Deep learning methods have received increasing interest by the remote sensing community for multi-temporal land cover classification in recent years. Convolutional Neural networks that elementwise compare a time series with learned kernels, and recurrent neural networks that sequentially process temporal data have dominated the state-of-the-art in the classification of vegetation from satellite time series. Self-attention allows a neural network to selectively extract features from specific times in the input sequence thus suppressing non-classification relevant information. Today, self-attention based neural networks dominate the state-of-the-art in natural language processing but are hardly explored and tested in the remote sensing context. In this work, we embed self-attention in the canon of deep learning mechanisms for satellite time series classification for vegetation modeling and crop type identification. We compare it quantitatively to convolution, and recurrence and test four models that each exclusively relies on one of these mechanisms. The models are trained to identify the type of vegetation on crop parcels using raw and preprocessed Sentinel 2 time series over one entire year. To obtain an objective measure we find the best possible performance for each of the models by a large-scale hyperparameter search with more than 2400 validation runs. Beyond the quantitative comparison, we qualitatively analyze the models by an easy-to-implement, but yet effective feature importance analysis based on gradient back-propagation that exploits the differentiable nature of deep learning models. Finally, we look into the self-attention transformer model and visualize attention scores as bipartite graphs in the context of the input time series and a low-dimensional representation of internal hidden states using t-distributed stochastic neighborhood embedding (t-SNE).
Time series classification using novel techniques has experienced a recent resurgence and growing interest from statisticians, subject-domain scientists, and decision makers in business and industry. This is primarily due to the ever increasing amount of big and complex data produced as a result of technological advances. A motivating example is that of Google trends data, which exhibit highly nonlinear behavior. Although a rich literature exists for addressing this problem, existing approaches mostly rely on first and second order properties of the time series, since they typically assume linearity of the underlying process. Often, these are inadequate for effective classification of nonlinear time series data such as Google Trends data. Given these methodological deficiencies and the abundance of nonlinear time series that persist among real-world phenomena, we introduce an approach that merges higher order spectral analysis (HOSA) with deep convolutional neural networks (CNNs) for classifying time series. The effectiveness of our approach is illustrated using simulated data and two motivating industry examples that involve Google trends data and electronic device energy consumption data.
Adversarial training is a method for enhancing neural networks to improve the robustness against adversarial examples. Besides the security concerns of potential adversarial examples, adversarial training can also improve the performance of the neural networks, train robust neural networks, and provide interpretability for neural networks. In this work, we take the first step to introduce adversarial training in time series analysis by taking the finance field as an example. Rethinking existing researches of adversarial training, we propose the adaptively scaled adversarial training (ASAT) in time series analysis, by treating data at different time slots with time-dependent importance weights. Experimental results show that the proposed ASAT can improve both the accuracy and the adversarial robustness of neural networks. Besides enhancing neural networks, we also propose the dimension-wise adversarial sensitivity indicator to probe the sensitivities and importance of input dimensions. With the proposed indicator, we can explain the decision bases of black box neural networks.
Time series classification (TSC) is home to a number of algorithm groups that utilise different kinds of discriminatory patterns. One of these groups describes classifiers that predict using phase dependant intervals. The time series forest (TSF) classifier is one of the most well known interval methods, and has demonstrated strong performance as well as relative speed in training and predictions. However, recent advances in other approaches have left TSF behind. TSF originally summarises intervals using three simple summary statistics. The `catch22' feature set of 22 time series features was recently proposed to aid time series analysis through a concise set of diverse and informative descriptive characteristics. We propose combining TSF and catch22 to form a new classifier, the Canonical Interval Forest (CIF). We outline additional enhancements to the training procedure, and extend the classifier to include multivariate classification capabilities. We demonstrate a large and significant improvement in accuracy over both TSF and catch22, and show it to be on par with top performers from other algorithmic classes. By upgrading the interval-based component from TSF to CIF, we also demonstrate a significant improvement in the hierarchical vote collective of transformation-based ensembles (HIVE-COTE) that combines different time series representations. HIVE-COTE using CIF is significantly more accurate on the UCR archive than any other classifier we are aware of and represents a new state of the art for TSC.
Due to the dynamic nature, chaotic time series are difficult predict. In conventional signal processing approaches signals are treated either in time or in space domain only. Spatio-temporal analysis of signal provides more advantages over conventional uni-dimensional approaches by harnessing the information from both the temporal and spatial domains. Herein, we propose an spatio-temporal extension of RBF neural networks for the prediction of chaotic time series. The proposed algorithm utilizes the concept of time-space orthogonality and separately deals with the temporal dynamics and spatial non-linearity(complexity) of the chaotic series. The proposed RBF architecture is explored for the prediction of Mackey-Glass time series and results are compared with the standard RBF. The spatio-temporal RBF is shown to out perform the standard RBFNN by achieving significantly reduced estimation error.
Co-evolving time series appears in a multitude of applications such as environmental monitoring, financial analysis, and smart transportation. This paper aims to address the following challenges, including (C1) how to incorporate explicit relationship networks of the time series; (C2) how to model the implicit relationship of the temporal dynamics. We propose a novel model called Network of Tensor Time Series, which is comprised of two modules, including Tensor Graph Convolutional Network (TGCN) and Tensor Recurrent Neural Network (TRNN). TGCN tackles the first challenge by generalizing Graph Convolutional Network (GCN) for flat graphs to tensor graphs, which captures the synergy between multiple graphs associated with the tensors. TRNN leverages tensor decomposition to model the implicit relationships among co-evolving time series. The experimental results on five real-world datasets demonstrate the efficacy of the proposed method.
In recent years, deep learning techniques have outperformed traditional models in many machine learning tasks. Deep neural networks have successfully been applied to address time series forecasting problems, which is a very important topic in data mining. They have proved to be an effective solution given their capacity to automatically learn the temporal dependencies present in time series. However, selecting the most convenient type of deep neural network and its parametrization is a complex task that requires considerable expertise. Therefore, there is a need for deeper studies on the suitability of all existing architectures for different forecasting tasks. In this work, we face two main challenges: a comprehensive review of the latest works using deep learning for time series forecasting; and an experimental study comparing the performance of the most popular architectures. The comparison involves a thorough analysis of seven types of deep learning models in terms of accuracy and efficiency. We evaluate the rankings and distribution of results obtained with the proposed models under many different architecture configurations and training hyperparameters. The datasets used comprise more than 50000 time series divided into 12 different forecasting problems. By training more than 38000 models on these data, we provide the most extensive deep learning study for time series forecasting. Among all studied models, the results show that long short-term memory (LSTM) and convolutional networks (CNN) are the best alternatives, with LSTMs obtaining the most accurate forecasts. CNNs achieve comparable performance with less variability of results under different parameter configurations, while also being more efficient.
Regression-based frameworks for streamflow regionalization are built around catchment attributes that traditionally originate from catchment hydrology, flood frequency analysis and their interplay. In this work, we deviated from this traditional path by formulating and extensively investigating the first regression-based streamflow regionalization frameworks that largely emerge from general-purpose time series features for data science and, more precisely, from a large variety of such features. We focused on 28 features that included (partial) autocorrelation, entropy, temporal variation, seasonality, trend, lumpiness, stability, nonlinearity, linearity, spikiness, curvature and others. We estimated these features for daily temperature, precipitation and streamflow time series from 511 catchments, and then merged them within regionalization contexts with traditional topographic, land cover, soil and geologic attributes. Precipitation and temperature features (e.g., the spectral entropy, seasonality strength and lag-1 autocorrelation of the precipitation time series, and the stability and trend strength of the temperature time series) were found to be useful predictors of many streamflow features. The same applies to traditional attributes, such as the catchment mean elevation. Relationships between predictor and dependent variables were also revealed, while the spectral entropy, the seasonality strength and several autocorrelation features of the streamflow time series were found to be more regionalizable than others.
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