100% grade = 30% labs, 30% class project, 30% presentation, 10% class participation; late assignments are not accepted; class attendance is required.
Topics:
We will cover concepts in data science and machine learning, and their applications to discovery of principles from biomedical data.
- Databases, e.g., the Cancer Genome Atlas (TCGA) at the Genomic Data Commons (GDC).
- Data types, from, e.g., omics, imaging, and patient clinical information to, e.g., tissue samples and model organisms and systems.
- Algorithms, from the singular value decomposition (SVD) and principal component analysis (PCA) to multi-tensor decompositions, neural networks, and deep learning.
- Applications toward a better understanding of biology, e.g., the Luria-Delbrück experiment, and a better practice of medicine, e.g., personalized cancer diagnostics, prognostics, and therapeutics.
Skills:
- Proving mathematical theorems and programming symbolic computations.
- Designing algorithms and programming numerical computations.
- Working with databases and modeling biomedical data.
Activities:
- In-class presentations of scientific journal articles and patents.
- Participation in guest lectures and seminars on campus and discussions of conference reports.
- End-of-class celebration.
Readings on the SVD and deep learning:
- Book 1: Linear Algebra and Learning from Data, Strang (2019).
Book 2: The Deep Learning Revolution, Sejnowski (2018).
August 22:
- Welcome!
August 24:
- Introduction:
How Bright Promise in Cancer Testing Fell Apart, New York Times (2011).
- The SVD in the news:
If You Liked This, You're Sure to Love That, New York Times (2008).
- PCA for face recognition:
Paper 1: Low-Dimensional Procedure for the Characterization of Human Faces, Sirovich and Kirby, Journal of the Optical Society of America. A, Optics, image science, and vision (1987).
Paper 2: Eigenfaces for Recognition, Turk and Pentland, Journal of Cognitive Neuroscience (1991).
- Lab 1:
Code the SVD or the tensor SVD of synthetic data and its visualization. Test and debug your code.
August 29:
- Mathematics of the SVD:
- Numerical Linear Algebra, Trefethen and Bau, III (1997).
- Notebook 1: Computation and Visualization of the SVD
Mathematica Code: Notebook_1.nb
February 29:
- Gene H. Golub's Birthday!
Paper 3: Calculating the Singular Values and Pseudo-Inverse of a Matrix, Golub and Kahan, SIAM Journal on Numerical Analysis (1965).
- Matrix Computations, Golub and Van Loan (1996).
August 31:
- Composition and decomposition of synthetic data:
- Notebook 2: The SVD of Synthetic Data
Mathematica Code: Notebook_2.nb
September 5:
- Happy Labor Day!
September 7:
- Mathematics of a tensor SVD, the higher-order SVD (HOSVD):
- Paper 4: A Multilinear Singular Value Decomposition, De Lathauwer et al., SIAM Journal on Matrix Analysis and Applications (2000).
September 12:
- Computation of the HOSVD:
- Notebook 3: The tensor SVD of Synthetic Data
Mathematica Code: Notebook_3.nb
September 14:
- Slides 1: Examples of the SVD of measured data
- More examples of the SVD of measured data:
Paper 5: Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling, Alter et al., Proceedings of the National Academy of Sciences (PNAS) USA (2000).
Patent 1: Method for Node Ranking in a Linked Database, Page, United States Patent (2001).
Paper 6: A Rapid Genome-Scale Response of the Transcriptional Oscillator to Perturbation Reveals a Period-Doubling Path to Phenotypic Change, Li and Klevecz, Proceedings of the National Academy of Sciences (PNAS) USA (2006).
Paper 7: Coordinated Metabolic Transitions During Drosophila Embryogenesis and the Onset of Aerobic Glycolysis, Tennessen, Bertagnolli et al., G3: Genes, Genomes, Genetics (2014).
September 19:
- Slides 2: Examples of the HOSVD of measured data
September 21:
- Example of TCGA data:
Paper 8: Comprehensive, Integrative Genomic Analysis of Diffuse Lower-Grade Gliomas, TCGA Research Network, Nature (2015).
September 26:
- Example of interpretation of TCGA data:
Paper 9: Mathematically Universal and Biologically Consistent Astrocytoma Genotype Encodes for Transformation and Predicts Survival Phenotype, Aiello et al., Applied Physics Letters (APL) Bioengineering (2018).
September 28:
- Lab 1 Due In-Class
- In-Class Work on Lab 2:
Compute and visualize the SVD or the tensor SVD of your data. Interpret your data based upon its SVD or its tensor SVD. Use at least two different approaches each for preprocessing and sorting your data and for assessing the statistical significance of your interpretation.
- From the SVD to PCA:
- Slides 3: The SVD vs. PCA
- Paper 10: Correspondence Analysis Applied to Microarray Data, Fellenberg et al., Proceedings of the National Academy of Sciences (PNAS) USA (2001).
October 3:
- Examples of assessing the statistical significance of an interpretation:
Paper 11: Systematic Determination of Genetic Network Architecture, Tavazoie et al., Nature Genetics (1999).
Paper 12: Discovering Motifs in Ranked Lists of DNA Sequences, Eden et al., Public Library of Science (PLoS) Computational Biology (2007).
Paper 13: GOrilla: A Tool for Discovery and Visualization of Enriched GO Terms in Ranked Gene Lists, Eden et al., BMC Bioinformatics (2009).
- Slides 4: The hypergeometric probability distribution and P-value for enrichment analysis
- Notebook 4: The Hypergeometric Probability Distribution and P-Value
Mathematica Code: Notebook_4.nb
October 5:
- Lab 2 "Data Clinic"
- Selection of a cutoff of the singular values:
Paper 14: Component Retention in Principal Component Analysis with Application to cDNA Microarray Data, Cangelosi and Goriely, Biology Direct (2007).
Paper 15: The Optimal Hard Threshold for Singular Values is 4/√3, Gavish and Donoho, IEEE Transactions on Information Theory (2014).
- Robust PCA and removal of outliers:
Paper 16: Sparsity Control for Robust Principal Component Analysis, Mateos and Giannakis, in IEEE Asilomar Conference on Signals, Systems, and Computers (2010).
Paper 17: Robust Principal Component Analysis? Candès et al., Journal of the ACM (2011).
October 10:
- Happy Fall Break!
October 12:
- Happy Fall Break!
October 17:
- More examples of the HOSVD of measured data:
Paper 18: A Tensor Higher-Order Singular Value Decomposition for Integrative Analysis of DNA Microarray Data from Different Studies, Omberg et al., Proceedings of the National Academy of Sciences (PNAS) USA (2007).
Paper 19: Characterizing the Evolution of Genetic Variance Using Genetic Covariance Tensors, Hines et al., Philosophical Transactions of the Royal Society B Biological Sciences (2009).
Paper 20: Integrative Analysis of Many Weighted Co-Expression Networks Using Tensor Computation, Li et al., Public Library of Science (PLoS) Computational Biology (2011).
Paper 21: MultiFacTV: Module Detection from Higher-Order Time Series Biological Data, Li et al., BMC Genomics (2013).
Paper 22: Subgraph Augmented Nonnegative Tensor Factorization (SANTF) for Modeling Clinical Narrative Text, Luo et al., Journal of the American Medical Informatics Association (2015).
October 19:
- Lab 2 "Data Clinic"
October 24:
- Slides 5: The SVD as a Transform
- Quantum Harmonic Oscillator from Wikipedia
- Image Compression via the SVD from Mathworld
- Image Compression via the Fourier Transform from Mathworld
October 26:
- Mathematical variations on the SVD and PCA for blind source separation (BSS):
- Independent component analysis (ICA):
Paper 23: Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images, Olshausen and Field, Nature (1996).
Paper 24: The "Independent Components" of Natural Scenes are Edge Filters, Bell and Sejnowski, Vision Ressearch (1997).
Paper 25: Linear Modes of Gene Expression Determined by Independent Component Analysis, Liebermeister, Bioinformatics (2002).
- Nonnegative matrix factorization (NMF):
Paper 26: Learning the Parts of Objects by Non-Negative Matrix Factorization, Lee and Seung, Nature (1999).
Paper 27: Metagenes and Molecular Pattern Discovery Using Matrix Factorization, Brunet et al., Proceedings of the National Academy of Sciences (PNAS) USA (2004).
October 31:
- The tensor SVD of measured data:
November 2:
- Notebook 5: The tensor SVD of Measured Data
Mathematica Code: Notebook_5.nb
November 7:
- Kaplan-Meier survival analysis
November 9:
- Lab 2 Due In-Class
- The "perceptron," i.e., single-layer neural network, as a mathematical variation on the SVD:
November 14:
- In-Class Work on Class Project
November 16:
- Neural networks:
Paper 28: Predicting Human Brain Activity Associated with the Meanings of Nouns, Mitchell et al., Science (2008).
Paper 29: Integrating Multiple-Study Multiple-Subject fMRI Datasets Using Canonical Correlation Analysis, Rustandi et al., in International Conference on Medical Image Computing and Computer-Assisted Intervention (2009).
November 21:
- Verification and validation
- Example of verification:
Paper 30: Global Effects of DNA Replication and DNA Replication Origin Activity on Eukaryotic Gene Expression, Omberg et al., Molecular Systems Biology (2009).
- Example of validation:
Paper 31: Retrospective Clinical Trial Experimentally Validates Glioblastoma Genome-Wide Pattern of DNA Copy-Number Alterations Predictor of Survival, Ponnapalli et al., Applied Physics Letters (APL) Bioengineering (2020).
November 24:
- Happy Thanksgiving!
November 28:
- "State of the project" presentations
November 30:
- "State of the project" presentations
December 5:
- "State of the project" presentations
December 7:
- "State of the project" presentations
- End-of-class celebration!
Happy Winter Break!
- DNA, xkcd (2015).
See you in Spring 2023 in BME 6770: Genomic Signal Processing!