A field guide to the families of methods that turn high-dimensional data into something we can look at, organized by the kind of structure each one protects.
Every dimensionality reduction algorithm is a decision about what matters. PCA says variance matters. t-SNE says who-is-near-whom matters. Mapper says shape matters. Poincaré embeddings say hierarchy matters. When you pick a method, you are picking a definition of structure.
The literature usually organizes these methods by how they are computed: eigendecompositions here, gradient descent there, neural networks in a third bucket. That works for implementers. For practitioners choosing a tool, a better axis is what the method is trying to preserve, because that is what tells you whether your data and your question match.
This series walks through the landscape that way. Each article takes a family of methods organized around a single notion of "structure," builds up intuition for what each preserves and what it discards, and shows where the tradeoffs show up in practice. The audience is machine-learning practitioners who work with high-dimensional data every day but want a sharper toolkit for understanding latent spaces, embeddings, and learned representations.
Why high-dimensional space is strange, what "structure" can mean, and how we tell whether a projection is honest.
PCA, ICA, NMF, Kernel PCA, random projection. Variance, independence, parts, and why old methods still matter.
Classical MDS, Sammon mapping, Isomap, diffusion maps. From Euclidean to geodesic to diffusion distance.
t-SNE, UMAP, and the neighbor-graph family. How "who is near whom" became the dominant paradigm.
Mapper, Reeb graphs, topological autoencoders. When shape matters more than position.
densMAP and PHATE. Why most methods flatten density, and what the exceptions buy you.
When you want the output to be a grid, not a cloud. Competitive learning, neighborhood functions, U-matrices.
When your data is tree-shaped, Euclidean space cramps it. Hyperbolic geometry does not.
Autoencoders, VAE, scVI, parametric UMAP. When the dimensionality reduction is itself a trained neural function.
Where current methods fail for understanding ML latent spaces, and directions the families in this series suggest but have not yet taken.
Articles are self-contained and can be read in any order, but the progression does matter. Each family tends to fix something that the previous family struggled with, and the framing article sets up the shared vocabulary. If you are new to this territory, read in sequence. If you are here for one method, jump directly to its article and let the prose pull in what it needs.
The literature backing these articles lives at latent-verse/research, 108 paper summaries across the methods covered here and the surrounding areas (clustering, evaluation, topological data analysis, embedding tools). The articles treat that as the grounding rather than reproducing it.