Automatic text summarization is an active research field for a long time. We focus here just on obtaining keywords and key sentences to be extracted automatically from a given text based on nonnegative matrix factorization as presented in (Zha, 2002 ). The basis is a term-sentence matrix with entrances a_ij being the occurences of terms in sentences. Interestingly enough, one first should de a so-called stemming, i.e. removing stop words and identifying words with the same stem, but different endings. The procedure finds the so-called saliency scores of terms and sentences based on eigenvalues of AA^T and A^TA respectively. By choosing the largest singular values, the components of the salicency vectors are positive. It is interesting that this method coincides with a rank-1 approximation of the term-sentence matrix. The drawback is that two very similar sentences may come out. Therefore the papers we refer to introduce a so-called rank-k approximation, where the dimension k is chosen greater than or equal to the number of key sentences that we want to extract. In fact, we can think of an iterative procedure which identifies the ""heaviest" columns of A in terms of Euclidean length for a given basis. The representation of A is given by a coordinate matrix D, where we are iteratively interested in the heaviest column. Practically, one can use a QR decomposition of D.

Eligius Hendrix

University of Malaga