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As I searched about this two terms, I found they are somehow like each other, both try to create a vector from raw data as I understood. But, what is the difference of this two term?

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Vector representation is a generic term used to talk about any type of feature encoding, embedding vectors are instead a special case of vector representation.

When talking about vector representation the only underlying assumption is that every variable was encoded into numerical values, without any restriction regarding the numbers or the vector itself.

Embedding vectors instead are specifically continuous vectors of fixed dimensions obtained trough matrix factorization techniques or deep learning models. They originally proposed to encode text in the Word2Vec paper, and since then they acquired more and more popularity due to the high generalization potential of the proposed method in other AI branched rather than natural language processing.

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To the best of my knowledge:

A latent representation, or code, $\mathbb{z}$ is a learned continuous vector representation of some input $\mathbb{x}$. E.g., we might have a code of an image.

An embedding is a type of code which specifically represents a discrete variable $\mathbb{x}_\text{discrete}$. One popular example is a word embedding, where words are encoded discretely using one-hot encoding.

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