One way for a writer or speaker to expand a sentence is through the use of embedding. When two clauses share a common category, one can often be embedded in the other. For example: **Norman brought the pastry.** **My sister had forgotten it.**

In a concrete category, **an embedding is a morphism ƒ: A → B which is an injective function from the underlying set of A to the underlying set of B** and is also an initial morphism in the following sense: If g is a function from the underlying set of an object C to the underlying set of A, and if its composition with ƒ

We also learned that **immersion includes language training and content teaching.** **In contrast, submersion approaches second language acquisition by teaching content in English with no attention to language preparation**. The result is language assimilation rather than bilingualism.

Embedding layer is **one of the available layers in Keras**. This is mainly used in Natural Language Processing related applications such as language modeling, but it can also be used with other tasks that involve neural networks. While dealing with NLP problems, we can use pre-trained word embeddings such as GloVe.

Embedding space is **the space in which the data is embedded after dimensionality reduction**. Its dimensionality is typically lower that than of the ambient space. Manifold Learning.

Definition

In other words, an open immersion is **a morphism of schemes which decomposes uniquely into an isomorphism of schemes and the identity inclusion of an open subscheme**.

Definition of embed

transitive verb. 1a : **to enclose closely in or as if in a matrix** fossils embedded in stone. b : to make something an integral part of the prejudices embedded in our language. c : to prepare (a microscopy specimen) for sectioning by infiltrating with and enclosing in a supporting substance.

What is Embedding? It is **a way to incorporate a document into an existing file**. Once a document is embedded into another file, they start to exist as a single file.

In mathematics, **one normed vector space is said to be continuously embedded in another normed vector space if the inclusion function between them is continuous**. In some sense, the two norms are "almost equivalent", even though they are not both defined on the same space.

In Maths, an injective function or injection or one-one function is **a function that comprises individuality that never maps discrete elements of its domain to the equivalent element of its codomain**. We can say, every element of the codomain is the image of only one element of its domain.

Embedding is **the process of converting high-dimensional data to low-dimensional data in the form of a vector in such a way that the two are semantically similar**. In its literal sense, “embedding” refers to an extract (portion) of anything.

An embedding of smooth manifolds is **a smooth function f:X↪Y between smooth manifolds X and Y such that**. **f is an immersion**; the underlying continuous function is an embedding of topological spaces.

We note that for any compact manifold, **an injective immersion defined over it is automatically proper, so is an embedding**. We can think of a tangent bundle as a way to organize the manifold along with all the tangent spaces at each point.

An embedding is **a representation of a topological object, manifold, graph, field, etc.** **in a certain space in such a way that its connectivity or algebraic properties are preserved**.

Represent words as semantically-meaningful dense real-valued vectors. This overcomes many of the problems that simple one-hot vector encodings have. Most importantly, embeddings **boost generalisation and performance for pretty much any NLP problem, especially if you don't have a lot of training data**.

An embedding is **a relatively low-dimensional space into which you can translate high-dimensional vectors**. Embeddings make it easier to do machine learning on large inputs like sparse vectors representing words.

Spectral Embedding is **a technique used for non-linear dimensionality reduction**. Under it's hood, the algorithm in action is Laplacian Eigenmaps. Laplacian Eigenmaps is considerably similar to Isometric Feature Mapping (also referred to as Isomap).

One way for a writer or speaker to expand a sentence is through the use of embedding. When two clauses share a common category, one can often be embedded in the other. For example: **Norman brought the pastry.** **My sister had forgotten it.**

In simple intuitive terms, the immersion of a topological object is a reasonably smooth injection or mapping of it into some containing space, while its embedding adds the stiffer condition that the mapping be bijective, i.e. point-to-point with no overlaps.

In the context of neural networks, **embeddings are low-dimensional, learned continuous vector representations of discrete variables**.

Sentence embedding techniques represent entire sentences and their semantic information as vectors. This **helps the machine in understanding the context, intention, and other nuances in the entire text**.

Dated : 16-May-2022

Category : Education