Date of Award

Spring 2021

Document Type


Degree Name

Doctor of Philosophy (PhD)



First Advisor

Krishnaswamy, Smita


Recent advances in microfluidic technologies facilitate the measurement of gene expression, DNA accessibility, protein content, or genomic mutations at unprecedented scale. The challenges imposed by the scale of these datasets are further exacerbated by non-linearity in molecular effects, complex interdependencies between features, and a lack of understanding of both data generating processes and sources of technical and biological noise. As a result, analysis of modern single-cell data requires the development of specialized computational tools. One solution to these problems is the use of manifold learning, a sub-field of unsupervised machine learning that seeks to model data geometry using a simplifying assumption that the underlying system is continuous and locally Euclidean. In this dissertation, I show how manifold learning is naturally suited for single-cell analysis and introduce three related algorithms for characterization of single-cell heterogeneity and perturbation response. I first describe Vertex Frequency Clustering, an algorithm that identifies groups of cells with similar responses to an experiment perturbation by analyzing the spectral representation of condition labels expressed as signals over a cell similarity graph. Next, I introduce MELD, an algorithm that expands on these ideas to estimate the density of each experimental sample over the graph to quantify the effect of an experimental perturbation at single cell resolution. Finally, I describe a neural network for archetypal analysis that represents the data as continuously distributed between a set of extrema. Each of these algorithms are demonstrated on a combination of real and synthetic datasets and are benchmarked against state-of-the-art algorithms.