On the verification of triangle inequality by dynamic time-warping dissimilarity measures

Abstract

The verification of the Triangle Inequality (TI) by Dynamic Time Warping (DTW) Dissimilarity Measures (DM) seems to be a fairly important prerequisite for the application of some new and promising methods recently proposed for reducing the number of DTW computations in Isolated Word Recognition. The degree of satisfaction of this property for real speech samples has been empirically studied by various authors, who have reported rather controversial results for the different DTW and DMs speech data utilized by each of them. Therefore, a systematic study seemed to be necessary of the impact of the different factors upon which the DTW-based DMs depend. This paper is concerned with such work. Throughout the extensive experiments carried out, it was found that the TI never failed for any of the many combinations of speech parameters. DTW productions, local metrics and speech data taken into account; moreover, this property was always observed as being “loosely” satisfied. In view of these results, a prospective study of some possible causes of TI violation was carried out. The conclusions suggest the use of time-compressing preprocessing techniques and the application of suboptimal DTW procedures (and especially if gross end-point detection errors are involved) as the most likely causes of the TI dissatisfaction rates reported elsewere.