How do I obtain the best representative sentence for a single sentence embedding vector?

I have a corpus of 30k articles, for which I have use the OpenAI API to find embeddings using text_embedding_3_large model.

I then apply PCA on the embeddings to perform dimensionality reduction down to 5 most important ones. But these are numerical, and I'd like to recover their semantics.

How do I do that? How, given an embedding, can I find a single canonical sentence, or a group of highly-representative sentences, for the given embedding?

I know I can simply look at my 30k embeddings and perform some distance metric on them versus the principal components, and choose the closest ones, but I am wondering if there is a theoretical way I can get a representative sample "analytically".



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