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  2. Embedding - Wikipedia

    en.wikipedia.org/wiki/Embedding

    In mathematics, an embedding (or imbedding [1]) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X {\displaystyle X} is said to be embedded in another object Y {\displaystyle Y} , the embedding is given by some injective and structure-preserving map f : X → ...

  3. 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]

  4. 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 ...

  5. Sentence embedding - Wikipedia

    en.wikipedia.org/wiki/Sentence_embedding

    In recent years, sentence embedding has seen a growing level of interest due to its applications in natural language queryable knowledge bases through the usage of vector indexing for semantic search. LangChain for instance utilizes sentence transformers for purposes of indexing documents. In particular, an indexing is generated by generating ...

  6. 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 ...

  7. 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]

  8. Compact embedding - Wikipedia

    en.wikipedia.org/wiki/Compact_embedding

    The embedding of X into Y is a compact operator: any bounded set in X is totally bounded in Y, i.e. every sequence in such a bounded set has a subsequence that is Cauchy in the norm ||•|| Y. If Y is a Banach space, an equivalent definition is that the embedding operator (the identity) i : X → Y is a compact operator.

  9. Inclusion map - Wikipedia

    en.wikipedia.org/wiki/Inclusion_map

    In mathematics, if is a subset of , then the inclusion map is the function that sends each element of to , treated as an element of ::, =. An inclusion map may also be referred to as an inclusion function , an insertion , [ 1 ] or a canonical injection .