Asymptotic theory for density ridges

Chen, Yen‐Chi; Genovese, Christopher R.; Wasserman, Larry

doi:10.1214/15-aos1329

Cited by 69 publications

(86 citation statements)

References 49 publications

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“…This distinction requires a robust statistical characterization of structural representations generated by single-cell analysis methods. Unlike prior single-cell trajectory estimators, NRE is uniquely capable of estimating confidence sets of ridge positions when applied with a linear representation (nonlinear or quasilinear representations are not yet supported in theoretical results) 18 (Figure 2a).…”

Section: Statistical Inference Of Uncertainties In Trajectory Estimationmentioning

confidence: 99%

“…We developed a quasilinear approach, StructDR, that leverages the nonparametric density ridge estimation (NRE) method [16][17][18] . It unifies the estimation of single-cell clusters and trajectories, with new, complex structure types such as surfaces and allowed rigorous estimation of statistical confidence of these structures via bootstrapping (Figure 2a, Methods).…”

Section: Supplementary Figure 2 Experimental Design Encoding Throughmentioning

confidence: 99%

“…The nonparametric density ridge estimation problem can be solved via the subspace constrained mean shift (SCMS) algorithm 17,23 . The statistical theory of nonparametric density ridge estimation is described in detail in 16,18 .…”

Section: Single-cell Data Structure Discovery With Nonparametric Densmentioning

confidence: 99%

“…As described in Chen et al 18 , the bootstrap confidence set can be constructed through the following procedure: 1. first generate bootstrap samples by via sampling with replacement; then estimate density ridges for each bootstrap sample; 2. for each position in the density ridge set estimated from the original sample, calculate the distance to its nearest position in each bootstrap sample density ridge set; 3. take -upper quantile of the distances . , and the -confidence set of each estimated ridge position is constructed as a sphere of radius .…”

Section: Single-cell Data Structure Discovery With Nonparametric Densmentioning

confidence: 99%

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An analytical framework for interpretable and generalizable ‘quasilinear’ single-cell data analysis

Zhou

Troyanskaya

2020

Preprint

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Scaling single-cell data exploratory analysis with the rapidly growing diversity and quantity of single-cell omics datasets demands more interpretable and robust data representation that is generalizable across datasets. To address this challenge, here we developed a novel 'quasilinear' framework that combines the interpretability and transferability of linear methods with the representational power of nonlinear methods. Within this framework, we introduce a data representation and visualization method, GraphDR, and a structure discovery method, StructDR, that unifies cluster, trajectory, and surface estimation and allows their confidence set inference. We applied both methods to diverse single-cell RNA-seq datasets from whole embryos and tissues. Unlike PCA and t-SNE, GraphDR and StructDR generated representations that both distinguished highly specific cell types and were comparable across datasets. In addition, GraphDR is at least an order of magnitude faster than commonly used nonlinear methods. Our visualizations of scRNAseq data from developing zebrafish and Xenopus embryos revealed extruding branches of lineages from a continuum of cell states, suggesting that the current branch view of cell specification may be oversimplified. Moreover, StructDR identified a novel neuronal population using scRNA-seq data from mouse hippocampus. An open-source python library and a user-friendly graphical interface for 3D data visualization and analysis with these methods are available at https://github.com/jzthree/quasildr. mature mouse brain cell types 10 (Figure 1a). GraphDR generated representations that preserved the interpretability of subspace like PCA and resolved the different cell types like t-SNE (Figure 1b-d). Therefore, importantly, this gain of interpretability was achieved without a loss of accuracy. Moreover, in a large-scale quantitative benchmark across a diverse set of seven single-cell datasets, GraphDR distinguished cell types/states as well as several current state-of-the-art nonlinear methods, measured by consistency of nearest neighbors in dimensionality-reduced embedding with literature-based cell type identities (Figure 1c-d, Methods).

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Section: Statistical Inference Of Uncertainties In Trajectory Estimationmentioning

confidence: 99%

Section: Supplementary Figure 2 Experimental Design Encoding Throughmentioning

confidence: 99%

Section: Single-cell Data Structure Discovery With Nonparametric Densmentioning

confidence: 99%

Section: Single-cell Data Structure Discovery With Nonparametric Densmentioning

confidence: 99%

See 2 more Smart Citations

An analytical framework for interpretable and generalizable ‘quasilinear’ single-cell data analysis

Zhou

Troyanskaya

2020

Preprint

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“…Specifically, we take R = R r ( p h ) to be the ridge of the kernel estimator. The properties of this estimator are studied in Genovese et al (2014) and Chen et al (2015b). An algorithm for finding the ridge set of p h was given by Ozertem & Erdogmus (2011) and is called the SCMS (subspace constrained mean shift algorithm).…”

Section: Ridgesmentioning

confidence: 99%

Topological Data Analysis

Wasserman

2018

Annu. Rev. Stat. Appl.

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402

267

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Multiple Penalized Principal Curves: Analysis and Computation

Kirov

Slepčev

2017

J Math Imaging Vis

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We study the problem of determining the one-dimensional structure that best represents a given data set. More precisely, we take a variational approach to approximating a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of principal curves and introduce a new functional which allows for multiple curves. We prove existence of minimizers and investigate their properties. While both of the functionals used are non-convex, we show that enlarging the configuration space to allow for multiple curves leads to a simpler energy landscape with fewer undesirable (high-energy) local minima. We provide an efficient algorithm for approximating minimizers of the functional and demonstrate its performance on real and synthetic data. The numerical examples illustrate the effectiveness of the proposed approach in the presence of substantial noise, and the viability of the algorithm for high-dimensional data.

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Asymptotic theory for density ridges

Cited by 69 publications

References 49 publications

An analytical framework for interpretable and generalizable ‘quasilinear’ single-cell data analysis

An analytical framework for interpretable and generalizable ‘quasilinear’ single-cell data analysis

Topological Data Analysis

Multiple Penalized Principal Curves: Analysis and Computation

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