# What does the embedding mean in the FaceNet?

I am reading the paper about FaceNet but I can't get what does the embedding mean in this paper? Is it a hidden layer of the deep CNN?
P.S. English isn't my native language.

Assume you have features wich lie in a $$R^n$$ space, e.g. your input is a picture with $$28 \times 28$$ pixels, then $$n$$ would be $$28 \times 28 = 784$$.

Now you can "embedd" your features into another $$R^d$$ space, where often $$d < n$$. This way you learn a rich representation of your input. When you compress your $$784$$ input-pixels to, lets say $$64$$ you compressed your input by more than a factor $$10$$ and can elimnate redundant/useless features.

This embedding learning is of course done in such a way, that you could fully restore your original $$784$$ pixels out of your $$64$$ compressed pixels.

• Thank you for simple and clear explanation, seems I could get it!
– Шах
Nov 14 '18 at 20:52

An embedding is a mapping from discrete objects, such as words, to vectors of real numbers.

With reference to the FaceNet paper, I should say that embedding here simply means the tensor obtained by performing a forward propagation over an image. The obtained embedding of the image and the target image are then compared to find the closeness among the images. The loss function specified by the equation $$L=\sum_{i}^N [ ||f(x_i^a)-f(x_i^p)||_2^2-||f(x_i^a)-f(x_i^n)||_2^2+\alpha]_+$$ is simply used here to to find the euclidean distance between the generated embedding of the anchor, positive and negative images obtained by performing forward propagation. This technique is also called as Siamese network.

I suggest you to read the full original FaceNet paper for clearer understanding of the FaceNet architecture and working.