In the last 5 years there have been a large number of new time series classification algorithms proposed in the literature. These algorithms have been evaluated on subsets of the 47 data sets in the University of California, Riverside time series classification archive. The archive has recently been expanded to 85 data sets, over half of which have been donated by researchers at the University of East Anglia. Aspects of previous evaluations have made comparisons between algorithms difficult. For example, several different programming languages have been used, experiments involved a single train/test split and some used normalised data whilst others did not. The relaunch of the archive provides a timely opportunity to thoroughly evaluate algorithms on a larger number of datasets. We have implemented 18 recently proposed algorithms in a common Java framework and compared them against two standard benchmark classifiers (and each other) by performing 100 resampling experiments on each of the 85 datasets. We use these results to test several hypotheses relating to whether the algorithms are significantly more accurate than the benchmarks and each other. Our results indicate that only nine of these algorithms are significantly more accurate than both benchmarks and that one classifier, the collective of transformation ensembles, is significantly more accurate than all of the others. All of our experiments and results are reproducible: we release all of our code, results and experimental details and we hope these experiments form the basis for more robust testing of new algorithms in the future.

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Several alternative distance measures for comparing time series have recently been proposed and evaluated on time series classification (TSC) problems. These include variants of dynamic time warping (DTW), such as weighted and derivative DTW, and edit distance-based measures, including longest common subsequence, edit distance with real penalty, time warp with edit, and move–split–merge. These measures have the common characteristic that they operate in the time domain and compensate for potential localised misalignment through some elastic adjustment. Our aim is to experimentally test two hypotheses related to these distance measures. Firstly, we test whether there is any significant difference in accuracy for TSC problems between nearest neighbour classifiers using these distance measures. Secondly, we test whether combining these elastic distance measures through simple ensemble schemes gives significantly better accuracy. We test these hypotheses by carrying out one of the largest experimental studies ever conducted into time series classification. Our first key finding is that there is no significant difference between the elastic distance measures in terms of classification accuracy on our data sets. Our second finding, and the major contribution of this work, is to define an ensemble classifier that significantly outperforms the individual classifiers. We also demonstrate that the ensemble is more accurate than approaches not based in the time domain. Nearly all TSC papers in the data mining literature cite DTW (with warping window set through cross validation) as the benchmark for comparison. We believe that our ensemble is the first ever classifier to significantly outperform DTW and as such raises the bar for future work in this area

Time-series classification (TSC) problems present a specific challenge for classification algorithms: how to measure similarity between series. A \emph{shapelet} is a time-series subsequence that allows for TSC based on local, phase-independent similarity in shape. Shapelet-based classification uses the similarity between a shapelet and a series as a discriminatory feature. One benefit of the shapelet approach is that shapelets are comprehensible, and can offer insight into the problem domain. The original shapelet-based classifier embeds the shapelet-discovery algorithm in a decision tree, and uses information gain to assess the quality of candidates, finding a new shapelet at each node of the tree through an enumerative search. Subsequent research has focused mainly on techniques to speed up the search. We examine how best to use the shapelet primitive to construct classifiers. We propose a single-scan shapelet algorithm that finds the best $k$ shapelets, which are used to produce a transformed dataset, where each of the $k$ features represent the distance between a time series and a shapelet. The primary advantages over the embedded approach are that the transformed data can be used in conjunction with any classifier, and that there is no recursive search for shapelets. We demonstrate that the transformed data, in conjunction with more complex classifiers, gives greater accuracy than the embedded shapelet tree. We also evaluate three similarity measures that produce equivalent results to information gain in less time. Finally, we show that by conducting post-transform clustering of shapelets, we can enhance the interpretability of the transformed data. We conduct our experiments on 29 datasets: 17 from the UCR repository, and 12 we provide ourselve

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The problem of time series classification (TSC), where we consider any real-valued ordered data a time series, presents a specific machine learning challenge as the ordering of variables is often crucial in finding the best discriminating features. One of the most promising recent approaches is to find shapelets within a data set. A shapelet is a time series subsequence that is identified as being representative of class membership. The original research in this field embedded the procedure of finding shapelets within a decision tree. We propose disconnecting the process of finding shapelets from the classification algorithm by proposing a shapelet transformation. We describe a means of extracting the k best shapelets from a data set in a single pass, and then use these shapelets to transform data by calculating the distances from a series to each shapelet. We demonstrate that transformation into this new data space can improve classification accuracy, whilst retaining the explanatory power provided by shapelets.

Recently, two ideas have been explored that lead to more accurate algorithms for time-series classification (TSC). First, it has been shown that the simplest way to gain improvement on TSC problems is to transform into an alternative data space where discriminatory features are more easily detected. Second, it was demonstrated that with a single data representation, improved accuracy can be achieved through simple ensemble schemes. We combine these two principles to test the hypothesis that forming a collective of ensembles of classifiers on different data transformations improves the accuracy of time-series classification. The collective contains classifiers constructed in the time, frequency, change, and shapelet transformation domains. For the time domain we use a set of elastic distance measures. For the other domains we use a range of standard classifiers. Through extensive experimentation on 72 datasets, including all of the 46 UCR datasets, we demonstrate that the simple collective formed by including all classifiers in one ensemble is significantly more accurate than any of its components and any other previously published TSC algorithm. We investigate alternative hierarchical collective structures and demonstrate the utility of the approach on a new problem involving classifying {\em Caenorhabditis elegans} mutant types

There have been many new algorithms proposed over the last five years for solving time series classification (TSC) problems. A recent experimental comparison of the leading TSC algorithms has demonstrated that one approach is significantly more accurate than all others over 85 datasets. That approach, the Flat Collective of Transformation-based Ensembles (Flat-COTE), achieves superior accuracy through combining predictions of 35 individual classifiers built on four representations of the data into a flat hierarchy. Outside of TSC, deep learning approaches such as convolutional neural networks (CNN) have seen a recent surge in popularity and are now state of the art in many fields. An obvious question is whether CNNs could be equally transformative in the field of TSC. To test this, we implement a common CNN structure and compare performance to Flat-COTE and a recently proposed time series-specific CNN implementation. We find that Flat-COTE is significantly more accurate than both deep learning approaches on 85 datasets. These results are impressive, but Flat-COTE is not without deficiencies. We improve the collective by adding new components and proposing a modular hierarchical structure with a probabilistic voting scheme that allows us to encapsulate the classifiers built on each transformation. We add two new modules representing dictionary and interval-based classifiers, and significantly improve upon the existing frequency domain classifiers with a novel spectral ensemble. The resulting classifier, the Hierarchical Vote Collective of Transformation-based Ensembles (HIVE-COTE) is significantly more accurate than Flat-COTE and represents a new state of the art for TSC. HIVE-COTE captures more sources of possible discriminatory features in time series and has a more modular, intuitive structure.