Dynamic Time Warping (DTW) has a quadratic time and space complexity that limits its use to small time series. In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity. FastDTW uses a multilevel approach that recursively projects a solution from a coarser resolution and refines the projected solution. We prove the linear time and space complexity of FastDTW both theoretically and empirically. We also analyze the accuracy of FastDTW by comparing it to two other types of existing approximate DTW algorithms: constraints (such as Sakoe-Chiba Bands) and abstraction. Our results show a large improvement in accuracy over existing methods.

/pdf/toward-accurate-dynamic-time-warping-in-linear-time-and-3p0rzztewt.pdf

Toward accurate dynamic time warping in linear time and space

Time-series clustering - A decade review

The dynamic time warping (DTW) algorithm is able to find the optimal alignment between two time series It is often used to determine time series similarity, classification, and to find corresponding regions between two time series DTW has a quadratic time and space complexity that limits its use to only small time series data sets In this paper we introduce FastDTW, an approximation of DTW that has a linear time and space complexity FastDTW uses a multilevel approach that recursively projects a solution from a coarse resolution and refines the projected solution We prove the linear time and space complexity of FastDTW both theoretically and empirically We also analyze the accuracy of FastDTW compared to two other existing approximate DTW algorithms: Sakoe-Chuba Bands and Data Abstraction Our results show a large improvement in accuracy over the existing methods

/pdf/fastdtw-toward-accurate-dynamic-time-warping-in-linear-time-4iz0xkinty.pdf

FastDTW: Toward Accurate Dynamic Time Warping in Linear Time and Space

After the generation of multimedia data turned digital, an explosion of interest in their data storage, retrieval, and processing has drastically increased. This includes videos, images, and audios, where we now have higher expectations in exploiting these data at hands. Typical manipulations are in some forms of video/image/audio processing, including automatic speech recognition, which require fairly large amount of storage and are computationally intensive. In our recent work, we have demonstrated the utility of time series representation in the task of clustering multimedia data using k-medoids method, which allows considerable amount of reduction in computational effort and storage space. However, k- means is a much more generic clustering method when Euclidean distance is used. In this work, we will demonstrate that unfortunately, k-means clustering will sometimes fail to give correct results, an unaware fact that may be overlooked by many researchers. This is especially the case when Dynamic Time Warping (DTW) is used as the distance measure in averaging the shape of time series. We also will demonstrate that the current averaging algorithm may not produce the real average of the time series, thus generates incorrect k-means clustering results, and then show potential causes why DTW averaging methods may not achieve meaningful clustering results. Lastly, we conclude with a suggestion of a method to potentially find the shape-based time series average that satisfies the required properties.

On Clustering Multimedia Time Series Data Using K-Means and Dynamic Time Warping

Clustering time-series data poses problems, which do not exist in traditional clustering in Euclidean space. Specifically, cluster prototype needs to be calculated, where common solution is to use cluster medoid. In this work, we define an optimal prototype as an optimization problem and propose a local search solution to it. We experimentally compare different time-series clustering methods and find out that the proposed prototype with agglomerative clustering followed by k-means algorithm provides best clustering accuracy.

http://cs.uef.fi/~villeh/time-series-clustering.pdf

Time-series clustering by approximate prototypes

One of the main problems in dynamic time-warping (DTW) based speech recognition systems are the preparation of reliable reference templates for the set of words to be recognised. This paper presents a simple novel technique for preparing reliable reference templates to improve the recognition rate score. The developed technique produces templates called crosswords reference templates (CWRTs). It extracts the reference template from a set of examples rather than one example. This technique can be adapted to any DTW-based speech recognition systems to improve its performance. The speaker-dependent recognition rate, as tested on the English digits, is improved from 85.3%, using the traditional technique to 99%, using the developed technique.

D. Chow

Papers

Cross-words reference template for DTW-based speech recognition systems