Trapezoidal DP matching with time reversibility

DP matching is widely used in speech recognition. But none of the conventional formulations (Rectangular DP Matching) seem to have all the three properties: pattern commutativeness, time reversibility, and linear matching consistency. In this paper, a new formulation named "Trapezoidal DP Matching" is proposed, which preserves time reversibility and can have all the three properties. In addition, the following points are clarified; (1) The formulation gives a better approximation of continuous-time pattern distance, and is expected to improve recognition accuracy. (2) It has an effect of smoothing the weighting coefficients on local distances. (3) It provides a clear viewpoint on the relationship between weighting coefficients and the normalized time. (4) Its evaluation is reliable even for a transient portion matching.