Mathematical features of semantic projections and word embeddings for automatic linguistic analysis
Embeddings in normed spaces are a widely used tool in automatic linguistic analysis, as they help model semantic structures. They map words, phrases, or even entire sentences into vectors within a high-dimensional space, where the geometric proximity of vectors corresponds to the semantic similarity...
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025185 |
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| author | Pedro Fernández de Córdoba Carlos A. Reyes Pérez Enrique A. Sánchez Pérez |
| author_facet | Pedro Fernández de Córdoba Carlos A. Reyes Pérez Enrique A. Sánchez Pérez |
| author_sort | Pedro Fernández de Córdoba |
| collection | DOAJ |
| description | Embeddings in normed spaces are a widely used tool in automatic linguistic analysis, as they help model semantic structures. They map words, phrases, or even entire sentences into vectors within a high-dimensional space, where the geometric proximity of vectors corresponds to the semantic similarity between the corresponding terms. This allows systems to perform various tasks like word analogy, similarity comparison, and clustering. However, the proximity of two points in such embeddings merely reflects metric similarity, which could fail to capture specific features relevant to a particular comparison, such as the price when comparing two cars or the size of different dog breeds. These specific features are typically modeled as linear functionals acting on the vectors of the normed space representing the terms, sometimes referred to as semantic projections. These functionals project the high-dimensional vectors onto lower-dimensional spaces that highlight particular attributes, such as the price, age, or brand. However, this approach may not always be ideal, as the assumption of linearity imposes a significant constraint. Many real-world relationships are nonlinear, and imposing linearity could overlook important non-linear interactions between features. This limitation has motivated research into non-linear embeddings and alternative models that can better capture the complex and multifaceted nature of semantic relationships, offering a more flexible and accurate representation of meaning in natural language processing. |
| format | Article |
| id | doaj-art-8beddc4e6c4646f39b5575780de429da |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-8beddc4e6c4646f39b5575780de429da2025-08-20T02:26:19ZengAIMS PressAIMS Mathematics2473-69882025-02-011023961398210.3934/math.2025185Mathematical features of semantic projections and word embeddings for automatic linguistic analysisPedro Fernández de Córdoba0Carlos A. Reyes Pérez1Enrique A. Sánchez Pérez2Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, SpainEmbeddings in normed spaces are a widely used tool in automatic linguistic analysis, as they help model semantic structures. They map words, phrases, or even entire sentences into vectors within a high-dimensional space, where the geometric proximity of vectors corresponds to the semantic similarity between the corresponding terms. This allows systems to perform various tasks like word analogy, similarity comparison, and clustering. However, the proximity of two points in such embeddings merely reflects metric similarity, which could fail to capture specific features relevant to a particular comparison, such as the price when comparing two cars or the size of different dog breeds. These specific features are typically modeled as linear functionals acting on the vectors of the normed space representing the terms, sometimes referred to as semantic projections. These functionals project the high-dimensional vectors onto lower-dimensional spaces that highlight particular attributes, such as the price, age, or brand. However, this approach may not always be ideal, as the assumption of linearity imposes a significant constraint. Many real-world relationships are nonlinear, and imposing linearity could overlook important non-linear interactions between features. This limitation has motivated research into non-linear embeddings and alternative models that can better capture the complex and multifaceted nature of semantic relationships, offering a more flexible and accurate representation of meaning in natural language processing.https://www.aimspress.com/article/doi/10.3934/math.2025185lipschitz functionsemantic projectionword embeddingmodelarens-eells |
| spellingShingle | Pedro Fernández de Córdoba Carlos A. Reyes Pérez Enrique A. Sánchez Pérez Mathematical features of semantic projections and word embeddings for automatic linguistic analysis AIMS Mathematics lipschitz function semantic projection word embedding model arens-eells |
| title | Mathematical features of semantic projections and word embeddings for automatic linguistic analysis |
| title_full | Mathematical features of semantic projections and word embeddings for automatic linguistic analysis |
| title_fullStr | Mathematical features of semantic projections and word embeddings for automatic linguistic analysis |
| title_full_unstemmed | Mathematical features of semantic projections and word embeddings for automatic linguistic analysis |
| title_short | Mathematical features of semantic projections and word embeddings for automatic linguistic analysis |
| title_sort | mathematical features of semantic projections and word embeddings for automatic linguistic analysis |
| topic | lipschitz function semantic projection word embedding model arens-eells |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025185 |
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