Word embedding
In natural language processing (NLP), word embedding is a term used for the representation of words for text analysis, typically in the form of a real-valued vector that encodes the meaning of the word such that the words that are closer in the vector space are expected to be similar in meaning. Word embeddings can be obtained using a set of language modeling and feature learning techniques where words or phrases from the vocabulary are mapped to vectors of real numbers. Conceptually it involves the mathematical embedding from space with many dimensions per word to a continuous  vector space with a much lower dimension. Methods to generate this mapping include neural networks, dimensionality reduction on the word co-occurrence matrix, probabilistic models, explainable knowledge base method, and explicit representation in terms of the context in which words appear. Word and phrase embeddings, when used as the underlying input representation, have been shown to boost the performance in NLP tasks such as syntactic parsing and sentiment analysis. Development and history of the approach. In Distributional semantics, a quantitative methodological approach to understanding meaning in observed language, word embeddings or semantic vector space models have been used as a  knowledge representation for some time . Such models aim to quantify and categorize semantic similarities between linguistic items based on their distributional properties in large samples of language data. The underlying idea that "a word is characterized by the company it keeps" was popularized by John Rupert Firth , but has also roots in the contemporaneous work on search systems and in cognitive psychology . The notion of a semantic space with lexical items (words or multi-word terms) represented as vectors or embeddings is based on the computational challenges of capturing distributional characteristics and using them for practical application to measure similarity  between words, phrases, or entire documents. The first generation of semantic space models is the vector space model for information retrieval. Such vector space models for words and their distributional data implemented in their simplest form results in a very sparse vector space of high dimensionality (cf. Curse of dimensionality). Reducing the number of dimensions using linear algebraic methods such as singular value decomposition then led to the introduction of latent semantic analysis in the late 1980s and the Random indexing approach for collecting word cooccurrence contexts. In 2000 Bengio et al. provided in a series of papers the "Neural  probabilistic language models" to reduce the high dimensionality of words representations in contexts by "learning a distributed representation for words". A study published in NeurIPS (NIPS) 2002 introduced the use of both word and document embeddings applying the method of kernel CCA to bilingual (and multi-lingual) corpora, also providing an early example of self-supervised learning of word embeddings Word embeddings come in two different styles, one in which words are expressed as vectors of co-occurring words, and another in which words are expressed as vectors of linguistic contexts in which the words occur; these different styles are  studied in (Lavelli et al., 2004). Roweis and Saul published in "Science" how to use "locally linear embedding" (LLE) to discover representations of high dimensional data structures. Most new word embedding techniques after about 2005 rely on a neural network architecture instead of more probabilistic and algebraic models, since some foundational work by Yoshua Bengio and colleagues. The approach has been adopted by many research groups after advances around year 2010 had been made on theoretical work on the quality of vectors and the training speed of the model and hardware advances allowed for a broader parameter space to be  explored profitably. In 2013, a team at Google led by Tomas Mikolov created word2vec, a word embedding toolkit that can train vector space models faster than the previous approaches. The word2vec approach has been widely used in experimentation and was instrumental in raising interest for word embeddings as a technology, moving the research strand out of specialised research into broader experimentation and eventually paving the way for practical application. Limitations. Traditionally, one of the main limitations of word embeddings (word vector space models in general) is that words with multiple meanings are conflated into a single representation (a single vector  in the semantic space). In other words, polysemy and homonymy are not handled properly. For example, in the sentence "The club I tried yesterday was great!", it is not clear if the term "club" is related to the word sense of a "club sandwich", "baseball club", "clubhouse", "golf club", or any other sense that "club" might have. The necessity to accommodate multiple meanings per word in different vectors (multi-sense embeddings) is the motivation for several contributions in NLP to split single-sense embeddings into multi-sense ones. Most approaches that produce multi-sense embeddings can be divided into two  main categories for their word sense representation, i.e., unsupervised and knowledge-based. Based on word2vec skip-gram, Multi-Sense Skip-Gram (MSSG) performs word-sense discrimination and embedding simultaneously, improving its training time, while assuming a specific number of senses for each word. In the Non-Parametric Multi-Sense Skip-Gram (NP-MSSG) this number can vary depending on each word. Combining the prior knowledge of lexical databases (e.g., WordNet, ConceptNet, BabelNet), word embeddings and word sense disambiguation, Most Suitable Sense Annotation (MSSA) labels word-senses through an unsupervised and knowledge-based approach considering a word's context in a  pre-defined sliding window. Once the words are disambiguated, they can be used in a standard word embeddings technique, so multi-sense embeddings are produced. MSSA architecture allows the disambiguation and annotation process to be performed recurrently in a self-improving manner. The use of multi-sense embeddings is known to improve performance in several NLP tasks, such as part-of-speech tagging, semantic relation identification, semantic relatedness, named entity recognition and sentiment analysis. Recently, contextually-meaningful embeddings such as ELMo and BERT have been developed. These embeddings use a word's context to disambiguate polysemes. They do so using  LSTM and Transformer neural network architectures. For biological sequences: BioVectors. Word embeddings for "n-"grams in biological sequences (e.g. DNA, RNA, and Proteins) for bioinformatics applications have been proposed by Asgari and Mofrad. Named bio-vectors (BioVec) to refer to biological sequences in general with protein-vectors (ProtVec) for proteins (amino-acid sequences) and gene-vectors (GeneVec) for gene sequences, this representation can be widely used in applications of deep learning in proteomics and genomics. The results presented by Asgari and Mofrad suggest that BioVectors can characterize biological sequences in terms of biochemical and biophysical interpretations of the underlying patterns. Thought  vectors. Thought vectors are an extension of word embeddings to entire sentences or even documents. Some researchers hope that these can improve the quality of machine translation. Software. Software for training and using word embeddings includes Tomas Mikolov's Word2vec, Stanford University's GloVe, GN-GloVe, Flair embeddings, AllenNLP's ELMo, BERT, fastText, Gensim, Indra and Deeplearning4j. Principal Component Analysis (PCA) and T-Distributed Stochastic Neighbour Embedding (t-SNE) are both used to reduce the dimensionality of word vector spaces and visualize word embeddings and clusters. Examples of application. For instance, the fastText is also used to calculate word embeddings  for text corpora in Sketch Engine that are available online.