Cross-correlations in medical data: theory, algorithms, and applications in disease analytics

Cancer, like other complex diseases, involves a multitude of interactions which make it challenging to understand, diagnose, and cure. With the advancements in data science, there is immense potential to characterize the complexities of cancer by taking advantage of datasets that provide patient information from different views or modalities. For example, the Cancer Genome Atlas (TCGA) and the Cancer Imaging Archive (TCIA) provide data from multiple modalities, including radiology, histopathology, and genomics, from the same set of patients. The relations and correlations across features from these different modalities capture the joint variation in cancer properties and enable the characterization of the underlying cancer state in patients. This dissertation explores the potential of correlations as a tool for prediction and disease understanding. Under a two-modality probabilistic graphical model, we first show mathematically that the outputs of canonical correlation analysis (CCA), a linear correlation tool, is effective in the prediction of the model's unknown latent variable. The CCA-based predictor can alternatively be viewed as an interpretable unsupervised embedding generator which captures the correlations across two sets of features using CCA, followed by a supervised predictor. To adapt CCA to high dimensional, low sample, real world medical data, penalties encouraging sparsity, group structures, or graph structures are frequently included in the CCA formulation. To solve the graph-constrained CCA problem in a computationally efficient manner, we develop an alternating algorithm utilizing proximal gradients. We introduce novel matrix deflation (update) rules which enforce orthogonality properties to generate informative embeddings for CCA with penalties. Our results on simulated data and TCGA breast cancer data highlight the potential of our proposed framework. Lastly, we work on spatially-resolved proteomics data which provide expression levels of proteins spatially across tissue. The application of CCA on a recent spatial proteomics data from breast cancer allows the discovery of cross-correlations between neighbourhoods and protein levels, and provides insights into the differences in tissue structure between normal and cancerous tissue. In summary, this dissertation presents algorithms, techniques and proofs to design approaches which utilize cross-correlations in medical data for disease analytics.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Vaishnavi Subramanian, -

Contributors dc:contributor

• Do, Minh N.
• Syeda-Mahmood, Tanveer
• Sinha, Saurabh
• Hajek, Bruce
• Bresler, Yoram

• mutli-modality
• canonical correlation analysis
• cancer

Statement dc:rights

• Copyright 2022 - Vaishnavi Subramanian

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/116232

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F116232