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We address the problem of unsupervised extractive document summarization,especially for long documents. We model the unsupervised problem as a sparseauto-regression one and approximate the resulting combinatorial problem via aconvex, norm-constrained problem. We solve it using a dedicated Frank-Wolfealgorithm. To generate a summary with $k$ sentences, the algorithm only needsto execute $\approx k$ iterations, making it very efficient. We explain how toavoid explicit calculation of the full gradient and how to include sentenceembedding information. We evaluate our approach against two other unsupervisedmethods using both lexical (standard) ROUGE scores, as well as semantic(embedding-based) ones. Our method achieves better results with both datasetsand works especially well when combined with embeddings for highly paraphrasedsummaries.

Sparse Optimization for Unsupervised Extractive Summarization of Long Documents with the Frank-Wolfe Algorithm