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

For example, a 300-dimensional embedding for English words could include:

`blue: (0.01359, 0.00075997, 0.24608, ..., -0.2524, 1.0048, 0.06259) blues: (0.01396, 0.11887, -0.48963, ..., 0.033483, -0.10007, 0.1158) orange: (-0.24776, -0.12359, 0.20986, ..., 0.079717, 0.23865, -0.014213) oranges: (-0.35609, 0.21854, 0.080944, ..., -0.35413, 0.38511, -0.070976)`

The individual dimensions in these vectors typically have no inherent meaning. Instead, it’s the overall patterns of location and distance between vectors that machine learning takes advantage of.

Embeddings are important for input to machine learning. Classifiers, and neural networks more generally, work on vectors of real numbers. They train best on dense vectors, where all values contribute to define an object. However, many important inputs to machine learning, such as words of text, do not have a natural vector representation. Embedding functions are the standard and effective way to transform such discrete input objects into useful continuous vectors.

Embeddings are suitable for any categorical variables.

They are actually just hidden units in one or more layers, you will need to decide on the number of units, each unit of the embedding will be one parameter to track, the bigger the number of units the more likely the network is to overfit.

The dot product of two embeddings is a measure of their similarity.

## Google Definition

A categorical feature represented as a continuous-valued feature. Typically, an embedding is a translation of a high-dimensional vector into a low-dimensional space. For example, you can represent the words in an English sentence in either of the following two ways:

- As a million-element (high-dimensional) sparse vector in which all elements are integers. Each cell in the vector represents a separate English word; the value in a cell represents the number of times that word appears in a sentence. Since a single English sentence is unlikely to contain more than 50 words, nearly every cell in the vector will contain a 0. The few cells that aren’t 0 will contain a low integer (usually 1) representing the number of times that word appeared in the sentence.
- As a several-hundred-element (low-dimensional) dense vector in which each element holds a floating-point value between 0 and 1. This is an embedding.

Embeddings are trained by backpropagating loss just like any other parameter in a neural network.

## Embedding space

The d-dimensional vector space that features from a higher-dimensional vector space are mapped to. Ideally, the embedding space contains a structure that yields meaningful mathematical results; for example, in an ideal embedding space, addition and subtraction of embeddings can solve word analogy tasks.