Responder Lab's platform is built on 15 years of academic research in topological data analysis, geometric learning, and pharmacogenomics. The work below forms the mathematical and biological foundation of Responder Atlas.
Nature Neuroscience2022
A tool for mapping microglial morphology, morphOMICs, reveals brain-region and sex-dependent phenotypes
Nature Neuroscience · doi:10.1038/s41593-022-01167-6
This landmark paper demonstrates the power of topological data analysis in mapping biological morphology at scale. Using a TDA-based pipeline, morphOMICs reveals previously invisible subpopulations within heterogeneous cell populations — identifying brain-region-specific and sex-dependent phenotypes that conventional methods miss entirely.
Directly demonstrates TDA's ability to identify hidden subpopulations in complex biological datasets — the same foundational principle driving Responder Atlas.
TDAsubpopulation-mappingheterogeneityNature
nature.com/articles/s41593-022-01167-6medRxiv Preprint2024
Geometric learning and topological data analysis for oncology drug response prediction
medRxiv · doi:10.1101/2024.07.01.24309803
This preprint presents the core methodology behind Responder Atlas — applying geometric learning and topological data analysis to large pharmacogenomic datasets to identify responder subpopulations in oncology. Demonstrates 82% out-of-sample accuracy in identifying responders from Phase 3 trial data across multiple cancer types and drug classes. Currently under peer review.
This is the primary methods paper for the Responder Atlas platform. The 82% out-of-sample accuracy result is the central validation of the approach.
Responder-Atlaspharmacogenomicsgeometric-learningpreprint
medrxiv.org · 2024.07.01.24309803Frontiers in Applied Mathematics2021
Supervised Learning Using Homology Stable Rank Kernels
Frontiers in Applied Mathematics and Statistics · doi:10.3389/fams.2021.668046
Introduces a novel supervised learning framework using homology stable rank kernels — a mathematically rigorous approach to encoding topological features of data for classification tasks. The method extracts persistent homological features and maps them into a kernel space suitable for support vector machines and other classifiers, enabling topology-aware prediction.
Provides the kernel-based learning framework used in Responder Atlas for mapping pharmacogenomic data into geometric architectures that preserve biological structure.
homologystable-rankkernel-methodssupervised-learning
frontiersin.org · fams.2021.668046Foundations of Computational Mathematics2017
Multidimensional Persistence and Noise
Foundations of Computational Mathematics · doi:10.1007/s10208-016-9323-y
A foundational theoretical paper establishing the mathematical framework for multidimensional persistence — the extension of topological persistence to high-dimensional data spaces. Addresses noise stability and develops the theoretical guarantees needed to apply persistent homology to real-world noisy biological datasets, proving that topological features are robust under perturbation.
Establishes the mathematical noise-robustness guarantees that make TDA applicable to high-dimensional pharmacogenomic data, where biological variation and measurement noise are unavoidable.
persistence-homologynoise-stabilitymultidimensional-TDAtheory
link.springer.com · s10208-016-9323-yBMC Bioinformatics2020
A topological data analysis based classification method for multiple measurements
Riihimäki H, Chachólski W, Theorell J et al. · BMC Bioinformatics 21, 336 · doi:10.1186/s12859-020-03659-3
Presents a TDA-based classifier specifically designed for repeated biological measurements — sampling from the data space, constructing a topology-preserving network graph, and applying cross-validated machine learning for classification. Demonstrates accuracy exceeding standard SVM approaches across multiple biological case studies, with the key advantage of identifying high-purity data subsets alongside classification.
The classification methodology and network graph construction pipeline in this paper are directly applied in Responder Atlas for identifying and characterising responder subpopulations within tumor populations.
TDA-classifierbioinformaticsnetwork-graphcross-validation
link.springer.com · s12859-020-03659-3arXiv2022
Data, Geometry and Homology
Agerberg J, Chacholski W, Ramanujam R · arXiv:2203.08306
Investigates how the geometry of a dataset changes when subsampled in various ways — introducing a framework where the dataset serves as a reference object and different points in ambient space are endowed with geometry defined relative to that reference. Demonstrates how this process extracts rich geometrical information sufficient to classify points from different data distributions, with direct applications to heterogeneous biological datasets.
The subsampling geometry framework described here underlies Responder Atlas's approach to mapping pharmacogenomic data — treating the tumor population as a reference geometry and locating responder subspaces within it.
data-geometryhomologysubsamplingdistribution-classification
arxiv.org · 2203.08306