Tensor Models and Methods for Medical Imaging

Large-scale data, such as that from common medical imaging applications, is often naturally multi-modal and represented well by a tensor (a higher-order generalization of a matrix).  The mathematics of tensors is notoriously more complex than that of matrices, which has created key gaps in development of tensor-based data analytic techniques, especially in topic modeling and dimensionality reduction.  This project will address three main aims:

  1. To develop tensor-based topic models which respect the natural multi-modal structure of the data and allow for incorporation of flexible expert supervision information;
  2. To design efficient training methods for tensor-based topic models and produce publicly available open-source implementations; and
  3. To illustrate the promise of these models and methods in an important case study application to echocardiogram analysis.   

In this project, students will generalize common supervised matrix factorization models to tensor data, develop efficient optimization methods for training these models, and produce open-source Python (and/or Matlab) packages for these models/methods.  The project will be guided by an application to the cardiac video imaging modality, echocardiograms.  In collaboration with cardiologists at UCLA-Harbor Medical Center Department of Cardiology, students will evaluate their models on the novel segmentation application of identifying coherent parts of the echocardiogram.  Our team will not only develop novel modeling tools that can utilize information from data experts (e.g., cardiologists), but will work to make these tools and their results available and interpretable to non-model experts.  

Student researchers in this project will develop mathematical skills in areas like (multi-)linear algebra, optimization, machine learning, probability, and statistics.  They will build and strengthen skills in literature review, scientific reading, technical writing and presentation, and programming and package development.

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Interested applicants should submit a CV, the name of a reference, and answers to the following prompts:

  • Why are you interested in this project?  What makes you a good fit?
  • What skills do you bring to this project?  What skills do you hope to develop?
  • What are your goal outcomes for your summer research project?
Name of research group, project, or lab
matH of Algorithms, Data & Decisions (HADD) research group
Why join this research group or lab?

In the matH of Algorithms, Data & Decisions (HADD) research group, we consider problems motivated by the study of real-world data. We consider the mathematics of data, models for making decisions with data, and methods for training such models.  We consist of fun and passionate people who encourage one another and help each other develop as mathematicians, data scientists, and researchers.  Our group has students working on various projects, and often interacts with collaborators from other institutions (graduate students, postdoctoral researchers, and faculty).  Students may continue their work in a senior thesis, present their findings at conferences, and/or coauthor resulting publications.

We work in areas like mathematical data science, optimization, and applied convex geometry, leveraging mathematical tools like probability, combinatorics, and convex geometry, on problems in data science and optimization. Our group has been active recently in randomized numerical linear algebra, combinatorial methods for convex optimization, tensor decomposition for topic modeling, network consensus and ranking problems, and community detection on graphs and hypergraphs.

Representative publication
Logistics Information:
Project categories
Mathematics
Algorithms
Data Science
Machine Learning
Numerical Modeling
Optimization
Student ranks applicable
First-year
Sophomore
Junior
Senior
Student qualifications

Required: completion of core courses in calculus and linear algebra, programming experience (Python and/or Matlab preferred)

Desireable (but not required): optimization, statistics, machine learning

Time commitment
Summer - Full Time
Compensation
Paid Research
Number of openings
2
Techniques learned

Students will build and strengthen skills in:

  • (multi-)linear algebra
  • optimization
  • machine learning
  • probability and statistics
  • literature review
  • scientific reading
  • technical writing and presentation
  • programming and package development
Contact Information:
Mentor name
Jamie Haddock
Mentor email
jhaddock@hmc.edu
Mentor position
Principal Investigator
Name of project director or principal investigator
Jamie Haddock
Email address of project director or principal investigator
jhaddock@g.hmc.edu
2 sp. | 19 appl.
Hours per week
Summer - Full Time
Project categories
Machine Learning (+5)
MathematicsAlgorithmsData ScienceMachine LearningNumerical ModelingOptimization