This paper contributes multivariate versions of seven commonly used elastic similarity and distance measures for time series data analytics. Elastic similarity and distance measures can compensate for misalignments in the time axis of time series data. We adapt two existing strategies used in a multivariate version of the well-known Dynamic Time Warping (DTW), namely, Independent and Dependent DTW, to these seven measures. While these measures can be applied to various time series analysis tasks, we demonstrate their utility on multivariate time series classification using the nearest neighbor classifier. On 23 well-known datasets, we demonstrate that each of the measures but one achieves the highest accuracy relative to others on at least one dataset, supporting the value of developing a suite of multivariate similarity and distance measures. We also demonstrate that there are datasets for which either the dependent versions of all measures are more accurate than their independent counterparts or vice versa. In addition, we also construct a nearest neighbor-based ensemble of the measures and show that it is competitive to other state-of-the-art single-strategy multivariate time series classifiers.

Time series data can be found in almost every domain, ranging from the medical field to manufacturing and wireless communication. Generating realistic and useful exemplars and prototypes is a fundamental data analysis task. In this paper, we investigate a novel approach to generating realistic and useful exemplars and prototypes for time series data. Our approach uses a new form of time series average, the ShapeDTW Barycentric Average. We therefore turn our attention to accurately generating time series prototypes with a novel approach. The existing time series prototyping approaches rely on the Dynamic Time Warping (DTW) similarity measure such as DTW Barycentering Average (DBA) and SoftDBA. These last approaches suffer from a common problem of generating out-of-distribution artifacts in their prototypes. This is mostly caused by the DTW variant used and its incapability of detecting neighborhood similarities, instead it detects absolute similarities. Our proposed method, ShapeDBA, uses the ShapeDTW variant of DTW, that overcomes this issue. We chose time series clustering, a popular form of time series analysis to evaluate the outcome of ShapeDBA compared to the other prototyping approaches. Coupled with the k-means clustering algorithm, and evaluated on a total of 123 datasets from the UCR archive, our proposed averaging approach is able to achieve new state-of-the-art results in terms of Adjusted Rand Index.

There are many applications that benefit from computing the exact divergence between 2 discrete probability measures, including machine learning. Unfortunately, in the absence of any assumptions on the structure or independencies within these distributions, computing the divergence between them is an intractable problem in high dimensions. We show that we are able to compute a wide family of functionals and divergences, such as the alpha-beta divergence, between two decomposable models, i.e. chordal Markov networks, in time exponential to the treewidth of these models. The alpha-beta divergence is a family of divergences that include popular divergences such as the Kullback-Leibler divergence, the Hellinger distance, and the chi-squared divergence. Thus, we can accurately compute the exact values of any of this broad class of divergences to the extent to which we can accurately model the two distributions using decomposable models.

Real-world time series data often have unequal lengths. These differences in length may arise from a number of fundamentally different mechanisms. In this work, we identify and evaluate two classes of such mechanism – variations in sampling rate relative to the relevant signal and variations between the start and end points of one time series relative to one another. We investigate how time series generated by each of these classes of mechanism are best addressed for time series similarity assessment. We perform extensive experiments and provide practical recommendations.

This paper studies time series extrinsic regression (TSER): a regression task of which the aim is to learn the relationship between a time series and a continuous scalar variable; a task closely related to time series classification (TSC), which aims to learn the relationship between a time series and a categorical class label. This task generalizes time series forecasting, relaxing the requirement that the value predicted be a future value of the input series or primarily depend on more recent values. In this paper, we motivate and study this task, and benchmark existing solutions and adaptations of TSC algorithms on a novel archive of 19 TSER datasets which we have assembled. Our results show that the state-of-the-art TSC algorithm Rocket, when adapted for regression, achieves the highest overall accuracy compared to adaptations of other TSC algorithms and state-of-the-art machine learning (ML) algorithms such as XGBoost, Random Forest and Support Vector Regression. More importantly, we show that much research is needed in this field to improve the accuracy of ML models. We also find evidence that further research has excellent prospects of improving upon these straightforward baselines.

Elastic similarity measures are a class of similarity measures specifically designed to work with time series data. When scoring the similarity between two time series, they allow points that do not correspond in timestamps to be aligned. This can compensate for misalignments in the time axis of time series data, and for similar processes that proceed at variable and differing paces. Elastic similarity measures are widely used in machine learning tasks such as classification, clustering and outlier detection when using time series data. There is a multitude of research on various univariate elastic similarity measures. However, except for multivariate versions of the well known Dynamic Time Warping (DTW) there is a lack of work to generalise other similarity measures for multivariate cases. This paper adapts two existing strategies used in multivariate DTW, namely, Independent and Dependent DTW, to several commonly used elastic similarity measures. Using 23 datasets from the University of East Anglia (UEA) multivariate archive, for nearest neighbour classification, we demonstrate that each measure outperforms all others on at least one dataset and that there are datasets for which either the dependent versions of all measures are more accurate than their independent counterparts or vice versa. This latter finding suggests that these differences arise from a fundamental property of the data. We also show that an ensemble of such nearest neighbour classifiers is highly competitive with other state-of-the-art multivariate time series classifiers.

Dynamic Time Warping (DTW) is a popular similarity measure for aligning and comparing time series. Due to DTW’s high computation time, lower bounds are often employed to screen poor matches. Many alternative lower bounds have been proposed, providing a range of different trade-offs between tightness and computational efficiency. LB_KEOGH provides a useful trade-off in many applications. Two recent lower bounds, LB_IMPROVED and LB_ENHANCED, are substantially tighter than LB_KEOGH. All three have the same worst case computational complexity—linear with respect to series length and constant with respect to window size. We present four new DTW lower bounds in the same complexity class. LB_PETITJEAN is substantially tighter than LB_IMPROVED, with only modest additional computational overhead. LB_WEBB is more efficient than LB_IMPROVED, while often providing a tighter bound. LB_WEBB is always tighter than LB_KEOGH. The parameter free LB_WEBB is usually tighter than LB_ENHANCED. A parameterized variant, LB_Webb_Enhanced, is always tighter than LB_ENHANCED. A further variant, LB_WEBB*, is useful for some constrained distance functions. In extensive experiments, LB_WEBB proves to be very effective for nearest neighbor search.

The problem of estimating the divergence between 2 high dimensional distributions with limited samples is an important problem in various fields such as machine learning. Although previous methods perform well with moderate dimensional data, their accuracy starts to degrade in situations with 100s of binary variables. Therefore, we propose the use of decomposable models for estimating divergences in high dimensional data. These allow us to factorize the estimated density of the high-dimensional distribution into a product of lower dimensional functions. We conduct formal and experimental analyses to explore the properties of using decomposable models in the context of divergence estimation. To this end, we show empirically that estimating the Kullback-Leibler divergence using decomposable models from a maximum likelihood estimator outperforms existing methods for divergence estimation in situations where dimensionality is high and useful decomposable models can be learnt from the available data.

Introduction. We investigated patterns in digital audiobook and e-book circulation through Australian libraries to identify and analyse trends in audiobook publishing and reading. Method. In partnership with four Australian library services we collated a dataset of 555,618 audiobook checkouts and 3,475,188 e-book checkouts, representing all OverDrive checkouts through these services from 2006 until July 2017. Analysis. We examined the availability and popularity of audiobook and e-book titles over time. We used bibliographic metadata and manual and automated coding to examine major publishers, sex and nationality of authors, and popular titles and genres. Results. Audiobooks and e-books have experienced substantial growth since 2006. Major publishers including the Big Five, Amazon, and Bolinda have historically been less important in audiobook publishing than in print or e-book markets, with numerous specialist audio publishers and producers prominent in the field. Audiobooks and e-books show disparities in the sex of authors. Crime, science fiction, and fantasy are the most popular audiobook genres. Conclusion. Library checkout data confirm audiobook publishing's recent volatility. Libraries are the keepers of valuable information about new media forms like audiobooks, and collaboration between libraries, publishers, and researchers directly supports understanding of this important new space of cultural production and consumption.

This paper studies Time Series Extrinsic Regression (TSER): a regression task of which the aim is to learn the relationship between a time series and a continuous scalar variable; a task closely related to time series classification (TSC), which aims to learn the relationship between a time series and a categorical class label. This task generalizes time series forecasting (TSF), relaxing the requirement that the value predicted be a future value of the input series or primarily depend on more recent values. In this paper, we motivate and study this task, and benchmark existing solutions and adaptations of TSC algorithms on a novel archive of 19 TSER datasets which we have assembled. Our results show that the state-of-the-art TSC algorithm Rocket, when adapted for regression, achieves the highest overall accuracy compared to adaptations of other TSC algorithms and state-of-the-art machine learning (ML) algorithms such as XGBoost, Random Forest and Support Vector Regression. More importantly, we show that much research is needed in this field to improve the accuracy of ML models. We also find evidence that further research has excellent prospects of improving upon these straightforward baselines.

Land cover maps are a vital input variable to many types of environmental research and management. While they can be produced automatically by machine learning techniques, these techniques require substantial training data to achieve high levels of accuracy, which are not always available. One technique researchers use when labelled training data are scarce is domain adaptation (DA)—where data from an alternate region, known as the source domain, are used to train a classifier and this model is adapted to map the study region, or target domain. The scenario we address in this paper is known as semi-supervised DA, where some labelled samples are available in the target domain. In this paper we present Sourcerer, a Bayesian-inspired, deep learning-based, semi-supervised DA technique for producing land cover maps from satellite image time series (SITS) data. The technique takes a convolutional neural network trained on a source domain and then trains further on the available target domain with a novel regularizer applied to the model weights. The regularizer adjusts the degree to which the model is modified to fit the target data, limiting the degree of change when the target data are few in number and increasing it as target data quantity increases. Our experiments on Sentinel-2 time series images compare Sourcerer with two state-of-the-art semi-supervised domain adaptation techniques and four baseline models. We show that on two different source-target domain pairings Sourcerer outperforms all other methods for any quantity of labelled target data available. In fact, the results on the more difficult target domain show that the starting accuracy of Sourcerer (when no labelled target data are available), 74.2%, is greater than the next-best state-of-the-art method trained on 20,000 labelled target instances.

Live fuel moisture content (LFMC) is an essential variable to model fire danger and behaviour. This paper presents the first application of deep learning to LFMC estimation based on the historical LFMC ground samples of the Globe-LFMC database, as a step towards operational daily LFMC mapping in the Contiguous United States (CONUS). One-year MODerate resolution Imaging Spectroradiometer (MODIS) time series preceding each LFMC sample were extracted as the primary data source for training. The proposed temporal convolutional neural network for LFMC (TempCNN-LFMC) comprises three 1-D convolutional layers that learn the multi-scale temporal dynamics (features) of one-year MODIS time series specific to LFMC estimation. The learned features, together with a few auxiliary variables (e.g., digital elevation model), are then passed to three fully connected layers to extract the non-linear relationships with LFMC. In the primary training and validation scenario, the neural network was trained using samples from 2002 to 2013 and then adopted to estimating the LFMC from 2014 to 2018, achieving an overall root mean square error (RMSE) of 25.57% and a correlation coefficient (R) of 0.74. Good consistency on spatial patterns and temporal trends of accuracy was observed. The trained model achieved a similar RMSE of 25.98%, 25.20% and 25.93% for forest, shrubland, and grassland, respectively, without requiring prior information on the vegetation type.

This dataset is part of the Monash, UEA & UCR time series regression repository. http://tseregression.org/ The goal of this dataset is to predict PM2.5 air quality in the city of Beijing. This dataset contains 17532 time series with 9 dimensions. This includes hourly air pollutants measurments (SO2, NO2, CO and O3), temperature, pressure, dew point, rainfall and windspeed measurments from 12 nationally controlled air quality monitoring sites. The air-quality data are from the Beijing Municipal Environmental Monitoring Center. The meteorological data in each air-quality site are matched with the nearest weather station from the China Meteorological Administration. The time period is from March 1st, 2013 to February 28th, 2017. Please refer to https://archive.ics.uci.edu/ml/datasets/Beijing+Multi-Site+Air-Quality+Data for more details Relevant Papers Zhang, S., Guo, B., Dong, A., He, J., Xu, Z. and Chen, S.X. (2017) Cautionary Tales on Air-Quality Improvement in Beijing. Proceedings of the Royal Society A, Volume 473, No. 2205, Pages 20170457 Citation Request Zhang, S., Guo, B., Dong, A., He, J., Xu, Z. and Chen, S.X. (2017) Cautionary Tales on Air-Quality Improvement in Beijing. Proceedings of the Royal Society A, Volume 473, No. 2205, Pages 20170457

Stream classification methods classify a continuous stream of data as new labelled samples arrive. They often also have to deal with concept drift. This paper focuses on seasonal drift in stream classification, which can be found in many real-world application data sources. Traditional approaches of stream classification consider seasonal drift by including seasonal dummy/indicator variables or building separate models for each season. But these approaches have strong limitations in high-dimensional classification problems, or with complex seasonal patterns. This paper explores how to best handle seasonal drift in the specific context of news article categorization (or classification/tagging), where seasonal drift is overwhelmingly the main type of drift present in the data, and for which the data are high-dimensional. We introduce a novel classifier named Seasonal Averaged One-Dependence Estimators (SAODE), which extends the AODE classifier to handle seasonal drift by including time as a super parent. We assess our SAODE model using two large real-world text mining related datasets each comprising approximately a million records, against nine state-of-the-art stream and concept drift classification models, with and without seasonal indicators and with separate models built for each season. Across five different evaluation techniques, we show that our model consistently outperforms other methods by a large margin where the results are statistically significant.

This dataset is part of the Monash, UEA & UCR time series regression repository. http://tseregression.org/ The goal of this dataset is to estimate respiratory rate using PPG and ECG data. This dataset contains 7949 time series obtained from the Physionet's BIDMC PPG and Respiration dataset, which was extracted from the much larger MIMIC II waveform database. Please refer to https://physionet.org/content/bidmc/1.0.0/ for more details Relevant papers Pimentel, M.A.F. et al. Towards a Robust Estimation of Respiratory Rate from Pulse Oximeters. IEEE Transactions on Biomedical Engineering, 64(8), pp.1914-1923, 2016. [DOI: 10.1109/TBME.2016.2613124](http://doi.org/10.1109/TBME.2016.2613124). Citation request Pimentel, M.A.F. et al. Towards a Robust Estimation of Respiratory Rate from Pulse Oximeters. IEEE Transactions on Biomedical Engineering, 64(8), pp.1914-1923, 2016. [DOI: 10.1109/TBME.2016.2613124](http://doi.org/10.1109/TBME.2016.2613124). Goldberger, A., Amaral, L., Glass, L., Hausdorff, J., Ivanov, P. C., Mark, R., ... & Stanley, H. E. (2000). PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation [Online]. 101 (23), pp. e215–e220.

Commercial microwave links (CMLs) have proven useful for providing rainfall information close to the ground surface. However, large uncertainties are associated with these retrievals, partly due to challenges in the type of data collection and processing. In particular, the most common case is when only minimum and maximum received signal levels (RSLs) over a given time interval (hereafter 15 min) are stored by mobile network operators. The average attenuation and the corresponding rainfall rate are then calculated based on a weighted average method using the minimum and maximum attenuation. In this study, an alternative to using a constant weighted average method is explored, based on a machine learning model trained to produce actual attenuation from minimum/maximum values. A rainfall retrieval deep learning model was designed based on a long short‐term memory (LSTM) model architecture and trained with disdrometer data in a form that is comparable to the data provided by mobile network operators. A first evaluation used only disdrometer data to mimic both attenuation from a CML and corresponding rainfall rates. For the test data set, the relative bias was reduced from 5.99% to 2.84% and the coefficient of determination (R2) increased from 0.86 to 0.97. The second evaluation used this disdrometer‐trained LSTM to retrieve rainfall rates from an actual CML located nearby the disdrometer. A significant improvement in the overall rainfall estimation compared to existing microwave link attenuation models was observed. The relative bias reduced from 7.39% to −1.14% and the R2 improved from 0.71 to 0.82.

Time Series Classification (TSC) has seen enormous progress over the last two decades. HIVE-COTE (Hierarchical Vote Collective of Transformation-based Ensembles) is the current state of the art in terms of classification accuracy. HIVE-COTE recognizes that time series data are a specific data type for which the traditional attribute-value representation, used predominantly in machine learning, fails to provide a relevant representation. HIVE-COTE combines multiple types of classifiers: each extracting information about a specific aspect of a time series, be it in the time domain, frequency domain or summarization of intervals within the series. However, HIVE-COTE (and its predecessor, FLAT-COTE) is often infeasible to run on even modest amounts of data. For instance, training HIVE-COTE on a dataset with only 1500 time series can require 8 days of CPU time. It has polynomial runtime with respect to the training set size, so this problem compounds as data quantity increases. We propose a novel TSC algorithm, TS-CHIEF (Time Series Combination of Heterogeneous and Integrated Embedding Forest), which rivals HIVE-COTE in accuracy but requires only a fraction of the runtime. TS-CHIEF constructs an ensemble classifier that integrates the most effective embeddings of time series that research has developed in the last decade. It uses tree-structured classifiers to do so efficiently. We assess TS-CHIEF on 85 datasets of the University of California Riverside (UCR) archive, where it achieves state-of-the-art accuracy with scalability and efficiency. We demonstrate that TS-CHIEF can be trained on 130 k time series in 2 days, a data quantity that is beyond the reach of any TSC algorithm with comparable accuracy.

This dataset is part of the Monash, UEA & UCR time series regression repository. http://tseregression.org/ This goal of this dataset is to predict benzene concentration in an Italian city. This dataset contains 8878 time series obtained from the Air Quality dataset from the UCI repository. The time series has 8 dimensions which consists of hourly averaged responses from an array of 5 metal oxide chemical sensors embedded in an Air Quality Chemical Multisensor Device, as well as temperature, relative humidity and absolute humidity. The Air Quality Chemical Multisensor device was located on the field in a significantly polluted area, at road level, within an Italian city. Data were recorded from March 2004 to February 2005 (one year) representing the longest freely available recordings of on field deployed air quality chemical sensor devices responses. Ground Truth hourly averaged concentrations for CO, Non Metanic Hydrocarbons, Benzene, Total Nitrogen Oxides (NOx) and Nitrogen Dioxide (NO2) and were provided by a co-located reference certified analyzer. Please refer to https://archive.ics.uci.edu/ml/datasets/Air+Quality for more details. Relevant papers S. De Vito, E. Massera, M. Piga, L. Martinotto, G. Di Francia, On field calibration of an electronic nose for benzene estimation in an urban pollution monitoring scenario, Sensors and Actuators B: Chemical, Volume 129, Issue 2, 22 February 2008, Pages 750-757, ISSN 0925-4005. Saverio De Vito, Marco Piga, Luca Martinotto, Girolamo Di Francia, CO, NO2 and NOx urban pollution monitoring with on-field calibrated electronic nose by automatic bayesian regularization, Sensors and Actuators B: Chemical, Volume 143, Issue 1, 4 December 2009, Pages 182-191, ISSN 0925-4005. S. De Vito, G. Fattoruso, M. Pardo, F. Tortorella and G. Di Francia, Semi-Supervised Learning Techniques in Artificial Olfaction: A Novel Approach to Classification Problems and Drift Counteraction, in IEEE Sensors Journal, vol. 12, no. 11, pp. 3215-3224, Nov. 2012. doi: 10.1109/JSEN.2012.2192425 Citation request S. De Vito, E. Massera, M. Piga, L. Martinotto, G. Di Francia, On field calibration of an electronic nose for benzene estimation in an urban pollution monitoring scenario, Sensors and Actuators B: Chemical, Volume 129, Issue 2, 22 February 2008, Pages 750-757, ISSN 0925-4005

This dataset is part of the Monash, UEA & UCR time series regression repository. http://tseregression.org/ The goal of this dataset is to predict maximum water depth for flood modelling. The dataset contains 673 hourly rainfall events time series which are used to predict the maximum water depth of a domain (Digital Elevation Model, DEM). The rainfall events and DEM are generated synthetically by researchers at Monash University because real DEM data with accurate rainfall events are rare. Data Donor Jihane Elyahyioui, jihane.elyahyioui@monash.edu

Spatio-temporal data sets such as satellite image series are of utmost importance for understanding global developments like climate change or urbanization. However, incompleteness of data can greatly impact usability and knowledge discovery. In fact, there are many cases where not a single data point in the set is fully observed. For filling gaps, we introduce a novel approach that utilizes Markov random fields (MRFs). We extend the probabilistic framework to also consider empirical prior information, which allows to train even on highly incomplete data. Moreover, we devise a way to make discrete MRFs predict continuous values via state superposition. Experiments on real-world remote sensing imagery suffering from cloud cover show that the proposed approach outperforms state-of-the-art gap filling techniques.