- For postdoctoral, graduate, and advanced undergraduate students in Engineering, Sciences, and Medicine, and professionals in industry.
- Fall 2018, Mondays and Wednesdays 11:50am–1:10pm, LCB 115.
- Databases, from the Cancer Genome Atlas (TCGA) at the Genomic Data Commons (GDC) to the Utah Population Database (UPDB).
- Data types, from omics, imaging, and patient clinical information to biomedical 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, from the Luria-Delbrück experiment to personalized cancer diagnostics, prognostics, and therapeutics.
- Proving mathematical theorems and programming symbolic computations.
- Designing algorithms and programming numerical computations.
- Working with databases and modeling biomedical data.
- 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.
- Fall 2018 Calendar
- Safety
- Health, Wellness, and Counseling
- Student Code

Prerequisites: Some experience programming and instructor approval.

100% grade = 30% labs, 30% presentation, 30% class project, 10% class participation; 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.

Skills:

Activities:

- How Bright Promise in Cancer Testing Fell Apart, from the New York Times

August 20:

- Welcome!

- SVD in the news:

If You Liked This, You're Sure to Love That, from the New York Times

- PCA for face recognition and independent component analysis (ICA) for edge detection:

Paper 1: Low-Dimensional Procedure for the Characterization of Human Faces, Sirovich and Kirby,

Paper 2: Eigenfaces for Recognition, Turk and Pentland,

Paper 3: Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images, Olshausen and Field,

February 29:

- Gene H. Golub's Birthday!

Paper 4: Calculating the Singular Values and Pseudo-Inverse of a Matrix, Golub and Kahan,

August 22:

- Mathematics of the SVD:

- Notebook 1: Computation and Visualization of the SVD

Mathematica Code: Notebook_1.nb

August 27 and 29:

- In-Class Work on Lab 1

Code the SVD of synthetic data and its visualization. Test and debug your code.

September 3:

- Happy Labor Day!

September 5:

- Mathematical Properties of the SVD

September 10:

- SVD of Synthetic Data:

- Notebook 2: SVD of Synthetic Data

Mathematica Code: Notebook_2.nb

September 12:

- Composition and Decomposition of Synthetic Data:

September 17:

- Lab 1 Due In-Class

September 19:

- Slides 1: Examples of SVD of measured data

- More examples of SVD of measured data:

Paper 5: Singular Value Decomposition for Genome-Wide Expression Data Processing and Modeling, Alter et al.,

Patent 1: Method for Node Ranking in a Linked Database, Page,

Paper 6: A Rapid Genome-Scale Response of the Transcriptional Oscillator to Perturbation Reveals a Period-Doubling Path to Phenotypic Change, Li and Klevecz,

Paper 7: Coordinated Metabolic Transitions During

September 24 and 26:

- In-Class Work on Lab 2:

Compute and visualize the SVD of your data. Test and debug your code. Interpret your data based upon its SVD. Use at least two different approaches each for preprocessing and sorting your data and for assessing the statistical significance of your interpretation.

October 3, Wednesday, 11:50am–1:10pm, WEB 2230:

- Undergraduate Bioengineering Colloquium

Comparative Spectral Decompositions for Personalized Cancer Diagnostics, Prognostics, and Therapeutics

Orly Alter

October 5, Friday, 2–3pm, WEB 3780, in lieu of Lab 3:

- Scientific Computing and Imaging (SCI) Institute Distinguished Seminar

Kirk E. Jordan

October 8 and 10:

- Happy Fall Break!

October 24:

- Lab 2 Due In-Class

- Mathematics of a Tensor SVD, the Higher-Order SVD (HOSVD):

- Slides 2: Examples of the HOSVD of measured data

- More examples of HOSVD of measured data:

Paper 8: A Multilinear Singular Value Decomposition, De Lathauwer et al.,

Paper 9: A Tensor Higher-Order Singular Value Decomposition for Integrative Analysis of DNA Microarray Data from Different Studies, Omberg et al.,

Paper 10: Characterizing the Evolution of Genetic Variance Using Genetic Covariance Tensors, Hines et al.,

Paper 11: Integrative Analysis of Many Weighted Co-Expression Networks Using Tensor Computation, Li et al.,

Paper 12: MultiFacTV: Module Detection from Higher-Order Time Series Biological Data, Li et al.,

Paper 13: Subgraph Augmented Nonnegative Tensor Factorization (SANTF) for Modeling Clinical Narrative Text, Luo et al.,

October 29:

- Computation of the HOSVD:

October 30:

- Last day to register online to vote in the State of Utah.

November 5:

- Advanced Topics

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,

Paper 15: The Optimal Hard Threshold for Singular Values is 4/√3, Gavish and Donoho,

- Robust PCA and removal of outliers:

Paper 16: Sparsity Control for Robust Principal Component Analysis, Mateos and Giannakis,

Paper 17: Robust Principal Component Analysis? Candès et al.,

- GSVD or two-matrix SVD:

Paper 18: Generalized Singular Value Decomposition for Comparative Analysis of Genome-Scale Expression Datasets of Two Different Organisms, Alter et al.,

Paper 19: Mathematically Universal and Biologically Consistent Astrocytoma Genotype Encodes for Transformation and Predicts Survival Phenotype, Aiello et al.,

- Tensor GSVD or two-tensor SVD:

Paper 20: Tensor GSVD of Patient- and Platform-Matched Tumor and Normal DNA Copy-Number Profiles Uncovers Chromosome Arm-Wide Patterns of Tumor-Exclusive Platform-Consistent Alterations Encoding for Cell Transformation and Predicting Ovarian Cancer Survival, Sankaranarayanan,* Schomay* et al.,

Paper 21: TNF-Insulin Crosstalk at the Transcription Factor GATA6 is Revealed by a Model that Links Signaling and Transcriptomic Data Tensors, Chitforoushzadeh et al.,

November 6:

- General Election

November 7:

- "State of the Project" Presentations

November 12:

- "State of the Project" Presentations

November 14:

- Tensor SVD of Measured Data:

- Notebook 3: Tensor SVD of Measured Data

Mathematica Code: Notebook_3.nb

November 26:

- Neural Networks and Deep Learning

December 5:

- End-of-Class Celebration!