Automatic Keyword Extraction for Text Summarization: A Survey <s> Algebraic Approach <s> We present algorithms for computing a semidiscrete approximation to a matrix in a weighted norm, with the Frobenius norm as a special case. The approximation is formed as a weighted sum of outer products of vectors whose elements are ±1 or 0, so the storage required by the approximation is quite small. We also present a related algorithm for approximation of a tensor. Applications of the algorithms are presented to data compression, filtering, and information retrieval; software is provided in C and in Matlab. <s> BIB001 </s> Automatic Keyword Extraction for Text Summarization: A Survey <s> Algebraic Approach <s> This paper presents a novel statistical method for factor analysis of binary and count data which is closely related to a technique known as Latent Semantic Analysis. In contrast to the latter method which stems from linear algebra and performs a Singular Value Decomposition of co-occurrence tables, the proposed technique uses a generative latent class model to perform a probabilistic mixture decomposition. This results in a more principled approach with a solid foundation in statistical inference. More precisely, we propose to make use of a temperature controlled version of the Expectation Maximization algorithm for model fitting, which has shown excellent performance in practice. Probabilistic Latent Semantic Analysis has many applications, most prominently in information retrieval, natural language processing, machine learning from text, and in related areas. The paper presents perplexity results for different types of text and linguistic data collections and discusses an application in automated document indexing. The experiments indicate substantial and consistent improvements of the probabilistic method over standard Latent Semantic Analysis. <s> BIB002 </s> Automatic Keyword Extraction for Text Summarization: A Survey <s> Algebraic Approach <s> Meta latent semantic analysis (MLSA) is a novel approach to automated document analysis and indexing which relies on symbolic ontologies to further enhance the traditional probabilistic latent semantic analysis (LSA) of documents. While LSA is able to discover clusters of related terms and documents in a given collection of documents, the proposed MLSA is able to meta-cluster such clusters by taking into account existing symbolic ontologies relevant for the analyzed collections of documents. Such an approach can be successfully used to improve the performance of fast LSA by random projection. <s> BIB003 </s> Automatic Keyword Extraction for Text Summarization: A Survey <s> Algebraic Approach <s> Multi-document summarization aims to create a compressed summary while retaining the main characteristics of the original set of documents. Many approaches use statistics and machine learning techniques to extract sentences from documents. In this paper, we propose a new multi-document summarization framework based on sentence-level semantic analysis and symmetric non-negative matrix factorization. We first calculate sentence-sentence similarities using semantic analysis and construct the similarity matrix. Then symmetric matrix factorization, which has been shown to be equivalent to normalized spectral clustering, is used to group sentences into clusters. Finally, the most informative sentences are selected from each group to form the summary. Experimental results on DUC2005 and DUC2006 data sets demonstrate the improvement of our proposed framework over the implemented existing summarization systems. A further study on the factors that benefit the high performance is also conducted. <s> BIB004 </s> Automatic Keyword Extraction for Text Summarization: A Survey <s> Algebraic Approach <s> In the area of information retrieval, the dimension of document vectors plays an important role. We may need to find a few words or concepts, which characterize the document based on its contents, to overcome the problem of the "curse of dimensionality", which makes indexing of high-dimensional data problematic. To do so, we earlier proposed a Wordnet and Wordnet+LSI (latent semantic indexing) based model for dimension reduction. While LSI concepts contain identifiable terms in top-level concepts, we show in this paper that semi-discrete decomposition provides mostly smaller list of terms and we need to cope only with ternary weights. With this size of term list, the identification of document's topic becomes much more feasible. <s> BIB005 </s> Automatic Keyword Extraction for Text Summarization: A Survey <s> Algebraic Approach <s> In existing unsupervised methods, Latent Semantic Analysis (LSA) is used for sentence selection. However, the obtained results are less meaningful, because singular vectors are used as the bases for sentence selection from given documents, and singular vector components can have negative values. We propose a new unsupervised method using Non-negative Matrix Factorization (NMF) to select sentences for automatic generic document summarization. The proposed method uses non-negative constraints, which are more similar to the human cognition process. As a result, the method selects more meaningful sentences for generic document summarization than those selected using LSA. <s> BIB006
In this approach, one use algebraic theories namely, matrix, transpose of matrix, Eigen vectors, etc. There are many algorithms used for text summarization using algebraic approach such as Latent Semantic Analysis (LSA)  [122] BIB002 , Meta Latent Semantic Analysis (MLSA) BIB003 [125], Symmetric nonnegative matrix factorization (SNMF) BIB004 , Sentence level semantic analysis (SLSS) BIB004 , Non-Negative Matrix factorization (NMF) BIB006 , Singular Value Decomposition (SVD) BIB001 , Semi-Discrete Decomposition (SDD) BIB005 .