Semantic analysis of problems in natural language processing and their mathematical interpretation
TL;DR
The section concludes with formal problem specification: given vocabulary V and corpus C, semantic analysis is formalized as a mapping problem preserving distributional properties, an optimization problem minimizing loss through gradient-based methods, and an evaluation problem assessing quality through semantic similarity, analogy, and downstream NLP task performance.
Abstract
Semantic analysis has become a central challenge in natural language processing, driven by exponential growth in digitized textual data and the need for automated content processing across multiple applications including machine translation, text classification, sentiment analysis, and information retrieval. However, while semantic analysis methods are well-developed for resource-rich languages such as English, morphologically complex languages like Uzbek suffer from deficiencies in annotated corpora, lexical-semantic resources, and high-quality vector models – a gap amplified by governmental initiatives in digital economy development and national language technology advancement. This section grounds semantic analysis in the distributional semantics hypothesis principle that words exhibiting similar contexts possess similar meanings – thereby recasting the problem as a geometric challenge within continuous vector spaces. Two principal mathematical strategies are formalized: (1) prediction-based models (word2vec: CBOW/Skip-gram), which optimize context prediction objectives, and (2) count-based models (GloVe), which leverage global co-occurrence statistics through matrix factorization. Both project high-dimensional word co-occurrence relationships into low-dimensional dense vector spaces, enabling semantic analogy representation. For resource-scarce languages like Uzbek, cross-lingual embedding alignment (Procrustes optimization) enables semantic knowledge transfer from resource-rich languages, facilitating shared semantic spaces across the Turkic language family. The section concludes with formal problem specification: given vocabulary V and corpus C, semantic analysis is formalized as (1) a mapping problem preserving distributional properties, (2) an optimization problem minimizing loss through gradient-based methods, and (3) an evaluation problem assessing quality through semantic similarity, analogy, and downstream NLP task performance.