Analysis of the Viterbi Algorithm Using Tropical Algebra and Geometry

The Viterbi algorithm and its pruning variant, are some of the most frequently used algorithms in communications and speech recognition. There has been extended research on improving the algorithms' computational complexity, however work trying to interpret their nonlinear structure and geometry has been limited. In this work we analyse the Viterbi algorithm in the field of tropical (min-plus) algebra, and we utilize its pruning variant in order to define a polytope. Then, we interpret certain faces of the polytope as the most probable states of the algorithm. This also provides a useful geometrical interpretation of the Viterbi algorithm.