Embedded Files
Instructor: Prof. INDIKA Rajapakse
Teaching Assistant: STEPHEN Lindsly
Class Time: Tuesday and Thursday, 4:00 - 5:30PM, Office Hours: Tuesday and Thursday, 5:30 - 7:00PM
References of Interest
NOTES, SLIDES, AND PAPERS
NOTES, SLIDES, AND PAPERS
Date: 1-21-2021
Date: 1-21-2021
Topics
Basic introduction to data representation: Vectors, matrices, and tensors
Introduction to Eigenvalues and Eigenvectors
Notes
Extra slides: The following slides are the data I showed you on 1-19-2021, with a bit more explanation to help you understand where the data comes from.
Papers
Donoho D. "50 years of data science." Journal of Computational and Graphical Statistics. 2017 Oct 2;26(4):745-66.
Lieberman-Aiden, Erez, ..., Groudine Mark, ..., Lander Eric. "Comprehensive mapping of long-range interactions reveals folding principles of the human genome." Science 326.5950 (2009): 289-293.
Date: 1-26-2021
Date: 1-26-2021
Notes
Resources
ImageSVD (.zip folder with MATLAB code)
Extra slides: The following slides contain the guest lecturers, helpful advice, and the course syllabus
Date: 1-28-2021
Date: 1-28-2021
Guest Lecture: Dr. Cleve Moler
Date: 2-2-2021
Date: 2-2-2021
Notes
Resources
Papers
Classics (just browse)
Turk, Matthew, and Alex Pentland. "Eigenfaces for recognition." Journal of cognitive neuroscience 3.1 (1991): 71-86.
Bott, Raoul. "Morse theory indomitable." Publications Mathématiques de l'IHÉS 68 (1988): 99-114.
Preparation for Spectral Clustering
Ng, Andrew Y., Michael I. Jordan, and Yair Weiss. "On spectral clustering: Analysis and an algorithm." Advances in neural information processing systems 2 (2002): 849-856.
Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416
Date: 2-4-2021
Date: 2-4-2021
Notes
Papers
Gavish, Matan, and David L. Donoho. "The optimal hard threshold for singular values is 4/sqrt(3)." IEEE Transactions on Information Theory 60.8 (2014): 5040-5053. (Amazing Paper!)
Chen, Jie, Alfred O. Hero III, and Indika Rajapakse. "Spectral identification of topological domains." Bioinformatics 32.14 (2016): 2151-2158.
Date: 2-9-2021
Date: 2-9-2021
Resources
Notes
Date: 2-11-2021
Date: 2-11-2021
Guest Lecture: Prof. Gilbert Strang
Resources
From Cleve’s Corner: Gil Strang and the CR Matrix Factorization and Notes on CR and west0479
Date: 2-16-2021
Date: 2-16-2021
Notes
Papers
Ng, Andrew Y., Michael I. Jordan, and Yair Weiss. "On spectral clustering: Analysis and an algorithm." Advances in neural information processing systems 2 (2002): 849-856.
Belkin, Mikhail, and Partha Niyogi. "Laplacian eigenmaps and spectral techniques for embedding and clustering." Advances in neural information processing systems. 2002.
Von Luxburg, Ulrike. "A tutorial on spectral clustering." Statistics and computing 17.4 (2007): 395-416. (Excellent Review!)
Date: 2-18-2021
Date: 2-18-2021
Guest Lecture: Col. Chris Macedonia
Date: 2-23-2021
Date: 2-23-2021
Notes
Book:
Kutz, J. Nathan, et al. Dynamic mode decomposition: data-driven modeling of complex systems. Society for Industrial and Applied Mathematics, 2016.
Chapter 1: Dynamic Mode Decomposition: An Introduction
Nice Video!
Date: 2-25-2021
Date: 2-25-2021
Notes
Book:
Kutz, J. Nathan, et al. Dynamic mode decomposition: data-driven modeling of complex systems. Society for Industrial and Applied Mathematics, 2016.
Chapter 1: Dynamic Mode Decomposition: An Introduction
Code
Papers
Champion K, Lusch B, Kutz JN, Brunton SL. "Data-driven discovery of coordinates and governing equations." Proceedings of the National Academy of Sciences. 2019 Nov 5;116(45):22445-51.
Ronquist S, Patterson G, Muir LA, Lindsly S, Chen H, Brown M, Wicha MS, Bloch A, Brockett R, Rajapakse I. "Algorithm for cellular reprogramming." Proceedings of the National Academy of Sciences. 2017 Nov 7;114(45):11832-7.
Date: 3-2-2021
Date: 3-2-2021
Notes
Slides
Papers
Hirsh, Seth M., et al. "Centering data improves the dynamic mode decomposition." SIAM Journal on Applied Dynamical Systems 19.3 (2020): 1920-1955.
Proctor, Joshua L., Steven L. Brunton, and J. Nathan Kutz. "Dynamic mode decomposition with control." SIAM Journal on Applied Dynamical Systems 15.1 (2016): 142-161.
Date: 3-4-2021
Date: 3-4-2021
Book:
Kutz, J. Nathan. Data-driven modeling & scientific computation: methods for complex systems & big data. Oxford University Press, 2013.
Independent Component Analysis
Papers
Data-guided Control (DGC)
Ronquist, Scott, et al. "Algorithm for cellular reprogramming." Proceedings of the National Academy of Sciences 114.45 (2017): 11832-11837.
Non-negative Matrix Factorization (NMF or NNMF)
Lee, Daniel D., and H. Sebastian Seung. "Learning the parts of objects by non-negative matrix factorization." Nature 401.6755 (1999): 788-791.
DMD with Control
Proctor, Joshua L., Steven L. Brunton, and J. Nathan Kutz. "Dynamic mode decomposition with control." SIAM Journal on Applied Dynamical Systems 15.1 (2016): 142-161.
Video: Dynamic Mode Decomposition (DMD) with Control
Date: 3-9-2021
Date: 3-9-2021
Guest Lecture: Dr. Reza Ghanadan from Google
Assuring AI for Real-World Decision Making with Robust AI System Design
Date: 3-11-2021
Date: 3-11-2021
Notes
Date: 3-16-2021
Date: 3-16-2021
Guest Lecture: Dr. David Heckerman from Amazon
Guest Lecture: Dr. David Heckerman from Amazon
Date: 3-18-2021
Date: 3-18-2021
Notes
Papers
Kobak, Dmitry, and George C. Linderman. "Initialization is critical for preserving global data structure in both t-SNE and UMAP." Nature Biotechnology (2021): 1-2.
McInnes, Leland, John Healy, and James Melville. "Umap: Uniform manifold approximation and projection for dimension reduction." arXiv preprint arXiv:1802.03426 (2018).
Van der Maaten, Laurens, and Geoffrey Hinton. "Visualizing data using t-SNE." Journal of machine learning research 9.11 (2008).
Date: 3-25-2021
Date: 3-25-2021
Notes
Papers
Candès, Emmanuel J., et al. "Robust principal component analysis?." Journal of the ACM (JACM) 58.3 (2011): 1-37.
Date: 3-30-2021
Date: 3-30-2021
Notes
Papers
Udell, Madeleine, and Alex Townsend. "Why are big data matrices approximately low rank?." SIAM Journal on Mathematics of Data Science 1.1 (2019): 144-160.
Date: 4-1-2021
Date: 4-1-2021
Slides
Notes
Book:
Eldén, Lars. Matrix methods in data mining and pattern recognition. Society for Industrial and Applied Mathematics, 2007.
Chapter 8: Tensor Decomposition
Papers
Bryan, Kurt, and Tanya Leise. "The $25,000,000,000 eigenvector: The linear algebra behind Google." SIAM review 48.3 (2006): 569-581.
Kolda, Tamara G., and Brett W. Bader. "Tensor decompositions and applications." SIAM review 51.3 (2009): 455-500. (Excellent Review!)
Chen C, Rajapakse I. "Tensor Entropy for Uniform Hypergraphs." IEEE Transactions on Network Science and Engineering 7.4 (2020): 2889-2900.
Benson, Austin R., David F. Gleich, and Desmond J. Higham. "Higher-order Network Analysis Takes Off, Fueled by Classical Ideas and New Data." arXiv preprint arXiv:2103.05031 (2021). (Nice Read!)
Date: 4-6-2021
Date: 4-6-2021
Slides
Notes
Book:
Eldén, Lars. Matrix methods in data mining and pattern recognition. Society for Industrial and Applied Mathematics, 2007.
Chapter 8: Tensor Decomposition
Papers
Kolda, Tamara G., and Brett W. Bader. "Tensor decompositions and applications." SIAM review 51.3 (2009): 455-500. (Excellent Review!)
Chen C, Rajapakse I. "Tensor Entropy for Uniform Hypergraphs." IEEE Transactions on Network Science and Engineering 7.4 (2020): 2889-2900.
Sweeney P, Chen C, Rajapakse I, Cone R. "Network Dynamics of Hypothalamic Feeding Neurons." Proceedings of the National Academy of Sciences (2021).
Williams, Alex H., et al. "Unsupervised discovery of demixed, low-dimensional neural dynamics across multiple timescales through tensor component analysis." Neuron 98.6 (2018): 1099-1115.
Wolf, Michael M., Alicia M. Klinvex, and Daniel M. Dunlavy. "Advantages to modeling relational data using hypergraphs versus graphs." 2016 IEEE High Performance Extreme Computing Conference (HPEC). IEEE, 2016.
Date: 4-8-2021
Date: 4-8-2021
Slides
Papers
Carlsson, Gunnar. "The shape of biomedical data." Current Opinion in Systems Biology 1 (2017): 109-113.
Carlsson, Gunnar. "Topology and data." Bulletin of the American Mathematical Society 46.2 (2009): 255-308.
Lum, Pek Y., et al. "Extracting insights from the shape of complex data using topology." Scientific reports 3.1 (2013): 1-8.
Date: 4-13-2021
Date: 4-13-2021
Notes
Papers
Brunton, Steven L., Joshua L. Proctor, and J. Nathan Kutz. "Discovering governing equations from data by sparse identification of nonlinear dynamical systems." Proceedings of the national academy of sciences 113.15 (2016): 3932-3937.
Date: 4-15-2021
Date: 4-15-2021
Data-guided Control
Notes
Papers
Ronquist S, Patterson G, Muir LA, Lindsly S, Chen H, Brown M, Wicha M, Bloch A, Brockett R and Rajapakse I. "Algorithm for Cellular Reprogramming." Proceedings of the National Academy of Sciences 114.45 (2017): 11832-11837.
Liu, Yang-Yu, Jean-Jacques Slotine, and Albert-László Barabási. "Controllability of complex networks." Nature 473.7346 (2011): 167-173.
Date: 4-20-2021
Date: 4-20-2021
Slides
Notes
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