Describing query expansion using logic-induced vectors of performance measures

Practical information retrieval is pervaded by Boolean variety as much as it is by term selection. One of the problems of building models that describe IR is therefore that of characterising the effect of Boolean variety on retrieval performance. An approach to this problem is described based on the use of vectors to characterise retrieval performance and focusing on the changes in direction and magnitude of these vectors under the joint influences of term addition (i.e. query expansion) and choice of logic operator. Several novel multivariate constructs are proposed based on this ‘logic/vector’ approach, including: (1) the centroid vector of the vectors defined by ANDing, ORing and AND NOTing a new term to a predecessor search expression, (2) the area defined by the vertices of these three terms, when two or three performance variables are used, and (3) changes to the vector angles induced by these logic operators. The way in which these constructs change during query expansion offers a characterisation of that process and may suggest stopping rules for it. An analysis of MEDLINE data is described which generates several initial hypotheses using these constructs.