Usage of singular value decomposition matrix for search latent semantic structures in natural language texts

摘要

Singular value decomposition is a powerful computational method used to analyze the matrix and which has many applications in various fields. Its essence lies in the expansion of the original matrix as a product of three matrices: two orthogonal and one diagonal. One consequence of this expansion is the possibility of approximating the original matrix, matrix of lower rank, which can significantly compress the information contained in the original matrix. In this work we investigate the impact of this mechanism on the compression frequency matrix "terms-documents" that are based on counting the occurrence of words in natural language texts. A specific example analyzes the physical meaning of such impacts, and provides a new interpretation of the results, useful for analyzing the structure of any real-world objects, for which we can construct a matrix of their states.