Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also intrigues great interests in the time series community. Among multiple advantages of transformers, the ability to capture long-range dependencies and interactions is especially attractive for time series modeling, leading to exciting progress in various time series applications. In this paper, we systematically review transformer schemes for time series modeling by highlighting their strengths as well as limitations through a new taxonomy to summarize existing time series transformers in two perspectives. From the perspective of network modifications, we summarize the adaptations of module level and architecture level of the time series transformers. From the perspective of applications, we categorize time series transformers based on common tasks including forecasting, anomaly detection, and classification. Empirically, we perform robust analysis, model size analysis, and seasonal-trend decomposition analysis to study how Transformers perform in time series. Finally, we discuss and suggest future directions to provide useful research guidance. To the best of our knowledge, this paper is the first work to comprehensively and systematically summarize the recent advances of Transformers for modeling time series data. We hope this survey will ignite further research interests in time series Transformers.
Autonomous driving systems validation remains one of the biggest challenges car manufacturers must tackle in order to provide safe driverless cars. The high complexity stems from several factors: the multiplicity of vehicles, embedded systems, use cases, and the very high required level of reliability for the driving system to be at least as safe as a human driver. In order to circumvent these issues, large scale simulations reproducing this huge variety of physical conditions are intensively used to test driverless cars. Therefore, the validation step produces a massive amount of data, including many time-indexed ones, to be processed. In this context, building a structure in the feature space is mandatory to interpret the various scenarios. In this work, we propose a new co-clustering approach adapted to high-dimensional time series analysis, that extends the standard model-based co-clustering. The FunCLBM model extends the recently proposed Functional Latent Block Model and allows to create a dependency structure between row and column clusters. This structured partition acts as a feature selection method, that provides several clustering views of a dataset, while discriminating irrelevant features. In this workflow, times series are projected onto a common interpolated low-dimensional frequency space, which allows to optimize the projection basis. In addition, FunCLBM refines the definition of each latent block by performing block-wise dimension reduction and feature selection. We propose a SEM-Gibbs algorithm to infer this model, as well as a dedicated criterion to select the optimal nested partition. Experiments on both simulated and real-case Renault datasets shows the effectiveness of the proposed tools and the adequacy to our use case.
Extracting the underlying trend signal is a crucial step to facilitate time series analysis like forecasting and anomaly detection. Besides noise signal, time series can contain not only outliers but also abrupt trend changes in real-world scenarios. To deal with these challenges, we propose a robust trend filtering algorithm based on robust statistics and sparse learning. Specifically, we adopt the Huber loss to suppress outliers, and utilize a combination of the first order and second order difference on the trend component as regularization to capture both slow and abrupt trend changes. Furthermore, an efficient method is designed to solve the proposed robust trend filtering based on majorization minimization (MM) and alternative direction method of multipliers (ADMM). We compared our proposed robust trend filter with other nine state-of-the-art trend filtering algorithms on both synthetic and real-world datasets. The experiments demonstrate that our algorithm outperforms existing methods.
Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data streams, resulting in a new efficiently computable universal metric for time series. The proposed metric is in the sense that we can compare and contrast data streams regardless of where and how they are generated and without any feature engineering step. The approach proposed in this paper is conceptually distinct from our previous work on data smashing, and vastly improves discrimination performance and computing speed. The core idea here is the generalization of the notion of KL divergence often used to compare probability distributions to a notion of divergence in time series. We call this the sequence likelihood (SL) divergence, which may be used to measure deviations within a well-defined class of discrete-valued stochastic processes. We devise efficient estimators of SL divergence from finite sample paths and subsequently formulate a universal metric useful for computing distance between time series produced by hidden stochastic generators.
Here we present a holistic approach for data exploration on dense knowledge graphs as a novel approach with a proof-of-concept in biomedical research. Knowledge graphs are increasingly becoming a vital factor in knowledge mining and discovery as they connect data using technologies from the semantic web. In this paper we extend a basic knowledge graph extracted from biomedical literature by context data like named entities and relations obtained by text mining and other linked data sources like ontologies and databases. We will present an overview about this novel network. The aim of this work was to extend this current knowledge with approaches from graph theory. This method will build the foundation for quality control, validation of hypothesis, detection of missing data and time series analysis of biomedical knowledge in general. In this context we tried to apply multiple-valued decision diagrams to these questions. In addition this knowledge representation of linked data can be used as FAIR approach to answer semantic questions. This paper sheds new lights on dense and very large knowledge graphs and the importance of a graph-theoretic understanding of these networks.
A time series is a collection of measurements in chronological order. Discovering patterns from time series is useful in many domains, such as stock analysis, disease detection, and weather forecast. To discover patterns, existing methods often convert time series data into another form, such as nominal/symbolic format, to reduce dimensionality, which inevitably deviates the data values. Moreover, existing methods mainly neglect the order relationships between time series values. To tackle these issues, inspired by order-preserving matching, this paper proposes an Order-Preserving sequential Pattern (OPP) mining method, which represents patterns based on the order relationships of the time series data. An inherent advantage of such representation is that the trend of a time series can be represented by the relative order of the values underneath the time series data. To obtain frequent trends in time series, we propose the OPP-Miner algorithm to mine patterns with the same trend (sub-sequences with the same relative order). OPP-Miner employs the filtration and verification strategies to calculate the support and uses pattern fusion strategy to generate candidate patterns. To compress the result set, we also study finding the maximal OPPs. Experiments validate that OPP-Miner is not only efficient and scalable but can also discover similar sub-sequences in time series. In addition, case studies show that our algorithms have high utility in analyzing the COVID-19 epidemic by identifying critical trends and improve the clustering performance.
sktime is an open source, Python based, sklearn compatible toolkit for time series analysis developed by researchers at the University of East Anglia, University College London and the Alan Turing Institute. A key initial goal for sktime was to provide time series classification functionality equivalent to that available in a related java package, tsml. We describe the implementation of six such classifiers in sktime and compare them to their tsml equivalents. We demonstrate correctness through equivalence of accuracy on a range of standard test problems and compare the build time of the different implementations. We find that there is significant difference in accuracy on only one of the six algorithms, and this difference was to be expected. We found a much wider range of difference in efficiency. Again, this was not unexpected, but it does highlight ways both toolkits could be improved. PLEASE NOTE THIS PAPER IS NOT COMPLETE. It is a work in progress and we have pushed it early so that we can reference it in another paper. More to follow!
This chapter presents an overview of techniques used for the analysis, edition, and synthesis of time series, with a particular emphasis on motion data. The use of mixture models allows the decomposition of time signals as a superposition of basis functions. It provides a compact representation that aims at keeping the essential characteristics of the signals. Various types of basis functions have been proposed, with developments originating from different fields of research, including computer graphics, human motion science, robotics, control, and neuroscience. Examples of applications with radial, Bernstein and Fourier basis functions will be presented, with associated source codes to get familiar with these techniques.
Predicting future stock prices and their movement patterns is a complex problem. Hence, building a portfolio of capital assets using the predicted prices to achieve the optimization between its return and risk is an even more difficult task. This work has carried out an analysis of the time series of the historical prices of the top five stocks from the nine different sectors of the Indian stock market from January 1, 2016, to December 31, 2020. Optimum portfolios are built for each of these sectors. For predicting future stock prices, a long-and-short-term memory (LSTM) model is also designed and fine-tuned. After five months of the portfolio construction, the actual and the predicted returns and risks of each portfolio are computed. The predicted and the actual returns of each portfolio are found to be high, indicating the high precision of the LSTM model.