Dynamic time warping

About: Dynamic time warping is a research topic. Over the lifetime, 6013 publications have been published within this topic receiving 133130 citations.

Warping indexes with envelope transforms for query by humming

Abstract: A Query by Humming system allows the user to find a song by humming part of the tune. No musical training is needed. Previous query by humming systems have not provided satisfactory results for various reasons. Some systems have low retrieval precision because they rely on melodic contour information from the hum tune, which in turn relies on the error-prone note segmentation process. Some systems yield better precision when matching the melody directly from audio, but they are slow because of their extensive use of Dynamic Time Warping (DTW). Our approach improves both the retrieval precision and speed compared to previous approaches. We treat music as a time series and exploit and improve well-developed techniques from time series databases to index the music for fast similarity queries. We improve on existing DTW indexes technique by introducing the concept of envelope transforms, which gives a general guideline for extending existing dimensionality reduction methods to DTW indexes. The net result is high scalability. We confirm our claims through extensive experiments.

Time Warp Edit Distance with Stiffness Adjustment for Time Series Matching

Abstract: In a way similar to the string-to-string correction problem, we address discrete time series similarity in light of a time-series-to-time-series-correction problem for which the similarity between two time series is measured as the minimum cost sequence of edit operations needed to transform one time series into another. To define the edit operations, we use the paradigm of a graphical editing process and end up with a dynamic programming algorithm that we call time warp edit distance (TWED). TWED is slightly different in form from dynamic time warping (DTW), longest common subsequence (LCSS), or edit distance with real penalty (ERP) algorithms. In particular, it highlights a parameter that controls a kind of stiffness of the elastic measure along the time axis. We show that the similarity provided by TWED is a potentially useful metric in time series retrieval applications since it could benefit from the triangular inequality property to speed up the retrieval process while tuning the parameters of the elastic measure. In that context, a lower bound is derived to link the matching of time series into down sampled representation spaces to the matching into the original space. The empiric quality of the TWED distance is evaluated on a simple classification task. Compared to edit distance, DTW, LCSS, and ERP, TWED has proved to be quite effective on the considered experimental task.

Alignment of curves by dynamic time warping

Abstract: When studying some process or development in different subjects or units--be it biological, chemical or physical--we usually see a typical pattern, common to all curves. Yet there is variation both in amplitude and dynamics between curves. Following some ideas of structural analysis introduced by Kneip and Gasser, we study a method--dynamic time warping with a proper cost function--for estimating the shift or warping function from one curve to another to align the two functions. For some models this method can identify the true shift functions if the data are noise free. Noisy data are smoothed by a nonparametric function estimate such as a kernel estimate. It is shown that the proposed estimator is asymptotically normal and converges to the true shift function as the sample size per subject goes to infinity. Some simulation results are presented to illustrate the performance of this method.

Two-level DP-matching--A dynamic programming-based pattern matching algorithm for connected word recognition

Abstract: This paper reports a pattern matching approach to connected word recognition. First, a general principle of connected word recognition is given based on pattern matching between unknown continuous speech and artificially synthesized connected reference patterns. Time-normalization capability is allowed by use of dynamic programming-based time-warping technique (DP-matching). Then, it is shown that the matching process is efficiently carried out by breaking it down into two steps. The derived algorithm is extensively subjected to recognition experiments. It is shown in a talker-adapted recognition experiment that digit data (one to four digits) connectedly spoken by five persons are recognized with as high as 99.6 percent accuracy. Computation time and memory requirement are both proved to be within reasonable limits.

A level building dynamic time warping algorithm for connected word recognition

Abstract: Dynamic time warping has been shown to be an effective method of handling variations in the time scale of polysyllabic words spoken in isolation. This class of techniques has recently been applied to connected word recognition with high degrees of success. In this paper a level building technique is proposed for optimally time aligning a sequence of connected words with a sequence of isolated word reference patterns. The resulting algorithm, which has been found to be a special case of an algorithm previously described by Bahl and Jelinek, is shown to be significantly more efficient than the one recently proposed by Sakoe for connected word recognition, while maintaining the same accuracy in estimating the best possible matching string. An analysis of the level building method shows that it can be obtained as a modification to the Sakoe method by reversing the order of minimizations in the two-pass technique with some subsequent processing. This level building algorithm has a number of implementation parameters that can be used to control the efficiency of the method, as well as its accuracy. The nature of these parameters is discussed in this paper. In a companion paper we discuss the application of this level building time warping method to a connected digit recognition problem.