Abstract
The applications of matrix factorization are an important tool for text summarization. In last years, several variations of the non-negative matrix factorization (NMF) methods have found their usage in multi-document summarization (MDS). For matrix factorization to work efficiently in MDS, it is essential to show the ability of selecting the most typical data points from the given data space. In the chapter, we first describe the archetypal analysis (AA) and its weighted version and then we present the AA-based document summarization method for the two most known summarization tasks, namely the general and the query-focused MDS. Archetypal analysis, also known as the convex NMF, in contrast to other NMF methods selects distinct (archetypal) sentences and therefore leads to variability and diversity in content of the generated summaries. We conducted experiments on the data of document understanding conference. Experimental results evidence the improvement of the proposed approach over other closely related methods including ones using the NMF.
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