Web document summarization by exploiting social context with matrix co-factorization

In the context of social media, users usually post relevant information corresponding to the contents of events mentioned in a Web document. This information posses two important values in that (i) it reflects the content of an event and (ii) it shares hidden topics with sentences in the main document. In this paper, we present a novel model to capture the nature of relationships between document sentences and post information (comments or tweets) in sharing hidden topics for summarization of Web documents by utilizing relevant post information. Unlike previous methods which are usually based on hand-crafted features, our approach ranks document sentences and user posts based on their importance to the topics. The sentence-user-post relation is formulated in a share topic matrix, which presents their mutual reinforcement support. Our proposed matrix co-factorization algorithm computes the score of each document sentence and user post and extracts the top ranked document sentences and comments (or tweets) as a summary. We apply the model to the task of summarization on three datasets in two languages, English and Vietnamese, of social context summarization and also on DUC 2004 (a standard corpus of the traditional summarization task). According to the experimental results, our model significantly outperforms the basic matrix factorization and achieves competitive ROUGE-scores with state-of-the-art methods.     

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On the p-norm joint spectral radius

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矩阵的初等变换法求特征值及特征向量

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利用差分方程巧解高等代数中的一些问题

主要利用差分方程巧妙的解决了高等代数中矩阵的乘方与行列式的计算.     

线性方程组教学中应注意的几个问题

本文通过几个例题讨论了在线性方程组的教学中应注意线性方程组矩阵表达式的强化,线性方程组的反问题等方面的问题,以便提高教学效果.     

一种基于H-矩阵的预条件对角占优矩阵的构造方法

对于线性方程组Ax=b,当A是严格对角占优矩阵时大部分迭代法都收敛。当A不是对角占优矩阵时,预条件技术常被采用。本文给出了一种构造预条件矩阵P和Q的方法,把一个非对角占优的H-矩阵转化为严格对角占优矩阵。     

《高等代数》课程中矩阵方法的应用

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