SCA: recovering single-cell heterogeneity through information-based dimensionality reduction.

Dimensionality reduction summarizes the complex transcriptomic landscape of single-cell datasets for downstream analyses. Current approaches favor large cellular populations defined by many genes, at the expense of smaller and more subtly defined populations. Here, we present surprisal component analysis (SCA), a technique that newly leverages the information-theoretic notion of surprisal for dimensionality reduction to promote more meaningful signal extraction.

Hopper: a mathematically optimal algorithm for sketching biological data.

Motivation: Single-cell RNA-sequencing has grown massively in scale since its inception, presenting substantial analytic and computational challenges. Even simple downstream analyses, such as dimensionality reduction and clustering, require days of runtime and hundreds of gigabytes of memory for today's largest datasets. In addition, current methods often favor common cell types, and miss salient biological features captured by small cell populations.

Geometric Sketching Compactly Summarizes the Single-Cell Transcriptomic Landscape.

Large-scale single-cell RNA sequencing (scRNA-seq) studies that profile hundreds of thousands of cells are becoming increasingly common, overwhelming existing analysis pipelines. Here, we describe how to enhance and accelerate single-cell data analysis by summarizing the transcriptomic heterogeneity within a dataset using a small subset of cells, which we refer to as a geometric sketch. Our sketches provide more comprehensive visualization of transcriptional diversity, capture rare cell types with high sensitivity, and reveal biological cell types via clustering.

Large-Margin Classification in Hyperbolic Space.

Representing data in hyperbolic space can effectively capture latent hierarchical relationships. To enable accurate classification of points in hyperbolic space while respecting their hyperbolic geometry, we introduce hyperbolic SVM, a hyperbolic formulation of support vector machine classifiers, and describe its theoretical connection to the Euclidean counterpart. We also generalize Euclidean kernel SVM to hyperbolic space, allowing nonlinear hyperbolic decision boundaries and providing a geometric interpretation for a certain class of indefinite kernels.