Time Series Classification and Extrinsic Regression are important and challenging machine learning tasks. Deep learning has revolutionized natural language processing and computer vision and holds great promise in other fields such as time series analysis where the relevant features must often be abstracted from the raw data but are not known a priori. This article surveys the current state of the art in the fast-moving field of deep learning for time series classification and extrinsic regression. We review different network architectures and training methods used for these tasks and discuss the challenges and opportunities when applying deep learning to time series data. We also summarize two critical applications of time series classification and extrinsic regression, human activity recognition and satellite earth observation.

We propose MultiRocket, a fast time series classification (TSC) algorithm that achieves state-of-the-art accuracy with a tiny fraction of the time and without the complex ensembling structure of many state-of-the-art methods. MultiRocket improves on MiniRocket, one of the fastest TSC algorithms to date, by adding multiple pooling operators and transformations to improve the diversity of the features generated. In addition to processing the raw input series, MultiRocket also applies first order differences to transform the original series. Convolutions are applied to both representations, and four pooling operators are applied to the convolution outputs. When benchmarked using the University of California Riverside TSC benchmark datasets, MultiRocket is significantly more accurate than MiniRocket, and competitive with the best ranked current method in terms of accuracy, HIVE-COTE 2.0, while being orders of magnitude faster.

Transformers have demonstrated outstanding performance in many applications of deep learning. When applied to time series data, transformers require effective position encoding to capture the ordering of the time series data. The efficacy of position encoding in time series analysis is not well-studied and remains controversial, e.g., whether it is better to inject absolute position encoding or relative position encoding, or a combination of them. In order to clarify this, we first review existing absolute and relative position encoding methods when applied in time series classification. We then proposed a new absolute position encoding method dedicated to time series data called time Absolute Position Encoding (tAPE). Our new method incorporates the series length and input embedding dimension in absolute position encoding. Additionally, we propose computationally Efficient implementation of Relative Position Encoding (eRPE) to improve generalisability for time series. We then propose a novel multivariate time series classification model combining tAPE/eRPE and convolution-based input encoding named ConvTran to improve the position and data embedding of time series data. The proposed absolute and relative position encoding methods are simple and efficient. They can be easily integrated into transformer blocks and used for downstream tasks such as forecasting, extrinsic regression, and anomaly detection. Extensive experiments on 32 multivariate time-series datasets show that our model is significantly more accurate than state-of-the-art convolution and transformer-based models. Code and models are open-sourced at https://github.com/Navidfoumani/ConvTran.

Time series classification maps time series to labels. The nearest neighbour algorithm (NN) using the Dynamic Time Warping (DTW) similarity measure is a leading algorithm for this task. NN compares each time series to be classified to every time series in the training database. With a training database of N time series of lengths L, each classification requires ν(N · L²) computations. The databases used in almost all prior research have been relatively small (with less than 10,000 samples) and much of the research has focused on making DTW's complexity linear with L, leading to a runtime complexity of O(N · L). As we demonstrate with an example in remote sensing, real-world time series databases are now reaching the million-to-billion scale. This wealth of training data brings the promise of higher accuracy, but raises a significant challenge because N is becoming the limiting factor. As DTW is not a metric, indexing objects induced by its space is extremely challenging. We tackle this task in this paper. We develop TSI, a novel algorithm for Time Series Indexing which combines a hierarchy of K-means clustering with DTW-based lower-bounding. We show that, on large databases, TSI makes it possible to classify time series orders of magnitude faster than the state of the art.