UMAP has largely replaced t-SNE in our toolkit as one of our top go-to viz pipelines. Unlike most examples out there, we post-process with k-nn to expose the graph of correlations over arbitrary data sets -- bank accounts fraud scores, cancer protein mutations, twitter bots, malware files, etc. -- and then investigate. Algorithms like UMAP figure out this connectivity anyways (see also: TDA), and useful for guiding subsequent explorations. If you're doing an interactive analysis, like looking at data in a Jupyter notebook, super powerful to expose that inferred connectivity and make it interactive (on-the-fly filtering, clustering, etc.) on it.

Tool-wise, we do it in a few lines over tables with many rows/columns via end-to-end GPU acceleration using https://www.RAPIDS.ai (GPU dataframes + UMAP) + Graphistry (GPU viz, which we make).

Do you mean principal component analysis? My naive understanding after reading the original paper is that the algorithm is training a transformation to project the high dimensional data into low dimensions by best preserving both the global and local proximity. So that the samples similar at high dim space should also be close in the low dim one. It has some assumption of the distribution of the data in low dim so it won't be a random guess. It's using the t-distribution at low dim hence the name t-SNE. Correct me if any mistakes.