Learning a Mahalanobis Distance-Based Dynamic Time Warping Measure for Multivariate Time Series Classification

Abstract

Multivariate time series (MTS) datasets broadly exist in numerous fields, including health care, multimedia, finance, and biometrics. How to classify MTS accurately has become a hot research topic since it is an important element in many computer vision and pattern recognition applications. In this paper, we propose a Mahalanobis distance-based dynamic time warping (DTW) measure for MTS classification. The Mahalanobis distance builds an accurate relationship between each variable and its corresponding category. It is utilized to calculate the local distance between vectors in MTS. Then we use DTW to align those MTS which are out of synchronization or with different lengths. After that, how to learn an accurate Mahalanobis distance function becomes another key problem. This paper establishes a LogDet divergence-based metric learning with triplet constraint model which can learn Mahalanobis matrix with high precision and robustness. Furthermore, the proposed method is applied on nine MTS datasets selected from the University of California, Irvine machine learning repository and Robert T. Olszewski's homepage, and the results demonstrate the improved performance of the proposed approach.

Human Motion Analysis with Deep Metric Learning

“…including our approach achieve up to 17% improvement in FPR relative to DTW [42], MDDTW [25], CTW [47] and GDTW [48]. Moreover, our approach further improves the results up to 6% and 0.8% for CMU mocap and Human3.6m datasets, respectively, against the state-of-the-art deep learning approaches [33,41,45,35].…”

“…We compare our MMD-NCA loss against the methods from DTW [42], MDDTW [25], CTW [47] and GDTW [48], as well as four state-of-the-art deep metric learning approaches: DCTW [41], triplet [33], triplet+GOR [45], and the N -Pairs deep metric loss [14]. Primarily, these methods are evaluated through action recognition task in Sec.…”

“…Here, all deep metric learning approaches including our work significantly improve the accuracy against the DTW, MDDTW, CTW and GDTW. Overall, our method outperforms all the approaches for all FPR with a 20% improvement against DTW [42], MDDTW [25], CTW [47] and GDTW [48], and a 2% improvement compared to the state-of-the-art deep learning approaches [33,41,45,35]. Moreover, when we evaluate the NMI and the F 1 score for the clustering quality in different embedding sizes, Fig.…”

Association Rules for Traffic Flow Management Decision Support

“…A natural next step is to likewise "smooth out" the distance calculation in the temporal domain. We borrow the approach of Mei et al, 14 which extends the Dynamic Time Warping (DTW) algorithm-leveraged in Section II.A.1 to compute the distance between single-variable WITI factor patterns-to multi-dimensional data. In single-variable DTW, the optimal degree of local stretching and/or compression in the time domain-subject to various user-defined constraints such as the width parameter w-is based upon comparing scalar distances of the form (x t − y τ ) 2 between two time-series x and y at potentially different times t and τ such that |t − τ | ≤ w. In the multi-variable case, the distance between the two time-series at times t and τ can, for instance, be measured via the Euclidean distance (x t − y τ ) (x − y).…”

Modified Multivariate Euclidean Dynamic Time Warping Based Spoken Keyword Detection

“…In this work, Wavelet transform is chosen to design a feature extraction method for noisy environment because it captures time-frequency information of transient signal and gives multi resolution of time-frequency information. Traditional DTW deals with univariate time series(UTS) [3] which may not capture the similarities of all the dimension of the feature vector and the similarity check of two univariate time series sequence would not reflect correctly [19]. Moreover feature vectors are multi-dimensional, so there is a necessity for Multivariate Time Series (MTS) based DTW.…”