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"Time Series Analysis": models, code, and papers

Dynamic Principal Component Analysis: Identifying the Relationship between Multiple Air Pollutants

Aug 10, 2016
Oleg Melnikov, Loren H. Raun, Katherine B. Ensor

The dynamic nature of air quality chemistry and transport makes it difficult to identify the mixture of air pollutants for a region. In this study of air quality in the Houston metropolitan area we apply dynamic principal component analysis (DPCA) to a normalized multivariate time series of daily concentration measurements of five pollutants (O3, CO, NO2, SO2, PM2.5) from January 1, 2009 through December 31, 2011 for each of the 24 hours in a day. The resulting dynamic components are examined by hour across days for the 3 year period. Diurnal and seasonal patterns are revealed underlining times when DPCA performs best and two principal components (PCs) explain most variability in the multivariate series. DPCA is shown to be superior to static principal component analysis (PCA) in discovery of linear relations among transformed pollutant measurements. DPCA captures the time-dependent correlation structure of the underlying pollutants recorded at up to 34 monitoring sites in the region. In winter mornings the first principal component (PC1) (mainly CO and NO2) explains up to 70% of variability. Augmenting with the second principal component (PC2) (mainly driven by SO2) the explained variability rises to 90%. In the afternoon, O3 gains prominence in the second principal component. The seasonal profile of PCs' contribution to variance loses its distinction in the afternoon, yet cumulatively PC1 and PC2 still explain up to 65% of variability in ambient air data. DPCA provides a strategy for identifying the changing air quality profile for the region studied.

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ECG synthesis with Neural ODE and GAN models

Oct 30, 2021
Mansura Habiba, Eoin Borphy, Barak A. Pearlmutter, Tomas Ward

Continuous medical time series data such as ECG is one of the most complex time series due to its dynamic and high dimensional characteristics. In addition, due to its sensitive nature, privacy concerns and legal restrictions, it is often even complex to use actual data for different medical research. As a result, generating continuous medical time series is a very critical research area. Several research works already showed that the ability of generative adversarial networks (GANs) in the case of continuous medical time series generation is promising. Most medical data generation works, such as ECG synthesis, are mainly driven by the GAN model and its variation. On the other hand, Some recent work on Neural Ordinary Differential Equation (Neural ODE) demonstrates its strength against informative missingness, high dimension as well as dynamic nature of continuous time series. Instead of considering continuous-time series as a discrete-time sequence, Neural ODE can train continuous time series in real-time continuously. In this work, we used Neural ODE based model to generate synthetic sine waves and synthetic ECG. We introduced a new technique to design the generative adversarial network with Neural ODE based Generator and Discriminator. We developed three new models to synthesise continuous medical data. Different evaluation metrics are then used to quantitatively assess the quality of generated synthetic data for real-world applications and data analysis. Another goal of this work is to combine the strength of GAN and Neural ODE to generate synthetic continuous medical time series data such as ECG. We also evaluated both the GAN model and the Neural ODE model to understand the comparative efficiency of models from the GAN and Neural ODE family in medical data synthesis.

* Proc. of the International Conference on Electrical, Computer and Energy Technologies (ICECET), 9-10 December 2021, Cape Town-South Africa 
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Validation Methods for Energy Time Series Scenarios from Deep Generative Models

Oct 27, 2021
Eike Cramer, Leonardo Rydin Gorjão, Alexander Mitsos, Benjamin Schäfer, Dirk Witthaut, Manuel Dahmen

The design and operation of modern energy systems are heavily influenced by time-dependent and uncertain parameters, e.g., renewable electricity generation, load-demand, and electricity prices. These are typically represented by a set of discrete realizations known as scenarios. A popular scenario generation approach uses deep generative models (DGM) that allow scenario generation without prior assumptions about the data distribution. However, the validation of generated scenarios is difficult, and a comprehensive discussion about appropriate validation methods is currently lacking. To start this discussion, we provide a critical assessment of the currently used validation methods in the energy scenario generation literature. In particular, we assess validation methods based on probability density, auto-correlation, and power spectral density. Furthermore, we propose using the multifractal detrended fluctuation analysis (MFDFA) as an additional validation method for non-trivial features like peaks, bursts, and plateaus. As representative examples, we train generative adversarial networks (GANs), Wasserstein GANs (WGANs), and variational autoencoders (VAEs) on two renewable power generation time series (photovoltaic and wind from Germany in 2013 to 2015) and an intra-day electricity price time series form the European Energy Exchange in 2017 to 2019. We apply the four validation methods to both the historical and the generated data and discuss the interpretation of validation results as well as common mistakes, pitfalls, and limitations of the validation methods. Our assessment shows that no single method sufficiently characterizes a scenario but ideally validation should include multiple methods and be interpreted carefully in the context of scenarios over short time periods.

* 16 pages, 8 figures, 1 table 
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A High GOPs/Slice Time Series Classifier for Portable and Embedded Biomedical Applications

Nov 01, 2018
Hamid Soleimani, Aliasghar, Makhlooghpour, Wilten Nicola, Claudia Clopath, Emmanuel. M. Drakakis

Nowadays a diverse range of physiological data can be captured continuously for various applications in particular wellbeing and healthcare. Such data require efficient methods for classification and analysis. Deep learning algorithms have shown remarkable potential regarding such analyses, however, the use of these algorithms on low-power wearable devices is challenged by resource constraints such as area and power consumption. Most of the available on-chip deep learning processors contain complex and dense hardware architectures in order to achieve the highest possible throughput. Such a trend in hardware design may not be efficient in applications where on-node computation is required and the focus is more on the area and power efficiency as in the case of portable and embedded biomedical devices. This paper presents an efficient time-series classifier capable of automatically detecting effective features and classifying the input signals in real-time. In the proposed classifier, throughput is traded off with hardware complexity and cost using resource sharing techniques. A Convolutional Neural Network (CNN) is employed to extract input features and then a Long-Short-Term-Memory (LSTM) architecture with ternary weight precision classifies the input signals according to the extracted features. Hardware implementation on a Xilinx FPGA confirm that the proposed hardware can accurately classify multiple complex biomedical time series data with low area and power consumption and outperform all previously presented state-of-the-art records. Most notably, our classifier reaches 1.3$\times$ higher GOPs/Slice than similar state of the art FPGA-based accelerators.

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Applications of Universal Source Coding to Statistical Analysis of Time Series

Sep 07, 2008
Boris Ryabko

We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a stationary and ergodic source asymptotically to the Shannon entropy, which, in turn, is the best achievable ratio for lossless data compressors. We consider finite-alphabet and real-valued time series and the following problems: estimation of the limiting probabilities for finite-alphabet time series and estimation of the density for real-valued time series, the on-line prediction, regression, classification (or problems with side information) for both types of the time series and the following problems of hypothesis testing: goodness-of-fit testing, or identity testing, and testing of serial independence. It is important to note that all problems are considered in the framework of classical mathematical statistics and, on the other hand, everyday methods of data compression (or archivers) can be used as a tool for the estimation and testing. It turns out, that quite often the suggested methods and tests are more powerful than known ones when they are applied in practice.

* accepted for publication 
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Two-dimensional cellular automata and the analysis of correlated time series

Jul 08, 2005
Luis O. Rigo Jr., Valmir C. Barbosa

Correlated time series are time series that, by virtue of the underlying process to which they refer, are expected to influence each other strongly. We introduce a novel approach to handle such time series, one that models their interaction as a two-dimensional cellular automaton and therefore allows them to be treated as a single entity. We apply our approach to the problems of filling gaps and predicting values in rainfall time series. Computational results show that the new approach compares favorably to Kalman smoothing and filtering.

* Pattern Recognition Letters 27 (2006), 1353-1360 
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GrowliFlower: An image time series dataset for GROWth analysis of cauLIFLOWER

Apr 01, 2022
Jana Kierdorf, Laura Verena Junker-Frohn, Mike Delaney, Mariele Donoso Olave, Andreas Burkart, Hannah Jaenicke, Onno Muller, Uwe Rascher, Ribana Roscher

This article presents GrowliFlower, a georeferenced, image-based UAV time series dataset of two monitored cauliflower fields of size 0.39 and 0.60 ha acquired in 2020 and 2021. The dataset contains RGB and multispectral orthophotos from which about 14,000 individual plant coordinates are derived and provided. The coordinates enable the dataset users the extraction of complete and incomplete time series of image patches showing individual plants. The dataset contains collected phenotypic traits of 740 plants, including the developmental stage as well as plant and cauliflower size. As the harvestable product is completely covered by leaves, plant IDs and coordinates are provided to extract image pairs of plants pre and post defoliation, to facilitate estimations of cauliflower head size. Moreover, the dataset contains pixel-accurate leaf and plant instance segmentations, as well as stem annotations to address tasks like classification, detection, segmentation, instance segmentation, and similar computer vision tasks. The dataset aims to foster the development and evaluation of machine learning approaches. It specifically focuses on the analysis of growth and development of cauliflower and the derivation of phenotypic traits to foster the development of automation in agriculture. Two baseline results of instance segmentation at plant and leaf level based on the labeled instance segmentation data are presented. The entire data set is publicly available.

* 23 pages, 21 figures, 5 tables 
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Enhancing Transformer Efficiency for Multivariate Time Series Classification

Mar 28, 2022
Yuqing Wang, Yun Zhao, Linda Petzold

Most current multivariate time series (MTS) classification algorithms focus on improving the predictive accuracy. However, for large-scale (either high-dimensional or long-sequential) time series (TS) datasets, there is an additional consideration: to design an efficient network architecture to reduce computational costs such as training time and memory footprint. In this work we propose a methodology based on module-wise pruning and Pareto analysis to investigate the relationship between model efficiency and accuracy, as well as its complexity. Comprehensive experiments on benchmark MTS datasets illustrate the effectiveness of our method.

* ICDM 2022 
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Deep Cellular Recurrent Network for Efficient Analysis of Time-Series Data with Spatial Information

Jan 12, 2021
Lasitha Vidyaratne, Mahbubul Alam, Alexander Glandon, Anna Shabalina, Christopher Tennant, Khan Iftekharuddin

Efficient processing of large-scale time series data is an intricate problem in machine learning. Conventional sensor signal processing pipelines with hand engineered feature extraction often involve huge computational cost with high dimensional data. Deep recurrent neural networks have shown promise in automated feature learning for improved time-series processing. However, generic deep recurrent models grow in scale and depth with increased complexity of the data. This is particularly challenging in presence of high dimensional data with temporal and spatial characteristics. Consequently, this work proposes a novel deep cellular recurrent neural network (DCRNN) architecture to efficiently process complex multi-dimensional time series data with spatial information. The cellular recurrent architecture in the proposed model allows for location-aware synchronous processing of time series data from spatially distributed sensor signal sources. Extensive trainable parameter sharing due to cellularity in the proposed architecture ensures efficiency in the use of recurrent processing units with high-dimensional inputs. This study also investigates the versatility of the proposed DCRNN model for classification of multi-class time series data from different application domains. Consequently, the proposed DCRNN architecture is evaluated using two time-series datasets: a multichannel scalp EEG dataset for seizure detection, and a machine fault detection dataset obtained in-house. The results suggest that the proposed architecture achieves state-of-the-art performance while utilizing substantially less trainable parameters when compared to comparable methods in the literature.

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Analysis of Temporal Difference Learning: Linear System Approach

Apr 26, 2022
Donghwan Lee, Do Wan Kim

The goal of this technical note is to introduce a new finite-time convergence analysis of temporal difference (TD) learning based on stochastic linear system models. TD-learning is a fundamental reinforcement learning (RL) to evaluate a given policy by estimating the corresponding value function for a Markov decision process. While there has been a series of successful works in theoretical analysis of TDlearning, it was not until recently that researchers found some guarantees on its statistical efficiency by developing finite-time error bounds. In this paper, we propose a simple control theoretic finite-time analysis of TD-learning, which exploits linear system models and standard notions in linear system communities. The proposed work provides new simple templets for RL analysis, and additional insights on TD-learning and RL based on ideas in control theory.

* arXiv admin note: text overlap with arXiv:2112.14417 
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