Topological analysis of single-cell data reveals shared glial landscape of macular degeneration and neurodegenerative diseases

Kuchroo, Manik; DiStasio, Marcello; Calapkulu, Eda; Ige, Maryam; Zhang, Le; Sheth, Amar H.; Menon, Madhvi; Yu, Xiuping; Gigante, Scott; Huang, Jessie; Dhodapkar, Rahul; Rieck, Bastian; Wolf, Guy; Krishnaswamy, Smita; Hafler, Brian P.

doi:10.1101/2021.01.19.427286

Cited by 3 publications

(6 citation statements)

References 65 publications

(80 reference statements)

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“…At each granularity level, image segmentation can be produced by mapping these clusters obtained from the embeddings back to the corresponding pixel locations in the image space. We perform this critical coarse-graining step with a method called diffusion condensation [31,32], Figure 3: The convolutional encoder maps pixel-centered patches into a structured and meaningful latent embedding space. CUTS combines two unsupervised objectives, respectively a contrastive loss and an autoencoderinspired reconstruction loss, to jointly guide the learning of the embedding space.…”

Section: Methodsmentioning

confidence: 99%

“…Diffusion condensation for multi-scale coarse-graining Diffusion condensation [31,32] is a dynamic process that sweeps through various levels of granularities to identify natural groupings of data. It iteratively condenses data points towards their neighbors through a diffusion process, at a rate defined by the diffusion probability between the points.…”

Section: Coarse-graining the Embeddings For Multi-scale Segmentationmentioning

confidence: 99%

“…To perform multi-step diffusion, one way is to simulate a timehomogeneous diffusion process by raising the diffusion operator to a power of t which leads to X t = P t X [36]. On the other hand, as shown in [32], we could simulate a time-inhomogeneous diffusion process by iteratively computing the diffusion operator and the data matrix in the following manner.…”

Section: Coarse-graining the Embeddings For Multi-scale Segmentationmentioning

confidence: 99%

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CUTS: A Fully Unsupervised Framework for Medical Image Segmentation

Liu

Amodio

Shen

et al. 2023

Preprint

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In this work we introduce CUTS (Contrastive and Unsupervised Training for Segmentation), the first fully unsupervised deep learning framework for medical image segmentation to better utilize the vast majority of imaging data that is not labeled or annotated. Segmenting medical images into regions of interest is a critical task for facilitating both patient diagnoses and quantitative research. A major limiting factor is the lack of labeled data, as obtaining expert annotations for each new set of imaging data or task can be expensive, labor intensive, and inconsistent across annotators. Thus, we utilize self-supervision from pixels and their local neighborhoods in the images themselves. Our unsupervised approach optimizes a training objective that leverages concepts from contrastive learning and autoencoding. Previous contrastive learning approaches either focused on image-level contrastive training and therefore lacked sufficient patch-level information necessary for segmentation or framed themselves as pre-training steps that require further supervised fine-tuning. In contrast, our framework segments medical images with a novel two-stage approach without relying on any labeled data at any stage. The first stage involves the creation of a "pixel-centered patch" that embeds every pixel along with its surrounding patch, using a vector representation in a high-dimensional latent embedding space. The second stage utilizes diffusion condensation, a multi-scale topological data analysis approach, to dynamically coarse-grain these embedding vectors at all levels of granularity. The final outcome is a series of coarse-to-fine segmentations that highlight image structures at various scales. In this work, we show successful multi-scale segmentation on natural images, retinal fundus images, and brain MRI images. Our framework delineates structures and patterns at different scales which, in the cases of medical images, may carry distinct information relevant to clinical interpretation. Quantitatively, our framework demonstrates beyond 100% improvement on dice coefficient and Hausdorff distance compared to existing unsupervised methods on geographic atrophy segmentation in retinal fundus images. When segmenting ventricles in the brain MRI images, our framework outperforms existing unsupervised methods by a factor between 2% to 300% on dice coefficient and between 14% and 77% on Hausdorff distance. As we tackle the problem of segmenting medical images at multiple meaningful granularities without relying on any label, we hope to demonstrate the possibility to circumvent tedious and repetitive manual annotations in future practice.

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Section: Methodsmentioning

confidence: 99%

Section: Coarse-graining the Embeddings For Multi-scale Segmentationmentioning

confidence: 99%

Section: Coarse-graining the Embeddings For Multi-scale Segmentationmentioning

confidence: 99%

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CUTS: A Fully Unsupervised Framework for Medical Image Segmentation

Liu

Amodio

Shen

et al. 2023

Preprint

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“…Kuchroo et al [23] applied diffusion condensation to embed and visualize single-cell proteomic data to explore the effect of COVID-19 on the immune system. Kuchroo et al [22] applied diffusion condensation on single-nucleus RNA sequencing data from human retinas with agerelated macular degeneration (AMD) and found a potential drug target by exploring the topological structure of the resulting diffusion condensation process. van Dijk et al [32] applied one step of diffusion condensation (t = 1) with high τ to single-cell RNA sequencing data to impute gene expression.…”

Section: Related Work Using Diffusion Condensation For Data Analysis ...mentioning

confidence: 99%

Time-inhomogeneous diffusion geometry and topology

Huguet¹,

Tong²,

Rieck³

et al. 2022

Preprint

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Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of high-dimensional data. Diffusion condensation is constructed as a time-inhomogeneous process where each step first computes and then applies a diffusion operator to the data. We theoretically analyze the convergence and evolution of this process from geometric, spectral, and topological perspectives. From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel. Our spectral results are of particular interest since most of the literature on data diffusion is focused on homogeneous processes. From a topological perspective, we show diffusion condensation generalizes centroidbased hierarchical clustering. We use this perspective to obtain a bound based on the number of data points, independent of their location. To understand the evolution of the data geometry beyond convergence, we use topological data analysis. We show that the condensation process itself defines an intrinsic diffusion homology. We use this intrinsic topology as well as an ambient topology to study how the data changes over diffusion time. We demonstrate both homologies in well-understood toy examples. Our work gives theoretical insights into the convergence of diffusion condensation, and shows that it provides a link between topological and geometric data analysis.

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“…TDA methods require a metric and approximate the shape of the data by building covers or sequences of higher order networks (i.e., filtrations) on the data. TDA methods have successfully analysed and visualised single-cell data (e.g., UMAP, which relies on fuzzy simplicial sets; or Mapper, which visualises data using covers and filters) [ 3 , 4 , 5 , 6 , 7 , 8 ]. In this paper, instead of studying the shape of data, we focus on the related task of quantifying how well signals on a given data set align with the topology of the data.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Methods for Signal Selection in Single-Cell Data

Hoekzema

Marsh

Sumray

et al. 2022

Entropy

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Analysis of single-cell transcriptomics often relies on clustering cells and then performing differential gene expression (DGE) to identify genes that vary between these clusters. These discrete analyses successfully determine cell types and markers; however, continuous variation within and between cell types may not be detected. We propose three topologically motivated mathematical methods for unsupervised feature selection that consider discrete and continuous transcriptional patterns on an equal footing across multiple scales simultaneously. Eigenscores (eigi) rank signals or genes based on their correspondence to low-frequency intrinsic patterning in the data using the spectral decomposition of the Laplacian graph. The multiscale Laplacian score (MLS) is an unsupervised method for locating relevant scales in data and selecting the genes that are coherently expressed at these respective scales. The persistent Rayleigh quotient (PRQ) takes data equipped with a filtration, allowing the separation of genes with different roles in a bifurcation process (e.g., pseudo-time). We demonstrate the utility of these techniques by applying them to published single-cell transcriptomics data sets. The methods validate previously identified genes and detect additional biologically meaningful genes with coherent expression patterns. By studying the interaction between gene signals and the geometry of the underlying space, the three methods give multidimensional rankings of the genes and visualisation of relationships between them.

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Topological analysis of single-cell data reveals shared glial landscape of macular degeneration and neurodegenerative diseases

Cited by 3 publications

References 65 publications

CUTS: A Fully Unsupervised Framework for Medical Image Segmentation

CUTS: A Fully Unsupervised Framework for Medical Image Segmentation

Time-inhomogeneous diffusion geometry and topology

Multiscale Methods for Signal Selection in Single-Cell Data

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