UMAP - topology manifold learning based method
Ivis - simese triplet network autoencoder
Both of them will blow PCA out of the water on basically all datasets. PCAs only advantages are speed and interpretability (easy to see explained covariance)
Ignoring the eigen aspect would miss a lot of both theory and practice.
Um, these seem to be perhaps the 2 most important advantages something could have? What are advantages that UMAP and Ivis have that are more important than speed and interpretability?
When you want to perform some sort of clustering on top of the dimensionality reduction its a very useful property.
Note that is it very common to get rid of 90% of the dimensionality with a PCA and then to apply something like UMAP on top to improve speed (and because PCA can be trusted to keep the relevant information for later postprocessig which cannot be said of other techniques).
I also think PCA still rules in a lot of cases like when people try to create a new index representative of a bunch of numeric variables
[1] https://www.kaggle.com/nulldata/umap-dim-reduction-viz-on-ka...