The great multivariate time series classification bake off: a review and experimental evaluation of recent algorithmic advances

Abstract

Time Series Classification (TSC) involves building predictive models for a discrete target variable from ordered, real valued, attributes. Over recent years, a new set of TSC algorithms have been developed which have made significant improvement over the previous state of the art. The main focus has been on univariate TSC, i.e. the problem where each case has a single series and a class label. In reality, it is more common to encounter multivariate TSC (MTSC) problems where the time series for a single case has multiple dimensions. Despite this, much less consideration has been given to MTSC than the univariate case. The UCR archive has provided a valuable resource for univariate TSC, and the lack of a standard set of test problems may explain why there has been less focus on MTSC. The UEA archive of 30 MTSC problems released in 2018 has made comparison of algorithms easier. We review recently proposed bespoke MTSC algorithms based on deep learning, shapelets and bag of words approaches. If an algorithm cannot naturally handle multivariate data, the simplest approach to adapt a univariate classifier to MTSC is to ensemble it over the multivariate dimensions. We compare the bespoke algorithms to these dimension independent approaches on the 26 of the 30 MTSC archive problems where the data are all of equal length. We demonstrate that four classifiers are significantly more accurate than the benchmark dynamic time warping algorithm and that one of these recently proposed classifiers, ROCKET, achieves significant improvement on the archive datasets in at least an order of magnitude less time than the other three.

HIVE-COTE 2.0: a new meta ensemble for time series classification

“…the classifier build can be resumed from a previous run) and works with multivariate time series classification (MTSC). A recent study (Ruiz et al 2021) concluded that that MTSC is at an earlier stage of development than univariate TSC. The only algorithms significantly better than the standard TSC benchmark, one nearest neighbour with dynamic time warping (DTW), were HC1, ROCKET, InceptionTime and CIF (Middlehurst et al The average rank for each classifier is shown, and solid lines group classifiers between which there is no significant difference.…”

“…There have also been a range of algorithms proposed for MTSC (Ruiz et al 2021). Dynamic Time Warping with pointwise multivariate distance and a one nearest neighbour classifier, characterised as dependent dynamic time warping (DTW-D) (Shokoohi-Yekta et al 2017), is the baseline for MTSC.…”

Pseudo Bidirectional Linear Discriminant Analysis for Multivariate Time Series Classification

“…Another future work is on deep learning extension. The ROCKET [4], which uses random convolutional kernel transform in conjunction with a simple linear classifier is found to…”

“…In this section, we perform experiments on several real-world MTS datasets to compare the proposed PBLDA with six related methods, including BLDA [17], BPCA [16], SVD-1 [19], SVD-2 [12], SVD-1+LPP, SVD-2+LPP [13] and multivariate 'dependent' DTW (MDTW) [4]. It has been reported in [15] that BPCA has good performance on the following five publicly available real-world MTS datasets 1 .…”

“…For univariate time series, dynamic time warping (DTW) [2] is known as an effective tool to measure the similarity between two time series that could have different lengths. For MTS, DTW is generalized to multivariate DTW to accommodate MTS data [3], [4]; Besides Euclidean distance, various distance measures for multivariate DTW have been proposed. For instance, correlation-based DTW [5], derivative DTW [6], Mahalanobis distance-based DTW [7], etc.…”