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A general matrix framework for modelling Information Retrieval

机译：用于信息检索建模的通用矩阵框架

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摘要

In this paper, we present a well-defined general matrix framework for modelling Information Retrieval (IR). In this framework, collections, documents and queries correspond to matrix spaces. Retrieval aspects, such as content, structure and semantics, are expressed by matrices defined in these spaces and by matrix operations applied on them. The dualities of these spaces are identified through the application of frequency-based operations on the proposed matrices and through the investigation of the meaning of their eigenvectors. This allows term weighting concepts used for content-based retrieval, such as term frequency and inverse document frequency, to translate directly to concepts for structure-based retrieval. In addition, concepts such as pagerank, authorities and hubs, determined by exploiting the structural relationships between linked documents, can be defined with respect to the semantic relationships between terms. Moreover, this mathematical framework can be used to express classical and alternative evaluation measures, involving, for instance, the structure of documents, and to further explain and relate IR models and theory. The high level of reusability and abstraction of the framework leads to a logical layer for IR that makes system design and construction significantly more efficient, and thus, better and increasingly personalised systems can be built at lower costs.
机译：在本文中，我们提出了一个定义良好的通用矩阵框架，用于建模信息检索（IR）。在此框架中，集合，文档和查询对应于矩阵空间。检索方面，例如内容，结构和语义，由这些空间中定义的矩阵以及对其应用的矩阵运算来表示。这些空间的对偶性是通过在建议的矩阵上应用基于频率的运算并研究其特征向量的含义来确定的。这允许用于基于内容的检索的术语加权概念（例如术语频率和反向文档频率）直接转换为用于基于结构的检索的概念。另外，可以利用术语之间的语义关系来定义通过利用链接文档之间的结构关系确定的诸如页面等级，权限和中心之类的概念。此外，该数学框架可用于表达经典的和备选的评估方法，例如涉及文档的结构，以及进一步解释和关联IR模型和理论。框架的高度可重用性和抽象性导致IR的逻辑层，使系统的设计和构建效率大大提高，因此，可以以更低的成本构建更好，越来越个性化的系统。

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