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The primer will go over graph and graph-diffusion based methods for manifold learning including diffusion maps and our new method PHATE (potential of heat-diffusion affinity-based transition embedding). We will also introduce graph signal processing and the general concept of treating measurements as signals on a cell-cell graph. We will show the utility of this view in our techniques such as MAGIC (markov affinity-based graph imputation of cells) for data denoising and imputation, and MELD (manifold-enhancement of latent dimensions) for enhancing latent experimental signals and performing causal inference on drivers of experimental differences.