TDAstats: R pipeline for computing persistent homology in topological data analysis

Area of Science:

• Data Science
• Computational Biology
• Medical Informatics

Background:

• High-dimensional datasets are prevalent across scientific fields, including biology and medicine.
• Dimension reduction techniques like Principal Component Analysis (PCA) are common but can lead to significant information loss.
• Topological Data Analysis (TDA) provides an alternative by analyzing data shape without dimension reduction.

Purpose of the Study:

• To explore the application of TDA for analyzing high-dimensional datasets.
• To highlight TDA's ability to extract robust features and provide insights invisible to traditional methods.
• To showcase TDA's potential in identifying clinically relevant patient subgroups.

Main Methods:

• Utilizing Topological Data Analysis (TDA) to study the 'shape' of high-dimensional data.
• Extracting persistent features that are robust to data perturbations.
• Visualizing persistent features using topological barcodes or persistence diagrams.
• Applying a TDA-based method, Progression Analysis of Disease, to patient data.

Main Results:

• TDA methods can provide greater insight into high-dimensional data.
• Persistent features can effectively describe and compare datasets.
• A specific TDA method identified a breast cancer patient subgroup with 100% survival.
• This subgroup was not discernible through conventional clustering methods.

Conclusions:

• TDA is a powerful tool for analyzing complex, high-dimensional datasets.
• TDA can uncover hidden structures and clinically relevant subgroups.
• The Progression Analysis of Disease method demonstrates TDA's clinical utility in oncology.