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  2. Embedding - Wikipedia

    en.wikipedia.org/wiki/Embedding

    An embedding, or a smooth embedding, is defined to be an immersion that is an embedding in the topological sense mentioned above (i.e. homeomorphism onto its image). [ 4 ] In other words, the domain of an embedding is diffeomorphic to its image, and in particular the image of an embedding must be a submanifold .

  3. Immersion (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Immersion_(mathematics)

    A smooth embedding is an injective immersion f : M → N that is also a topological embedding, so that M is diffeomorphic to its image in N. An immersion is precisely a local embedding – that is, for any point x ∈ M there is a neighbourhood, U ⊆ M, of x such that f : U → N is an embedding, and conversely a local embedding is an ...

  4. Word embedding - Wikipedia

    en.wikipedia.org/wiki/Word_embedding

    In natural language processing, a word embedding is a representation of a word. The embedding is used in text analysis.Typically, the representation is a real-valued vector that encodes the meaning of the word in such a way that the words that are closer in the vector space are expected to be similar in meaning. [1]

  5. Graph embedding - Wikipedia

    en.wikipedia.org/wiki/Graph_embedding

    An embedded graph uniquely defines cyclic orders of edges incident to the same vertex. The set of all these cyclic orders is called a rotation system.Embeddings with the same rotation system are considered to be equivalent and the corresponding equivalence class of embeddings is called combinatorial embedding (as opposed to the term topological embedding, which refers to the previous ...

  6. Regular embedding - Wikipedia

    en.wikipedia.org/wiki/Regular_embedding

    For example, if X and Y are smooth over a scheme S and if i is an S-morphism, then i is a regular embedding. In particular, every section of a smooth morphism is a regular embedding. [1] If ⁡ is regularly embedded into a regular scheme, then B is a complete intersection ring. [2]

  7. Word2vec - Wikipedia

    en.wikipedia.org/wiki/Word2vec

    Word2vec is a technique in natural language processing (NLP) for obtaining vector representations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a large corpus.

  8. Nash embedding theorems - Wikipedia

    en.wikipedia.org/wiki/Nash_embedding_theorems

    The Nash embedding theorem is a global theorem in the sense that the whole manifold is embedded into R n. A local embedding theorem is much simpler and can be proved using the implicit function theorem of advanced calculus in a coordinate neighborhood of the manifold. The proof of the global embedding theorem relies on Nash's implicit function ...

  9. Embedding problem - Wikipedia

    en.wikipedia.org/wiki/Embedding_problem

    In Galois theory, a branch of mathematics, the embedding problem is a generalization of the inverse Galois problem. Roughly speaking, it asks whether a given Galois extension can be embedded into a Galois extension in such a way that the restriction map between the corresponding Galois groups is given.