Multidimensional Time Series Analysis Research Articles

SINGULAR SPECTRAL ANALYSIS OF TEMPERATURE MULTIDIMENSIONAL TIME SERIES

In the paper the algorithm of singular structural analysis and forecasting of a multidimensional series by the MSSA method is used. The program was developed, in which the steps of the method for the selection of singular decomposition components were implemented, the analysis and forecast of real time series was carried out. Singular spectrum analysis (SSA) is increasingly used in the study of time series. Unlike other methods of statistical research of time series, this method is used to study the structure, selection of individual components and forecast of both stationary and non-stationary time series. It does not require an analytical model of the series. In fact, this approach is based on the method of principal components. It is based on the transformation of a series into a matrix and its singular decomposition. After identifying the components of the singular decomposition, their grouping takes place, which leads to the decomposition of the original series into additive components, such as trend, oscillations (periodics), and noise. The SSA method allows you to continue the structure of the time series, thus building a forecast (continuation). An important direction of the development of the SSA method as a method of time series analysis is its generalization for the analysis of multidimensional time series. The method is known as MSSA (Multi-Channel SSA) or E-EOFs (Extended Empirical Orthogonal Functions). In this case, the expected result is the simultaneous decomposition of several series into interpreted components. However, a sufficiently complete theory for MSSA does not exist.

Predicting Student Performance in Online Learning: A Multidimensional Time-Series Data Analysis Approach

As an emerging teaching method, online learning is becoming increasingly popular among learners. However, one of the major drawbacks of this learning style is the lack of effective communication and feedback, which can lead to a higher risk of students failing or dropping out. In response to this challenge, this paper proposes a student performance prediction model based on multidimensional time-series data analysis by considering multidimensional data such as students’ learning behaviors, assessment scores, and demographic information, which is able to extract the characteristics of students’ learning behaviors and capture the connection between multiple characteristics to better explore the impact of multiple factors on students’ performance. The model proposed in this paper helps teachers to individualize education for students at different levels of proficiency and identifies at-risk students as early as possible to help teachers intervene in a timely manner. In experiments on the Open University Learning Analytics Dataset (OULAD), the model achieved 74% accuracy and 73% F1 scores in a four-category prediction task and was able to achieve 99.08% accuracy and 99.08% F1 scores in an early risk prediction task. Compared with the benchmark model, both the multi-classification prediction ability and the early prediction ability, the model in this paper has a better performance.

A Dam Safety State Prediction and Analysis Method Based on EMD-SSA-LSTM

The safety monitoring information of the dam is an indicator reflecting the operational status of the dam. It is a crucial source for analyzing and assessing the safety state of reservoir dams, possessing strong real-time capabilities to detect anomalies in the dam at the earliest possible time. When using neural networks for predicting and warning dam safety monitoring data, there are issues such as redundant model parameters, difficulty in tuning, and long computation times. This study addresses real-time dam safety warning issues by first employing the Empirical Mode Decomposition (EMD) method to decompose the effective time-dependent factors and construct a dam in a service state analysis model; it also establishes a multi-dimensional time series analysis equation for dam seepage monitoring. Simultaneously, by combining the Sparrow Optimization Algorithm to optimize the LSTM neural network computation process, it reduces the complexity of model parameter selection. The method is compared to other approaches such as RNN, GRU, BP neural networks, and multivariate linear regression, demonstrating high practicality. It can serve as a valuable reference for reservoir dam state prediction and engineering operation management.

Assessment of the state of a landslide slope based on the analysis of multidimensional time series of geotechnical monitoring data

Assessment of the state of a landslide slope based on the analysis of multidimensional time series of geotechnical monitoring data

Research on the model of martial arts classroom ideological practice for college students based on time-series data analysis

Abstract This study employs multidimensional time-series data analysis to explore college students’ learning behaviors in martial arts civics classes. By analyzing learner interactions in three categories and time-series data from educational videos, we assess student engagement in mastery of knowledge and quantify learning outcomes for a detailed and accurate evaluation of their learning status. Our team has crafted a targeted learning path network that enhances offline teaching approaches by leveraging insights from online learning trends and in-class performance in martial arts civics education. The results show that the most popular and highest-rated course is Military Poetry (4.7 points) based on the analysis of recall data, and more elements of military poetry should be included in the design of teaching content. Student A64 had the lowest online note quality rating of 0.02, which can be hypothesized to indicate that the student’s attitude was not active enough. Online and offline Mixed Martial Arts classroom Civics education had a mean score of 46.856, with a p-value of 0, and there was a significant difference between traditional offline education and online mixed martial arts classroom Civics education. Most of the students’ personal patriotism, professional knowledge, and abilities were significantly enhanced after participating in online and offline mixed martial arts classroom Civic and Political Education.

Granger causality based on vector time series and quaternion algebra with possible applications to molecular dynamics data analysis.

Causal analysis plays a significant role in physics, chemistry, and biology. Dynamics of complex (bio)molecular and nanosystems, from the microscopic to the macroscopic scale, are characterized by time-dependent vectors such as positions, forces, momenta, angular momenta, or torques. Identification and analysis of causal relationships between these time-dependent signals is an important problem in the multidimensional time-series analysis and is of great practical importance in describing the properties of such dynamical systems, and to understanding their functionality. For linear stochastic systems characterized by multidimensional scalar signals, Granger proposed a simple procedure to detect causal relationships, called Granger causality. In this study we extended this formalism to vector signals representing physical vector quantities. For this purpose, we used quaternion algebra, where vector signals are treated as time-dependent quaternions. The developed analytical model is based on the autoregressive formalism. This formalism (Q-MVAR) and its numerical implementation were validated using two simple dynamic models: a rigid body model represented by a benzenelike molecular fragment, interacting with a short-range harmonic potential with a wall, as well as a system of three model atomic balls moving inside a soft spherical surface and interacting with long range electrostatic forces. Although the motivation to these studies was the analysis of classical motions in complex (bio)molecular systems, described with a mechanical model and based on molecular dynamics (MD) simulations, in particular coarse-grained ones, it should be noted that the developed extended formalism can be applied to any system composed of many rigid elements that interact with arbitrary potentials and are characterized by complex internal motions. A description of the detailed procedure for calculating causality measures is provided in the Appendicesof the Supplemental Material. This formalism and the prototype of its numerical implementation can be further developed and applied in many different fields of physical, natural, and engineering sciences.

Abstract 6674: Multi-dimensional time-series analysis to reveal pharmacodynamic changes induced by immunotherapy

Abstract Background: Immune checkpoint inhibitors currently represent the most promising cancer therapeutics to produce durable responses. Many studies have highlighted checkpoint inhibitors' targets for future monotherapies or combination therapies. However, due to the complexity of tumor microenvironment, different types of cells exhibit different reaction time and order. To understand the MoA of immune checkpoint inhibitors in cell or animal models, time-series analysis will help select proper PD sampling time, as well as administration time & order in combination therapy. However, such analysis has limited application in syngeneic tumor models in the early stage of drug treatment due to the small tumor volumes. Methods and Results: In this study, we combined NanoString technology and flow cytometry in an in-vivo efficacy study to explore the therapeutic response mechanism in mouse breast cancer EMT-6 model by the combinational treatment with anti-PD1 and an undisclosed compound A. Through time-course sampling of tumor tissues of EMT-6 xenograft tumors in the early stage of treatment, we found that anti-PD1 could enhance antigen-presentation and T cell priming as a single agent, and this effect could be enhanced by combination with compound A. In addition, we found the change of antigen-presentation induced by anti-PD1 occurs at RNA level, but not at protein level by flow cytometry analysis, which might imply to employ different time points to combine with RNA-targeted or protein-targeted drugs on T cell priming. Summary: We have developed a time-series analysis combining in vivo efficacy study and NanoString technology with flow cytometry, to evaluate the dynamic changes of TME after immune checkpoint blocker treatment. This can be a powerful method to reveal time-dependent drug-induced pharmacodynamic changes, and help us to select the best time course for combination therapy. Citation Format: Jingjing Wang, Panpan Wang, Wenli Zhang, Qiyao Zhang, Qingyang Gu, Qunsheng Ji. Multi-dimensional time-series analysis to reveal pharmacodynamic changes induced by immunotherapy [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 6674.

A machine-learning phase classification scheme for anomaly detection in signals with periodic characteristics

In this paper, we propose a novel machine-learning method for anomaly detection applicable to data with periodic characteristics where randomly varying period lengths are explicitly allowed. A multi-dimensional time series analysis is conducted by training a data-adapted classifier consisting of deep convolutional neural networks performing phase classification. The entire algorithm including data pre-processing, period detection, segmentation, and even dynamic adjustment of the neural networks is implemented for fully automatic execution. The proposed method is evaluated on three example datasets from the areas of cardiology, intrusion detection, and signal processing, presenting reasonable performance.

Analysis and visualization of multidimensional time series: Particulate matter (PM10) from São Carlos-SP (Brazil)

Data visualization techniques have been successfully used in a time series context for many years. In this work, a web-based data visualization system was developed to support the evolutionary analysis of atmospheric particulate matter (PM10) behavior, collected in the central region of São Carlos, São Paulo State, Brazil. The samples were acquired following two patterns: daily in the first stage and on alternate days in the second stage. Each measurement covered a period of 23 h and 30 min, using a large volume sampler (high-volume). To interrogate the acquired data, an interactive visualization tool was developed in JavaScript and D3 library. The tool is portable and can be used in all modern web browsers, not requiring any software installation. The values obtained from São Carlos’ PM10 monitoring campaign from 2014 to 2017 clearly showed a decrease of PM10 in the city atmosphere, in comparison with past data from the 1997 to 2005 campaign. This decreasing trend in PM10 concentrations could be due to an increase in the severity of law n° 997 of 05/31/1976 and decree 54.487 of 06/26/2009, which charges the anthropogenic agents with air pollution control.

Multi-sensors based condition monitoring of rotary machines: An approach of multidimensional time-series analysis

Multi-sensors configuration has been popular in the field of condition monitoring of rotary machines. This paper proposes a novel multi-sensors based monitoring strategy that can be used to detect changes of machine running status during continuous operations. The base of the method is automatic change detection which is implemented via combining the multidimensional time-series analysis (MultiDTSA) with an extended autoregressive-integrated-moving-average (ARIMA) regression process. The ARIMA regression process is to quantify temporal anomalies for each deployed sensor, such that decision fusion can be allowed from all sensors under the architecture of MultiDTSA. In particular, a new fusion strategy is developed to consider differentiating contributes among multi-sensors for decision making. The final result is obtained by testing a null hypothesis. The proposed method has been evaluated based on an experimental setup: comparison with five representative techniques shows its promising results.

Dynamic Mode Decomposition for Multi-dimensional Time Series Analysis

Dynamic Mode Decomposition for Multi-dimensional Time Series Analysis

Key-frame selection for video summarization: an approach of multidimensional time series analysis

This paper presents a novel method of key-frame selection for video summarization based on multidimensional time series analysis. In the proposed scheme, the given video is first segmented into a set of sequential clips containing a number of similar frames. Then the key frames are selected by a clustering procedure as the frames closest to the cluster centres in each resulting video clip. The proposed algorithm is implemented experimentally on a wide range of testing data, and compared with state-of-the-art approaches in the literature, which demonstrates excellent performance and outperforms existing methods on frame selection in terms of fidelity-based metric and subjective perception.

Subsidence at Cerro Prieto Geothermal Field and postseismic slip along the Indiviso fault from 2011 to 2016 RADARSAT‐2 DInSAR time series analysis

AbstractWe present RADARSAT‐2 Differential Interferometric Synthetic Aperture Radar (DInSAR) observations of deformation due to fluid extraction at the Cerro Prieto Geothermal Field (CPGF) and afterslip on the 2010 M7.2 El Mayor‐Cucapah (EMC) earthquake rupture during 2011–2016. Advanced multidimensional time series analysis reveals subsidence at the CPGF with the maximum rate greater than 100 mm/yr accompanied by horizontal motion (radial contraction) at a rate greater than 30 mm/yr. During the same time period, more than 30 mm of surface creep occurred on the Indiviso fault ruptured by the EMC earthquake. We performed inversions of DInSAR data to estimate the rate of volume changes at depth due to the geothermal production at the CPGF and the distribution of afterslip on the Indiviso fault. The maximum coseismic slip due to the EMC earthquake correlates with the Coulomb stress changes on the Indiviso fault due to fluid extraction at the CPGF. Afterslip occurs on the periphery of maximum coseismic slip areas. Time series analysis indicates that afterslip still occurs 6 years after the earthquake.

Multidimensional Time Series Analysis of Financial Markets Based on the Complex Network Approach

In this study, a modeling method to analyze multidimensional time series based on complex networks is proposed. The rate of return sequence of the closing price and the trading volume fluctuation sequence of the Shanghai Composite Index, the Shenzhen Component Index, the S & P 500 index, and the Dow Jones Industrial Average are analyzed. The two-dimensional time series is transformed into a complex network. We analyze the spatial distribution characteristics of the network to determine the relationship between volume and price. It is found that the interaction of stock return and volume in China’ stock market is more obvious than that in the American market.

A Proposal for Classification of Multisensor Time Series Data based on Time Delay Embedding

Abstract Multisensor time series data is common in many ap- plications of process industry, medical and health care, biometrics etc.Analysis of multisensor time series data requires analysis of multidimensional time series(MTS) which is challenging as they constitute a huge volume of data of dynamic nature. Traditional machine learning algorithms for classification and clustering developed for static data can not be applied directly to MTS data. Various techniques have been developed to represent MTS data in a suitable manner for analysis by popular machine learning algorithms. Though a plethora of different approaches have been developed so far, 1NN classifier based on dynamic time warping (DTW) has been found to be the most popular due to its simplicity. In this work, an approach for time series classification is proposed based on multidimensional delay vector representation of time series. Multivariate time series is considered here as a group of single time series and each time series is processed separately to be represented by a multidimensional delay vector (MDV). A simple simulation experiment with online handwritten signature data has been done with a similarity measure based on the MDV representation and classification performance is compared with DTW based classifier. The simulation results show that classification accuracy of the proposed approach is satisfactory while computational cost is lower than DTW method.

Beyond the Modernization Theory: So-cio-Demographic Changes, Economic Structure and Forest Transition in a Multi-Dimensional Time-Series Analysis for Italy

In the light of the modernization theory, the present paper proposes an empirical assessment of the population-economy-environment nexus in Italy by investigating the historical trends (1862- 2009) in 58 variables describing five themes (environment, demography, education, trade, agriculture). Socioeconomic variables representing changes in population structure and demographic dynamics compared with indicators of forest expansion allowed verifying the temporal coherence between demographic and forest transitions at the country scale. The study develops an exploratory data analysis framework based on principal component analysis, hierarchical and non-hiera- rchical clustering and identifies four homogeneous time intervals (1862-1899, 1900-1930, 1931- 1970, 1971-2009) in socioeconomic and environmental attributes. Different trends (positive linear, negative linear and non-linear) in the studied variables were identified through hierarchical clustering.

Multidimensional time-series analysis of ground deformation from multiple InSAR data sets applied to Virunga Volcanic Province

SUMMARY A novel, multidimensional small baseline subset (MSBAS) methodology is presented for integration of multiple interferometric synthetic aperture radar (InSAR) data sets for computation of 2- or 3-D time-series of deformation. The proposed approach allows the combination of all possible air-borne and space-borne SAR data acquired with different acquisition parameters, temporal and spatial sampling and resolution, wave-band and polarization. The produced time-series have improved temporal resolution and can be enhanced by applying either regularization or temporal filtering to remove high-frequency noise. We apply this methodology to map 2003–2010 ground deformation of the Virunga Volcanic Province (VVP), North Kivu, Democratic Republic of Congo. The horizontal and vertical time-series of ground displacement clearly identify lava compaction areas, long-term deformation of Mt Nyamuragira and 2004, 2006 and 2010 pre- and coeruptive deformation. Providing that enough SAR data is available, the method opens new opportunities for detecting ground motion in the VVP and elsewhere.

Quality Monitoring and Prognostic of Electronics Using Multidimensional Time Series Method

This paper presents a quality monitoring and prognostic method to evaluating quality of electronics through monitoring degradation path. Electronics multiple performance parameter degradation data are treated as multidimensional time series and described using multidimensional time series model to take into account implements of stochastic nature of environmental variables and to predict long-term trend of performance degradation. A degradation test is processed for certain electronics and three kinds of performance parameters degradation data are monitored for prognostics. A comparison between the predicted degradation path using multidimensional time series analysis, the predicted degradation path using one-dimensional time series analysis and the real degradation path of the electronics is processed and the results show that the degradation path prediction using the suggested method is more effective than one-dimensional time series analysis.

An algorithm for analysis of multidimensional time series with smoothly varying regularities and its application

A new approach to revealing regularities in nonstationary k-valued multidimensional time series is proposed. It allows one to discover regularities that are subject to gentle structural changes with time. A measure of similarity between regularities is proposed to describe such changes, and its application in the form of weight in the graph of regularities is discussed. The discovered regularities can be used to predict the subsequent elements in multidimensional time series, to analyze the phenomenon described by this series, and to model the phenomenon. This allows one to use the proposed algorithm in a wide variety of problems concerning prediction of time series and for examining and describing the processes that can be represented by multidimensional time series. Means for direct practical application of the proposed methods of the analysis and prediction of time series are described, and the use of these methods for short-term prediction of model series and a real-life multidimensional time series consisting of the stock prices of companies operating in similar fields is discussed.

Common singular spectrum analysis of several time series

Singular spectrum analysis (SSA) is a non-parametric time series modelling technique where an observed time series is unfolded into the column vectors of a Hankel structured matrix, known as a trajectory matrix. For noise-free signals the column vectors of the trajectory matrix lie on a single R-flat. Singular value decomposition (SVD) can be used to find the orthonormal base vectors of the linear subspace parallel to this R-flat. SSA can essentially handle functions that are governed by a linear recurrent formula (LRF) and include the broad class of functions that was proposed by Buchstaber [1994. Time series analysis and Grassmannians. Amer. Math. Soc. Transl. 162 (2), 1–17]. SSA is useful to model time series with complex cyclical patterns that increase over time. Various methods have been studied to extend SSA for application to several time series, see Golyandina et al. [2003. Variants of the Caterpillar SSA-method for analysis of multidimensional time series (in Russian) 〈hhttp://www.gistatgroup.com/cat/i〉]. Prior to that Von Storch and Zwiers (1999) and Allen and Robertson (1996) (see Ghil et al. [2002. Advanced spectral methods for climatic time series. Rev. Geophys. 40 (1), 3.1–3.41]) used multi-channel SSA (M-SSA), to apply SSA to “grand” block matrices. Our approach is different from all of these by using the common principal components approaches introduced by Flury [1988. Common Principal Components and Related Multivariate Models. Wiley, New York]. In this paper SSA is extended to several time series which are similar in some respects, like cointegrated, i.e. sharing a common R-flat. By using the common principal component (CPC) approach of Flury [1988. Common Principal Components and Related Multivariate Models. Wiley, New York] the SSA method is extended to common singular spectrum analysis (CSSA) where common features of several time series can be studied. CSSA decomposes the different original time series into the sum of a common small number of components which are related to common trend and oscillatory components and noise. The determination of the most likely dimension of the supporting linear subspace is studied using a heuristic approach and a hierarchical selection procedure.