Max-product dynamical systems and applications to audio-visual salient event detection in videos

Abstract

This paper introduces a theory for max-product systems by analyzing them as discrete-time nonlinear dynamical systems that obey a superposition of a weighted maximum type and evolve on nonlinear spaces which we call complete weighted lattices. Special cases of such systems have found applications in speech recognition as weighted finite-state transducers and in belief propagation on graphical models. Our theoretical approach establishes their representation in state and input-output spaces using monotone lattice operators, finds analytically their state and output responses using nonlinear convolutions, studies their stability, and provides optimal solutions to solving max-product matrix equations. Further, we apply these systems to extend the Viterbi algorithm in HMMs by adding control inputs and model cognitive processes such as detecting audio and visual salient events in multimodal video streams, which shows good performance as compared to human attention.