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

Abstract

We address the problem of unsupervised extractive document summarization, especially for long documents. We model the unsupervised problem as a sparse auto-regression one and approximate the resulting combinatorial problem via a convex, norm-constrained problem. We solve it using a dedicated Frank-Wolfe algorithm. To generate a summary with k sentences, the algorithm only needs to execute ≈ k iterations, making it very efficient. We explain how to avoid explicit calculation of the full gradient and how to include sentence embedding information. We evaluate our approach against two other unsupervised methods using both lexical (standard) ROUGE scores, as well as semantic (embedding-based) ones. Our method achieves better results with both datasets and works especially well when combined with embeddings for highly paraphrased summaries.

Low Resource Quadratic Forms for Knowledge Graph Embeddings

“…Our SVM program is both sparse and convex. We note that very recent work (Tsai and El Ghaoui, 2020) in the space of extractive text summarization also leverages sparsity and convexity to efficiently solve an optimization program. In our program, when both terms in the objective are the 1-norm, the SVM may be written as a linear program.…”