More Like this

1. A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science

   https://doi.org/10.1175/AIES-D-22-0039.1  

   Ver Hoef, Lander ; Adams, Henry ; King, Emily J. ; Ebert-Uphoff, Imme ( January 2023 , Artificial Intelligence for the Earth Systems)

   Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is particularly useful for the analysis of imagery, namely, persistent homology. We briefly discuss the theoretical background but focus primarily on understanding the output of this tool and discussing what information it can glean. To this end, we frame our discussion around a guiding example of classifying satellite images from the sugar, fish, flower, and gravel dataset produced for the study of mesoscale organization of clouds by Rasp et al. We demonstrate how persistent homology and its vectorization, persistence landscapes, can be used in a workflow with a simple machine learning algorithm to obtain good results, and we explore in detail how we can explain this behavior in terms of image-level features. One of the core strengths of persistent homology is how interpretable it can be, so throughout this paper we discuss not just the patterns we find but why those results are to be expected given what we know about the theory of persistent homology. Our goal is that readers of this paper will leave with a better understanding of TDA and persistent homology, will be able to identify problems and datasets of their own for which persistent homology could be helpful, and will gain an understanding of the results they obtain from applying the included GitHub example code.

   Information such as the geometric structure and texture of image data can greatly support the inference of the physical state of an observed Earth system, for example, in remote sensing to determine whether wildfires are active or to identify local climate zones. Persistent homology is a branch of topological data analysis that allows one to extract such information in an interpretable way—unlike black-box methods like deep neural networks. The purpose of this paper is to explain in an intuitive manner what persistent homology is and how researchers in environmental science can use it to create interpretable models. We demonstrate the approach to identify certain cloud patterns from satellite imagery and find that the resulting model is indeed interpretable.

    

   more » « less
2. Minimal Cycle Representatives in Persistent Homology Using Linear Programming: An Empirical Study With User’s Guide

   https://doi.org/10.3389/frai.2021.681117  

   Li, Lu ; Thompson, Connor ; Henselman-Petrusek, Gregory ; Giusti, Chad ; Ziegelmeier, Lori ( October 2021 , Frontiers in Artificial Intelligence)

   Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creates ambiguity and can lead to many different interpretations of the same set of classes. One approach to solving this problem is to optimize the choice of representative against some measure that is meaningful in the context of the data. In this work, we provide a study of the effectiveness and computational cost of several ℓ 1 minimization optimization procedures for constructing homological cycle bases for persistent homology with rational coefficients in dimension one, including uniform-weighted and length-weighted edge-loss algorithms as well as uniform-weighted and area-weighted triangle-loss algorithms. We conduct these optimizations via standard linear programming methods, applying general-purpose solvers to optimize over column bases of simplicial boundary matrices. Our key findings are: 1) optimization is effective in reducing the size of cycle representatives, though the extent of the reduction varies according to the dimension and distribution of the underlying data, 2) the computational cost of optimizing a basis of cycle representatives exceeds the cost of computing such a basis, in most data sets we consider, 3) the choice of linear solvers matters a lot to the computation time of optimizing cycles, 4) the computation time of solving an integer program is not significantly longer than the computation time of solving a linear program for most of the cycle representatives, using the Gurobi linear solver, 5) strikingly, whether requiring integer solutions or not, we almost always obtain a solution with the same cost and almost all solutions found have entries in { ‐ 1,0,1 } and therefore, are also solutions to a restricted ℓ 0 optimization problem, and 6) we obtain qualitatively different results for generators in Erdős-Rényi random clique complexes than in real-world and synthetic point cloud data. 

   more » « less
3. Platform-integrated mRNA isoform quantification

   https://doi.org/10.1093/bioinformatics/btz932  

   Sun, Jiao ; Chang, Jae-Woong ; Zhang, Teng ; Yong, Jeongsik ; Kuang, Rui ; Zhang, Wei ; Gorodkin, ed., Jan ( December 2019 , Bioinformatics)

   Accurate estimation of transcript isoform abundance is critical for downstream transcriptome analyses and can lead to precise molecular mechanisms for understanding complex human diseases, like cancer. Simplex mRNA Sequencing (RNA-Seq) based isoform quantification approaches are facing the challenges of inherent sampling bias and unidentifiable read origins. A large-scale experiment shows that the consistency between RNA-Seq and other mRNA quantification platforms is relatively low at the isoform level compared to the gene level. In this project, we developed a platform-integrated model for transcript quantification (IntMTQ) to improve the performance of RNA-Seq on isoform expression estimation. IntMTQ, which benefits from the mRNA expressions reported by the other platforms, provides more precise RNA-Seq-based isoform quantification and leads to more accurate molecular signatures for disease phenotype prediction.

   In the experiments to assess the quality of isoform expression estimated by IntMTQ, we designed three tasks for clustering and classification of 46 cancer cell lines with four different mRNA quantification platforms, including newly developed NanoString’s nCounter technology. The results demonstrate that the isoform expressions learned by IntMTQ consistently provide more and better molecular features for downstream analyses compared with five baseline algorithms which consider RNA-Seq data only. An independent RT-qPCR experiment on seven genes in twelve cancer cell lines showed that the IntMTQ improved overall transcript quantification. The platform-integrated algorithms could be applied to large-scale cancer studies, such as The Cancer Genome Atlas (TCGA), with both RNA-Seq and array-based platforms available.

   Source code is available at: https://github.com/CompbioLabUcf/IntMTQ.

   Supplementary data are available at Bioinformatics online.

    

   more » « less
4. DeepGAMI: deep biologically guided auxiliary learning for multimodal integration and imputation to improve genotype–phenotype prediction

   https://doi.org/10.1186/s13073-023-01248-6  

   Chandrashekar, Pramod Bharadwaj ; Alatkar, Sayali ; Wang, Jiebiao ; Hoffman, Gabriel E. ; He, Chenfeng ; Jin, Ting ; Khullar, Saniya ; Bendl, Jaroslav ; Fullard, John F. ; Roussos, Panos ; et al ( October 2023 , Genome Medicine)

   Genotypes are strongly associated with disease phenotypes, particularly in brain disorders. However, the molecular and cellular mechanisms behind this association remain elusive. With emerging multimodal data for these mechanisms, machine learning methods can be applied for phenotype prediction at different scales, but due to the black-box nature of machine learning, integrating these modalities and interpreting biological mechanisms can be challenging. Additionally, the partial availability of these multimodal data presents a challenge in developing these predictive models.

   To address these challenges, we developed DeepGAMI, an interpretable neural network model to improve genotype–phenotype prediction from multimodal data. DeepGAMI leverages functional genomic information, such as eQTLs and gene regulation, to guide neural network connections. Additionally, it includes an auxiliary learning layer for cross-modal imputation allowing the imputation of latent features of missing modalities and thus predicting phenotypes from a single modality. Finally, DeepGAMI uses integrated gradient to prioritize multimodal features for various phenotypes.

   We applied DeepGAMI to several multimodal datasets including genotype and bulk and cell-type gene expression data in brain diseases, and gene expression and electrophysiology data of mouse neuronal cells. Using cross-validation and independent validation, DeepGAMI outperformed existing methods for classifying disease types, and cellular and clinical phenotypes, even using single modalities (e.g., AUC score of 0.79 for Schizophrenia and 0.73 for cognitive impairment in Alzheimer’s disease).

   We demonstrated that DeepGAMI improves phenotype prediction and prioritizes phenotypic features and networks in multiple multimodal datasets in complex brains and brain diseases. Also, it prioritized disease-associated variants, genes, and regulatory networks linked to different phenotypes, providing novel insights into the interpretation of gene regulatory mechanisms. DeepGAMI is open-source and available for general use.

    

   more » « less
5. The shape of things to come: Topological data analysis and biology, from molecules to organisms

   https://doi.org/10.1002/dvdy.175  

   Amézquita, Erik J. ; Quigley, Michelle Y. ; Ophelders, Tim ; Munch, Elizabeth ; Chitwood, Daniel H. ( April 2020 , Developmental Dynamics)

   Shape is data and data is shape. Biologists are accustomed to thinking about how the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. Less often do we consider that data itself has shape and structure, or that it is possible to measure the shape of data and analyze it. Here, we review applications of topological data analysis (TDA) to biology in a way accessible to biologists and applied mathematicians alike. TDA uses principles from algebraic topology to comprehensively measure shape in data sets. Using a function that relates the similarity of data points to each other, we can monitor the evolution of topological features—connected components, loops, and voids. This evolution, a topological signature, concisely summarizes large, complex data sets. We first provide a TDA primer for biologists before exploring the use of TDA across biological sub‐disciplines, spanning structural biology, molecular biology, evolution, and development. We end by comparing and contrasting different TDA approaches and the potential for their use in biology. The vision of TDA, that data are shape and shape is data, will be relevant as biology transitions into a data‐driven era where the meaningful interpretation of large data sets is a limiting factor.

    

   more » « less