In general these are referred to as embedding techniques
PCA/SVD is still common along with other linear methods like ICA, CCA, PLS
t-sne is pretty popular statistically inspired with some manifold learning
non-negative matrix factorization is useful recommender systems
topologically inspired techniques are gaining traction, like UMAP, LLE
the author notes neural embeddings, like autoencoders.
Around the time that this article was written I was putting the finishing touches on a neural autoencoder that was part of a search engine for patents. (The training was done with assembly language SIMD instructions so we weren't in a hurry to make any changes in the network, training algorithms, ...)
The search engine worked amazingly well. When we first demoed it we heard from the USPTO in the first week, they wanted to buy a license...
Yeah. I was kind of infatuated with the UMAP paper when it first came up (and working through it to build intuition led me to persistent homology and other fun stuff), but it's far too complex to work as a "plug-in tool" that people naive to statistics can blindly use.
This is the power of ANOVA, CCA, linear regression and factor analysis, etc. It's much, much, much, much harder to shoot yourself in the foot, particularly with experimental data (usage in the social sciences is another bag of johnsons.)
