecture 18: HD, 10/24/2019
Embedding tensor factorization domains in Machine Learning
Guest Lecture By Prof. Shandian Zhe
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Week 11

Lecture 19: NV, 10/29/2019
Foundations for network visualization
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Lecture 20: NV, 10/31/2019
Graph layout and edge bundling I.
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Mandatory Reading and Tasks:
  1. [FruchtermanReingold1991]: Graph drawing by force-directed placement. T. M. Fruchterman and E. M. Reingold. Software: Practice and experience, 21(11):1129-1164, 1991.
  2. [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.
  3. [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:
  1. [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.
  2. [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.

Week 12

Lecture 21: NV, 11/05/2019
Graph layout and edge bundling II.
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Lecture 22: NV, 11/07/2019
Graph layout and edge bundling III.
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Mandatory Reading and Tasks:
  1. [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.
  2. Brain Connectivity Toolbox: List of network measures.

Recommended Reading:
  1. [BehrischBachRiche2016]: Matrix Reordering Methods for Table and Network Visualization. Michael Behrisch, Benjamin Bach, Nathalie Henry Riche, Tobias Schreck, Jean-Daniel Fekete. Computer Graphics Forum, 35(3), pages 693-716, 2016.
  2. VIS 2019: accepted papers in IEEE VIs conference on graph/network visualization: Drawing Nodes and Edges.
  3. [ZhouXuYuan2013]: Edge Bundling in Information Visualization. Hong Zhou, Panpan Xu, Xiaoru Yuan, Huamin Qu. Tsinghua Science and Technology, 18(2), pages 145-156, 2013.
  4. [Zhou2017]: A Survey of Edge Bundling Methods for Graph Visualization. Chaofeng Zhou, 2017.

Week 13

Lecture 23: NV, 11/12/2019
Emerging techniques in network visualization with ML.
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Lecture 24: TOPO, 11/14/2019
Topological structures in visualization I.
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Mandatory Reading and Tasks:
  1. Semi-Supervised Learning Tutorial: Xiaojin Zhu, ICML 2007.
  2. [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.
  3. [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:
  1. Graph-Based Semi-Supervised Learning Tutorial: Zoubin Ghahramani, 2012.
  2. [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.
  3. [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.
  4. [Masui1994]: Evolutionary Learning of Graph Layout Constraints from Examples. Toshiyuki Masui, Proc. ACM Symposium on User Interface Software and Technology, pages 103-108, 1994.
  5. [OstingPalandeWang2017]: Towards Spectral Sparsification of Simplicial Complexes Based on Generalized Effective Resistance. Braxton Osting, Sourabh Palande, Bei Wang, 2017.

Week 14

Lecture 25: TOPO, 11/19/2019
Topological structures in visualization II.
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Lecture 26: HD/TOPO, 11/21/2019
Structural Inference.
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Mandatory Reading and Tasks:
  1. Read the documentation of TTK; follow the instructions to install TTK on your own computer.
  2. Lecture Notes on Morse-Smale Complex by Prof. Guoning Chen.

Recommended Reading:
  1. [CarrSnoeyinkAxen2003]: Computing contour trees in all dimensions. Hamish Carr, Jack Snoeyink,Ulrike Axen. Computational Geometry, 24(2), pages 75-94, 2003.
  2. [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.
  3. [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.

Week 15

Lecture 27: TOPO, 11/26/2019
Discrete Morse theory for discrete data.
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Mandatory Reading and Tasks:
  1. [Forman2002]: A User's Guide To Discrete Morse Theory. Robin Forman. Séminare Lotharinen de Combinatore 48, 2002.

Recommended Reading:
  1. [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.
  2. [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.
  3. [KingKnudsonMramor2005]: Generating Discrete Morse Functions from Point Data. Henry King, Kevin Knudson, and Neza Mramor. Experimental Mathematics, 14(4), page 435, 2005.
  4. [GuntherReininghausSeidel2014]: Notes on the Simplification of the Morse-Smale Complex. D Gunther, J Reininghaus, HP Seidel, T Weinkauf. Topological Methods in Data Analysis and Visualization III, pages 135-150, 2014.

Data on the Web:

Awesome Public Datasets
Stanford Large Network Dataset Collection (SNAP)

Coding resources on the Web:

Interactive Data Visualization for the Web, 2nd Edition by Scott Murray (2017)