A Simplified Latent Semantic Indexing Approach for Multi-Linguistic Information Retrieval

A Simplified Latent Semantic Indexing Approach for Multi-Linguistic Information Retrieval 1 Liu Yi, Lu Haiming, Lu Zengxiang, Wang Pu Department of Automation, Tsinghua University Beijing 100084 P.R.China yiliu00@mails.tsinghua.edu.cn Abstract Latent Semantic Indexing (LSI) approach provides a promising solution to overcome the language barrier between queries and documents, but unfortunately the high dimensions of the training matrix is computationally prohibitive for its key step of Singular Value Decomposition (SVD). Based on the semantic parallelism of the multi-linguistic training corpus we prove in this paper that, theoretically if the training term-by-document matrix can appear in either of two symmetry forms, strong or weak, the dimension of the matrix under decomposition can be reduced to the size of a monolingual matrix. The retrieval accuracy will not deteriorate in such a simplification. And we also discuss what these two forms of symmetry mean in the context of multi-linguistic information retrieval. Although in real world data the term-by-document matrices are not naturally in either symmetry form, we suggest a way to make them appear more symmetric in the strong form by means of word clustering and term weighting. A real data experiment is also given to support our method of simplification. 1� Introduction Multi-linguistic Information Retrieval (MLIR for short, also "translingual" or "cross-language" IR) enables a query in one language to search document collection in another one or more languages. Many monolingual IR approaches can be extended to multi-linguistic environment and among them Latent Semantic Indexing (LSI for short, Deerwester et al., 1990) has proved effective (Y. Yang et al., 1997, Douglas William Oard, 1996). The particular technique used in LSI is singular-value decomposition (SVD for short), in which a large term-by-document matrix is decomposed into a set of orthogonal factors from which the original matrix can be approximated by linear combination. However, SVD on the large term-by-document matrix whose size increases with the size of the training corpus brings huge computation costs. This situation becomes even worse when we use LSI for MLIR because the training matrix consisting of various languages is always several times larger. To reduce the cost of SVD in LSI and thus make it feasible in MLIR, we try to exploit the semantic symmetry hidden in the training corpus. We find that theoretically if the term-by-document matrices of multi-linguistic training set have either a weak symmetry form or a strong symmetry form, the SVD step of LSI in multi-linguistic environment can be simplified. Both symmetry forms have clear meanings in the context of MLIR. Further, though we can never reach precisely either of two symmetry forms from real world data, two possible methods are raised to enhance the strong form symmetry of the term-by-document matrices. Our small-scale experiment gives a satisfying result though we only roughly keep the strong symmetry. In section 2 we will briefly introduce how LSI approach can be extended to multi-linguistic environment. In section 3 we will prove some theorems for the LSI simplification in the two symmetry forms, then discuss symmetry enhancement issues for real …

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