Attribute Fusion-based Evidential Classifier on Quantum Circuits

Abstract: Dempster-Shafer Theory (DST) as an effective and robust framework for handling uncertain information is applied in decision-making and pattern classification. Unfortunately, its real-time application is limited by the exponential computational complexity. People attempt to address the issue by taking advantage of its mathematical consistency with quantum computing to implement DST operations on quantum circuits and realize speedup. However, the progress so far is still impractical for supporting large-scale DST applications. In this paper, we find that Boolean algebra as an essential mathematical tool bridges the definition of DST and quantum computing. Based on the discovery, we establish a flexible framework mapping any set-theoretically defined DST operations to corresponding quantum circuits for implementation. More critically, this new framework is not only uniform but also enables exponential acceleration for computation and is capable of handling complex applications. Focusing on tasks of classification, we based on a classical attribute fusion algorithm putting forward a quantum evidential classifier, where quantum mass functions for attributes are generated with a simple method and the proposed framework is applied for fusing the attribute evidence. Compared to previous methods, the proposed quantum classifier exponentially reduces the computational complexity to linear. Tests on real datasets validate the feasibility.