A Survey of Unstructured Text Summarization Techniques <s> C. Latent Semantic Analysis using SVD <s> This paper presents a method for combining ::: query-relevance with information-novelty in the context ::: of text retrieval and summarization. The Maximal ::: Marginal Relevance (MMR) criterion strives to reduce ::: redundancy while maintaining query relevance in ::: re-ranking retrieved documents and in selecting appropriate passages for text summarization. Preliminary results ::: indicate some benefits for MMR diversity ranking ::: in document retrieval and in single document summarization. ::: The latter are borne out by the recent results of the ::: SUMMAC conference in the evaluation of summarization ::: systems. However, the clearest advantage is demonstrated ::: in constructing non-redundant multi-document ::: summaries, where MMR results are clearly superior to ::: non-MMR passage selection. <s> BIB001 </s> A Survey of Unstructured Text Summarization Techniques <s> C. Latent Semantic Analysis using SVD <s> In this paper, we propose two generic text summarization methods that create text summaries by ranking and extracting sentences from the original documents. The first method uses standard IR methods to rank sentence relevances, while the second method uses the latent semantic analysis technique to identify semantically important sentences, for summary creations. Both methods strive to select sentences that are highly ranked and different from each other. This is an attempt to create a summary with a wider coverage of the document's main content and less redundancy. Performance evaluations on the two summarization methods are conducted by comparing their summarization outputs with the manual summaries generated by three independent human evaluators. The evaluations also study the influence of different VSM weighting schemes on the text summarization performances. Finally, the causes of the large disparities in the evaluators' manual summarization results are investigated, and discussions on human text summarization patterns are presented. <s> BIB002
Singular value decomposition (SVD) is a method of word co-occurrence analysis using a dimensionality reduction approach. In the process of dimensional reduction, cooccurring terms are mapped onto the same dimensions in the reduced space, thus increasing similarity in the representation of semantically similar sentences BIB001 . In this method, the weight of the sentences is first obtained using the same principle as described in BIB002 and then a sentence matrix A= [A1, A2, …An] with each column vector Ai representing the weighted term vector of sentence i is created. If there are m terms and n sentences, then matrix A is of dimension m*n. Using singular value decomposition, A= USV T , where the columns of U (m*dimension) are left singular vectors, S (dimension * dimension) gives the non-negative singular values, and V T (dimension *n) columns are right singular vectors. The first right singular vector is selected and the sentence with the largest index value is selected and included in the summary BIB002 . The next right singular vector representing the next dimension is selected and the largest index valued sentence is added to the summary. Thus, this method chooses sentences from every dimension covering all topics in the document. In Enhanced Latent Semantic Analysis using SVD  , for each sentence vector in matrix V, its components are multiplied by corresponding singular values, to compute each sentence length. The reason for using the multiplication is to favor the index values in the matrix V that correspond to the highest singular values; i.e. the most significant topics. The sentence weight is calculated as follows: where S k is the sentence with sentence number k and n = number of dimensions. The Latent Semantic Analysis using SVD, though a good dimensionality reduction technique, has two disadvantages. It is necessary to use the same number of dimensions as the number of sentences chosen for a summary. If a high number of dimensions of the reduced space is chosen, the probability of selecting a significant topic in the summary is reduced. Hence, it may not give the most relevant sentences for longer documents. Also, sentences with large sentence weights, but not the largest (they do not win in any dimension), will not be chosen although contents may be very suitable for the summary  . Hence in Enhanced Latent Semantic Analysis technique, the weight of each sentence is further calculated with respect to the entire document, not just with respect to each dimension, so that sentences can be correctly ranked.