Information-theoretic perspectives for problems in information fusion

© 2012 Dr. Peter PongInformation fusion has remained an important field of research for over two decades. Decision makers often combine information from multiple sources to make better decisions. Since there are no unique laws for information fusion, every one ‘fuses’ information in their own way. Consequently it is difficult to evaluate or classify outcomes of such fusion and indeed difficult to make meaningful statements about “improvements” in fusions. This issue can also pervade some seemingly rigorous mathematical methods of information fusion. To address such major issues in information fusion, this thesis aims to undertake a study and analysis of prominent fusion methods in the literature, but to do so from an information-theoretic perspective. The core aim is to establish some methods to assess (for a given scheme) if: • the information fusion method is legitimate (defined later), • if the scheme actually informs the decision makers in a meaningful way, and • how different the fusion rule copes with different kinds of heterogeneous information sources, including the fusion of Human Originated Information (HOI) when viewed from the information theoretic perspective. To this end, Chapter 1 begins with an overview of the scope of the thesis and summarises the original contributions of this thesis. Chapter 2 introduces several well-known information fusion approaches within literature including fusion of information in probabilistic, fuzzy and evidential reasoning frameworks. We also introduce the concept of fusion within the context of multiple criteria decision making process. Chapter 3 begins with the review of heterogeneous information fusion - methods of combining information when information is provided in the form of probabilities, beliefs and linguistic information. It first reviews a well-known example from literature for combining probabilistic and evidential reasoning methods. We later extend this concept to incorporate HOI. This chapter proposes to use compatibility values generated by the Ordered Weighted Average (OWA) as a likelihood function and demonstrates the impact of combining linguistic information with probabilistic and belief measure based information. Chapter 4 begins by introducing the concept of uncertainty, and then introduce a new concept to quantify as well as visualise the measures. This insight presents the need for studying the variation of uncertainty through the information fusion process. Using well-known illustrative examples in literature, the uncertainty variation of most prevalent fusion rules in literature are demonstrated. Chapter 5 takes a closer look at fusion rules to establish the ground rules of legitimacy. It first considers entropy reduction as a pre-condition for information fusion. Under this assumption, we derive conditions under which Bayes' rule can be considered as a legitimate fusion rule. To simplify the derivation of such conditions, it uses conjugate prior pairs referenced from literature. We then review Yager's framework for establishing information fusion legitimacy. After reviewing Yager’s framework, the chapter reviews if any of the fusion rules considered in this thesis satisfy the fusion framework. It demonstrates that none of them satisfies the Yager's framework. This insight establishes that the framework is too restrictive, and has no room to incorporate measures of uncertainty. The framework for establishing legitimacy and appropriateness of information fusion methods remains an unsolved problem. Finally, Chapter 6 provides a summary of contributions of the thesis and presents future research directions that can be pursued based on the work done in this thesis