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The term feature embedding appears to be a synonym for feature extraction, feature learning etc. I.e. a form of embedding/dimension reduction (with the caveat the goal may not be a lower dimensional representation but one of equal dimensionality, but more meaningfully expressed):
Feature embedding is an emerging research area which intends to transform features from the original space into a new space to support effective learning.
Feature embeddings are basically anything that can act as a hidden representation for given object.
In the case of images, a CNN architecture is built to create such hidden representation. Usually, the outcome of the bottleneck layer is flattened (and sometimes, converted to even lower dimensional space by adding one more dense layer) and used as feature embeddings.