Tensor Field Model for higher-order information retrieval

There is an implied assumption for keywords in the traditional Information Retrieval (IR) models: keywords are parallel to each other. In fact, there are some relations between terms in quite a few queries, and in these queries, perhaps one term is subordinate to another term according to the inner meanings of information needs. This is "Higher-order IR"(HIR) defined in this paper, and we call traditional IR "first-order IR" instead. Some research fields such as Public Opinion Analysis, Chain of Events Analysis and Trend Analysis which reflect the vague concept of HIR are all special form of HIR. Apparently, traditional IR models cannot deal with HIR directly. We need a new HIR model to represent and organize the documents, queries and relevance relationship between them. In this paper, we propose "Tensor Field Model" (TFM), and its perspectives are field theory in physics and multilinear algebra in maths. We construct the tensor representations of documents and queries in TFM, presenting some key concepts such as term field, tensor product of term array and term field constant. Empirical results show that TFM is appropriate for HIR theoretically and formally compared with traditional models which simplify the HIR problems as first-order IR problems to some extent.