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

Serial-EMD: Fast Empirical Mode Decomposition Method for Multi-dimensional Signals Based on Serialization

Jun 22, 2021
Jin Zhang, Fan Feng, Pere Marti-Puig, Cesar F. Caiafa, Zhe Sun, Feng Duan, Jordi Solé-Casals

Empirical mode decomposition (EMD) has developed into a prominent tool for adaptive, scale-based signal analysis in various fields like robotics, security and biomedical engineering. Since the dramatic increase in amount of data puts forward higher requirements for the capability of real-time signal analysis, it is difficult for existing EMD and its variants to trade off the growth of data dimension and the speed of signal analysis. In order to decompose multi-dimensional signals at a faster speed, we present a novel signal-serialization method (serial-EMD), which concatenates multi-variate or multi-dimensional signals into a one-dimensional signal and uses various one-dimensional EMD algorithms to decompose it. To verify the effects of the proposed method, synthetic multi-variate time series, artificial 2D images with various textures and real-world facial images are tested. Compared with existing multi-EMD algorithms, the decomposition time becomes significantly reduced. In addition, the results of facial recognition with Intrinsic Mode Functions (IMFs) extracted using our method can achieve a higher accuracy than those obtained by existing multi-EMD algorithms, which demonstrates the superior performance of our method in terms of the quality of IMFs. Furthermore, this method can provide a new perspective to optimize the existing EMD algorithms, that is, transforming the structure of the input signal rather than being constrained by developing envelope computation techniques or signal decomposition methods. In summary, the study suggests that the serial-EMD technique is a highly competitive and fast alternative for multi-dimensional signal analysis.

* 19 pages, 17 figures 

An analysis of deep neural networks for predicting trends in time series data

Sep 22, 2020
Kouame Hermann Kouassi, Deshendran Moodley

Recently, a hybrid Deep Neural Network (DNN) algorithm, TreNet was proposed for predicting trends in time series data. While TreNet was shown to have superior performance for trend prediction to other DNN and traditional ML approaches, the validation method used did not take into account the sequential nature of time series data sets and did not deal with model update. In this research we replicated the TreNet experiments on the same data sets using a walk-forward validation method and tested our optimal model over multiple independent runs to evaluate model stability. We compared the performance of the hybrid TreNet algorithm, on four data sets to vanilla DNN algorithms that take in point data, and also to traditional ML algorithms. We found that in general TreNet still performs better than the vanilla DNN models, but not on all data sets as reported in the original TreNet study. This study highlights the importance of using an appropriate validation method and evaluating model stability for evaluating and developing machine learning models for trend prediction in time series data.


A CNN based method for Sub-pixel Urban Land Cover Classification using Landsat-5 TM and Resourcesat-1 LISS-IV Imagery

Dec 16, 2021
Krishna Kumar Perikamana, Krishnachandran Balakrishnan, Pratyush Tripathy

Time series data of urban land cover is of great utility in analyzing urban growth patterns, changes in distribution of impervious surface and vegetation and resulting impacts on urban micro climate. While Landsat data is ideal for such analysis due to the long time series of free imagery, traditional per-pixel hard classification fails to yield full potential of the Landsat data. This paper proposes a sub-pixel classification method that leverages the temporal overlap of Landsat-5 TM and Resourcesat-1 LISS-IV sensors. We train a convolutional neural network to predict fractional land cover maps from 30m Landsat-5 TM data. The reference land cover fractions are estimated from a hard-classified 5.8m LISS-IV image for Bengaluru from 2011. Further, we demonstrate the generalizability and superior performance of the proposed model using data for Mumbai from 2009 and comparing it to the results obtained using a Random Forest classifier. For both Bengaluru (2011) and Mumbai (2009) data, Mean Absolute Percentage Error of our CNN model is in the range of 7.2 to 11.3 for both built-up and vegetation fraction prediction at the 30m cell level. Unlike most recent studies where validation is conducted using data for a limited spatial extent, our model has been trained and validated using data for the complete spatial extent of two mega cities for two different time periods. Hence it can reliably generate 30m built-up and vegetation fraction maps from Landsat-5 TM time series data to analyze long term urban growth patterns.

* 29 pages, 14 figures (including appendix), 8 tables (including appendix) 

Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series

Aug 10, 2021
Annie E. Paine, Vincent E. Elfving, Oleksandr Kyriienko

We propose a quantum algorithm for sampling from a solution of stochastic differential equations (SDEs). Using differentiable quantum circuits (DQCs) with a feature map encoding of latent variables, we represent the quantile function for an underlying probability distribution and extract samples as DQC expectation values. Using quantile mechanics we propagate the system in time, thereby allowing for time-series generation. We test the method by simulating the Ornstein-Uhlenbeck process and sampling at times different from the initial point, as required in financial analysis and dataset augmentation. Additionally, we analyse continuous quantum generative adversarial networks (qGANs), and show that they represent quantile functions with a modified (reordered) shape that impedes their efficient time-propagation. Our results shed light on the connection between quantum quantile mechanics (QQM) and qGANs for SDE-based distributions, and point the importance of differential constraints for model training, analogously with the recent success of physics informed neural networks.

* v2, minor update 

Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series

Apr 21, 2021
Sylvain Calinon

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.

* Bouguila, N. and Fan, W. (eds). Mixture Models and Applications, pp. 39-57. Springer, 2019 
* 20 pages, 7 figures 

Change of human mobility during COVID-19: A United States case study

Sep 18, 2021
Justin Elarde, Joon-Seok Kim, Hamdi Kavak, Andreas Züfle, Taylor Anderson

With the onset of COVID-19 and the resulting shelter in place guidelines combined with remote working practices, human mobility in 2020 has been dramatically impacted. Existing studies typically examine whether mobility in specific localities increases or decreases at specific points in time and relate these changes to certain pandemic and policy events. In this paper, we study mobility change in the US through a five-step process using mobility footprint data. (Step 1) Propose the delta Time Spent in Public Places (Delta-TSPP) as a measure to quantify daily changes in mobility for each US county from 2019-2020. (Step 2) Conduct Principal Component Analysis (PCA) to reduce the Delta-TSPP time series of each county to lower-dimensional latent components of change in mobility. (Step 3) Conduct clustering analysis to find counties that exhibit similar latent components. (Step 4) Investigate local and global spatial autocorrelation for each component. (Step 5) Conduct correlation analysis to investigate how various population characteristics and behavior correlate with mobility patterns. Results show that by describing each county as a linear combination of the three latent components, we can explain 59% of the variation in mobility trends across all US counties. Specifically, change in mobility in 2020 for US counties can be explained as a combination of three latent components: 1) long-term reduction in mobility, 2) no change in mobility, and 3) short-term reduction in mobility. We observe significant correlations between the three latent components of mobility change and various population characteristics, including political leaning, population, COVID-19 cases and deaths, and unemployment. We find that our analysis provides a comprehensive understanding of mobility change in response to the COVID-19 pandemic.

* Current under review at PLOS One 

Unsupervised Discovery of Temporal Structure in Noisy Data with Dynamical Components Analysis

May 23, 2019
David G. Clark, Jesse A. Livezey, Kristofer E. Bouchard

Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than meaningful dynamics when applied to time series data. At the same time, many successful unsupervised learning methods for temporal, sequential and spatial data extract features which are predictive of their surrounding context. Combining these approaches, we introduce Dynamical Components Analysis (DCA), a linear dimensionality reduction method which discovers a subspace of high-dimensional time series data with maximal predictive information, defined as the mutual information between the past and future. We test DCA on synthetic examples and demonstrate its superior ability to extract dynamical structure compared to commonly used linear methods. We also apply DCA to several real-world datasets, showing that the dimensions extracted by DCA are more useful than those extracted by other methods for predicting future states and decoding auxiliary variables. Overall, DCA robustly extracts dynamical structure in noisy, high-dimensional data while retaining the computational efficiency and geometric interpretability of linear dimensionality reduction methods.

* 15 pages, 4 figures 

Recursive Sparse Point Process Regression with Application to Spectrotemporal Receptive Field Plasticity Analysis

Jul 16, 2015
Alireza Sheikhattar, Jonathan B. Fritz, Shihab A. Shamma, Behtash Babadi

We consider the problem of estimating the sparse time-varying parameter vectors of a point process model in an online fashion, where the observations and inputs respectively consist of binary and continuous time series. We construct a novel objective function by incorporating a forgetting factor mechanism into the point process log-likelihood to enforce adaptivity and employ $\ell_1$-regularization to capture the sparsity. We provide a rigorous analysis of the maximizers of the objective function, which extends the guarantees of compressed sensing to our setting. We construct two recursive filters for online estimation of the parameter vectors based on proximal optimization techniques, as well as a novel filter for recursive computation of statistical confidence regions. Simulation studies reveal that our algorithms outperform several existing point process filters in terms of trackability, goodness-of-fit and mean square error. We finally apply our filtering algorithms to experimentally recorded spiking data from the ferret primary auditory cortex during attentive behavior in a click rate discrimination task. Our analysis provides new insights into the time-course of the spectrotemporal receptive field plasticity of the auditory neurons.


Heterogeneous Relational Kernel Learning

Aug 24, 2019
Andre T. Nguyen, Edward Raff

Recent work has developed Bayesian methods for the automatic statistical analysis and description of single time series as well as of homogeneous sets of time series data. We extend prior work to create an interpretable kernel embedding for heterogeneous time series. Our method adds practically no computational cost compared to prior results by leveraging previously discarded intermediate results. We show the practical utility of our method by leveraging the learned embeddings for clustering, pattern discovery, and anomaly detection. These applications are beyond the ability of prior relational kernel learning approaches.

* MileTS '19: 5th KDD Workshop on Mining and Learning from Time Series