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From what I understand from this and this paper on dimensionality reduction, spectral embeddings refer to any technique that conducts an eigendecomposition of an affinity matrix, not just Laplacian Eigenmaps. Those papers, and numerous other explicitly state the algorithms "spectral embedding" includes.
"... for spectral embedding algorithms such as metric multidimensional scaling (MDS) (Cox & Cox, 1994), spectral clustering (see Weiss, 1999, for a review), Laplacian eigenmaps, LLE, and Isomap..." 3
In fact, the sklearn documentation was the only source I could find that refers to laplacian eigenmaps and spectral embedding synonymously.
If I am correct, I propose renaming spectral embedding to laplacian eigenmaps, or, at the very least, correct the misleading documentation that says "Spectral Embedding (also known as Laplacian Eigenmaps)...".
"Spectral methods ... are able to reveal low dimensional structure in high dimensional data from the top or bottom eigenvectors of specially constructed matrices" 4