The use of the latent semantic analysis (LSA) in text mining demands large space and time requirements. This paper proposes a new text extraction method that sets a framework on how to employ the statistical semantic analysis in the text extraction in an efficient way. The method uses the centrality feature and omits the segments of the text that have a high verbatim, statistical, or semantic similarity with previously processed segments. The identification of similarity is based on a new multi-layer similarity method that computes the similarity in three statistical layers, it uses the Jaccard similarity and the vector space model in the first and second layers respectively, and uses the LSA in the third layer. The multi-layer similarity restricts the use of the third layer for the segments that the first and second layers failed to estimate their similarities. Rouge tool is used in the evaluation, but because Rouge does not consider the extract’s size, we supplemented it with a new evaluation strategy based on the compression rate and the ratio of the sentences intersections between the automatic and the reference extracts. Our comparisons with classical LSA and traditional statistical extractions showed that we reduced the use of the LSA procedure by 52%, and we obtained 65% reduction on the original matrix dimensions, also, we obtained remarkable accuracy results. It is concluded that the employment of the centrality feature with the proposed multi-layer framework yields a significant solution in terms of efficiency and accuracy in the field of text extraction.