A Geometric Framework for Data Fusion

Quite a few data fusion methods have been proposed, but questions such as why data fusion can bring improvement in effectiveness and what are the favourable conditions for data fusion algorithms are only partially or vaguely answered due to the uncertainty of the problem. In this chapter, we set up a geometric framework to formally describe score-based data fusion methods, in which each component result returned from an information retrieval system for a given query is represented as a point in a multi-dimensional space. The performance of any result and the similarity between any pair of results can be evaluated by the same metric – the Euclidean distance. Then all the component results and the fused results can be explained using geometrical principles. In such a framework, data fusion becomes a deterministic problem. The performance of the fused result is determined by the performances of all component results and the similarities among all of them. Several interesting features of the centroid-based data fusion method and the linear combination method can be deduced. As a formal model of data fusion, this framework enable us to have a better understanding of the nature of data fusion and use the data fusion technique more precisely and effectively [105].