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TDA
Predicting phenotypes using topology and machine learning
TDA helps to identify phenotypes.
Sayan Mandal
,
Soham Mukherjee
Code
Video
Determining clinically relevant features in cytometry data using persistent homology
TDA helps to identify structural difference in single-cell cytometry data.
Code
A Jacobi-set based loss function for segmentation task
Segmentation of fine-scale structures in natural and bio-medical images are gaining importance with the development of high resolution electron microscopy images. The task still remains challenging as per-pixel accuracy is not only the metric of concern because of the imbalance in the dataset. In this project, a new loss function based on the Jacobi-sets are proposed.
Soham Mukherjee
PDF
Graph generation with Geometrical and Topological Constraints
Persistent homology, a tool from computational topology we computed persistent diagrams of graphs and incorporated topological & geometrical constraints while generating graphs.
GEFL: Extended Filtration Learning for Graph Classification
Learning Extended filtration on graphs
Simon Zhang
,
Soham Mukherjee
,
Tamal K. Dey
PDF
Code
GEFL: Extended Filtration Learning for Graph Classification
Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called persistence barcodes. We introduce extended persistence into a supervised learning framework for graph classification. Global topological information, in the form of a barcode with four different types of bars and their explicit cycle representatives, is combined into the model by the readout function which is computed by extended persistence. The entire model is end-to-end differentiable
Simon Zhang
,
Soham Mukherjee
,
Tamal K. Dey
PDF
Code
Denoising with discrete Morse theory
Denoising noisy datasets is a crucial task in this data-driven world. In this paper, we develop a persistence-guided discrete Morse …
Soham Mukherjee
PDF
Code
DOI
Determining clinically relevant features in cytometry data using persistent homology
Identifying differences between cytometry data seen as a point cloud can be complicated by random variations in data collection and data sources. We apply
persistent homology
used in
topological data analysis
to describe the shape and structure of the data representing immune cells in healthy donors and COVID-19 patients. By looking at how the shape and structure differ between healthy donors and COVID-19 patients, we are able to definitively conclude how these groups differ despite random variations in the data. Furthermore, these results are novel in their ability to capture shape and structure of cytometry data, something not described by other analyses.
Soham Muhkerjee
,
Darren Wethington
,
Tamal K. Dey
,
Jayajit Das
PDF
Code
Dataset
DOI
Gene expression data classification using topology and machine learning models
We show that the representative cycles we compute have an unsupervised inclination towards phenotype labels. This work thus shows that topological signatures are able to comprehend gene expression levels and classify cohorts accordingly.
Soham Mukherjee
,
Sayan Mandal
,
Tamal K. Dey
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