Dynamic mode decomposition for decentralized spectral clustering of graphs
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Blog posts
2023
2022
A computational understanding of Uniform Manifold Approximation and Projection (UMAP)
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Uniform Manifold Approximation and Projection (UMAP) is a nonlinear dimensionality reduction technique developed by McIness et al. in 2018. Though its use is often called into question in the biological sciences, it has become a key visualization tool for many computational biologists wanting to tease apart important differences between cellular transcription or genetic profiles. While UMAP has been widely adopted as the state-of-the-art in nonlinear dimensionality reduction, it is often poorly understood by its users, leading to its misuse. The difficulty in understanding UMAP is in part due to the tremendous effort by the original authors in exposing mathematical ideas that ground UMAP as the first graph-based approach with theoretical understanding of its functionality. The authors use ideas from Riemannian geometry and algebraic topology to construct the theoretical framework on which UMAP is built. It is then good news that UMAP can be thoroughly understood from an entirely computational perspective.
Metric spaces of microbial essential gene landscapes
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Essential genes are those which are crucial for survival of an organism in a given context. This post will introduce manifold and metric learning to characterize and classify essential genes from the chaos game representation of a genetic sequence.