Multivariate Singular Spectrum Analysis Research Articles

Multivariate Singular Spectrum Analysis by Robust Diagonalwise Low-Rank Approximation

Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous conclusions. In this paper a new MSSA method is proposed, named RObust Diagonalwise Estimation of SSA (RODESSA), which is robust against the presence of cellwise and casewise outliers. In particular, the decomposition step of MSSA is replaced by a new robust low-rank approximation of the trajectory matrix that takes its special structure into account. A fast algorithm is constructed, and it is proved that each iteration step decreases the objective function. In order to visualize different types of outliers, a new graphical display is introduced, called an enhanced time series plot. An extensive Monte Carlo simulation study is performed to compare RODESSA with competing approaches in the literature. A real data example about temperature analysis in passenger railway vehicles demonstrates the practical utility of the proposed approach.

MULTIVARIATE SINGULAR SPECTRUM ANALYSIS MODEL IN FORECASTING RED CHILI AND CAYENNE PEPPER PRICES

North Sumatra is one of the provinces that contributes the most prominent agricultural commodities of red chilies and cayenne peppers in Indonesia. This study aims to determine the outcomes of price forecasts for cayenne and red chilies in the province of North Sumatra. The method used is multivariate singular spectrum analysis. Results were grouped into six groups based on 12 eigenvectors with a forecast length of 9 monthly periods. Further, the level of accuracy was obtained from MAPE for each variable, with the highest MAPE being 30% for the curly red chili, 27.55% for the big red chili, and the lowest at 23.44% for mixed cayenne pepper. So, the price forecast for red chilies and cayenne peppers in North Sumatra Province for October 2023 to June 2024 using the Multivariate Singular Spectrum Analysis model is included in the forecast category with reasonable capabilities.

Extraction of atmospheric corrosion monitoring sensor signals using MSSA and corrosion progress prediction with an LSTM model

The sensitivity of corrosion signals to temperature fluctuations often presents significant challenges for signals acquired from corrosion sensors. The main objective of this study is to assess these signals collected by the atmospheric corrosion monitoring sensor based on strain measurement through the application of multivariate singular spectrum analysis (MSSA) for extracting corrosion signal data. The study results demonstrate that MSSA has consistently exhibited exceptional performance in isolating corrosion signals, particularly in scenarios where they are affected by inherent noise resulting from abrupt temperature changes, corrosion products and residual stress. Moreover, the corrosion signals extracted via MSSA were harnessed to create a long short-term memory (LSTM) model, with the aim of predicting future corrosion processes. The results of this study emphasize the effectiveness and reliability of the LSTM model in forecasting corrosion processes. This study holds a crucial role in the management of corrosion processes in materials exposed to atmospheric conditions, ensuring both structural integrity and industrial safety.

Crack detection in low carbon steel using Rotating Uniform Eddy Current probe and noise signal filtering based on Multivariate Singular Spectrum Analysis

Crack detection in low carbon steel using Rotating Uniform Eddy Current probe and noise signal filtering based on Multivariate Singular Spectrum Analysis

Non-contact human respiratory rate measurement based on two-level fusions of video and FMCW radar information

In this paper, we propose a robust respiratory rate (RR) measurement method using a two-level fusion of video and FMCW (frequency modulated continuous wave) radar information. Specifically, the video pixel displacement signals and the radar phase variation signals are extracted independently in shoulders and chest regions, which are then denoised by the serial-CEEMDAN (SCEEMDAN) method to obtain the corresponding single modal RR values. Next, at the feature level, the multivariate singular spectrum analysis (MSSA) is employed to extract the shared respiratory components in the video and radar modalities. Finally, at the decision level, we calculate the target RR value based on a signal-to-noise ratio (SNR) weighting of all single-modality and MSSA results. The proposed two-level fusion method is evaluated on a self-collected dataset, which includes 15 healthy subjects acting five challenging activities. The experimental results show that the proposed fusion method significantly outperform that of the single modality.

New dipole instabilities in spherical stellar systems

ABSTRACT Spherical stellar systems have weakly damped response modes. The dipole modes are seiche modes. The quadrupole are zero pattern-speed prolate modes, the stable precursors to the radial orbit instability (ROI). We demonstrate that small wiggles in the distribution function (DF) can destabilize the dipole modes and describe the newly identified instabilities in NFW-like dark-matter (DM) haloes and other power-law spherical systems. The modes were identified in N-body simulations using multivariate singular spectrum analysis and corroborated using linear-response theory. The new mode peaks inside the half-mass radius but has a pattern speed typical of an outer-halo orbit. As it grows, the radial angle of the eccentric orbits that make up the mode correlates and loses angular momentum by a resonant couple to outer-halo orbits. This leads to an unsteady pattern with a density enhancement that swings from one side of the halo to another along a diameter, like the orbits that comprise the instability. In this way, the dipole mode is similar to the ROI. Since the DF found in Nature is unlikely to be smooth and isotropic with df(E)/dE < 0 necessary for Antonov stability, these modes may be ubiquitous albeit slowly growing. Haloes that are less extended than NFW, such as the Hernquist model, tend to be stable to this dipole instability. We present the critical stability exponents for one- and two-power models. These different critical outer power-law exponents illustrate that the gravitational coupling between the inner and outer DM halo depends on the global shape of density profile.

Multivariate Spectral Analysis and Hypothesis Testing-Based Robust Attack Detection for Multiarea Frequency Control

Frequency control is one of the critical systems responsible for maintaining grid stability, making it a vulnerable and attractive choice for cyber-attacks. This article presents a multivariate singular spectrum analysis (MSSA) for extracting the system’s dynamics under normal operation and proposes a projection-based distance tracking and hypothesis testing method to detect multiarea load frequency control (MA-LFC) attacks. The proposed methodology is robust, adaptive, and computationally efficient, especially, when system and measurement noises are considered. The three main features of the proposed method are that: 1) it uses standard SCADA data and does not require attack data; 2) it can be integrated with the existing grid control system with minimal hardware; and 3) it is independent of system configuration and upgrades. The attack detection algorithm can successfully detect different types of false data injection attacks (FDIAs), including stealth attacks on multiple sensors. The algorithm is tested on an IEEE 39-bus New England test system, 300 bus test system, and 1888 bus RTE system. The attack detection algorithm was found to be reliable, fast, robust, and scalable under noisy measurements compared to the existing methods.

Time-series image denoising of pressure-sensitive paint data by projected multivariate singular spectrum analysis

Time-series data, such as unsteady pressure-sensitive paint (PSP) measurement data, may contain a significant amount of random noise. Thus, in this study, we investigated a noise-reduction method that combines multivariate singular spectrum analysis (MSSA) with low-dimensional data representation. MSSA is a state-space reconstruction technique that utilizes time-delay embedding, and the low-dimensional representation is achieved by projecting data onto the singular value decomposition (SVD) basis. The noise-reduction performance of the proposed method for unsteady PSP data, i.e., the projected MSSA, is compared with that of the truncated SVD method, one of the most employed noise-reduction methods. The result shows that the projected MSSA exhibits better performance in reducing random noise than the truncated SVD method. Additionally, in contrast to that of the truncated SVD method, the performance of the projected MSSA is less sensitive to the truncation rank. The projected MSSA achieves denoising effectively by extracting smooth trajectories in a state space from noisy input data. Expectedly, the projected MSSA will be effective for reducing random noise in not only PSP measurement data, but also various high-dimensional time-series data.Graphic abstract

Multiscale Domain Gradient Boosting Models for the Automated Recognition of Imagined Vowels Using Multichannel EEG Signals

This letter proposes the multiscale domain gradient boosting-based approach for the automated recognition of imagined vowels using the multichannel electroencephalogram (MCEEG) signals. The multiscale analysis of the MCEEG signals is performed using multivariate automatic singular spectrum analysis and multivariate fast and adaptive empirical mode decomposition methods. The features such as bubble entropy, energy, slope domain entropy, sample entropy, and L1-norm are evaluated from the multiscale domain modes of the MCEEG signals. The extreme gradient boosting and light gradient boosting machine models are employed for imagined vowel recognition task as //a// versus //e// versus //i// versus //o// versus //u// using the multiscale domain features of the MCEEG signals. A publicly available MCEEG database has been used to test the performance of the proposed approach. The results demonstrate that the proposed approach has achieved an overall accuracy of 51.47%, which is higher as compared to other imagined vowel recognition methods using the same database comprising the MCEEG signals.

Peramalan Harga Saham Serentak Menggunakan Model Multivariate Singular Spectrum Analysis

Stock price fluctuations in the stock market are widely influenced by financial environment changes in both micro and macro that are usually unpredictable and can not be controlled by stock players. On the other side, stock price information is very essential and much needed for both buyers and traders. Stock price forecasting is one of the analytical techniques to obtain stock price prediction based on the previous historical stock prices. The open and close prices are important information in stock trading. The opening price can influence the movement towards the closing price, and the closing price becomes important for the next day's opening price. In technical analysis, the relationship between the two stock prices can be parametric or non-parametric. This study discusses the stock price prediction or forecasting through the non-parametric approach using a multivariate singular spectrum analysis method with the consideration that open and close prices are simultaneously working in the same system and time. Performance evaluation using Mean Absolute Percentage Error shows that the multivariate singular spectrum analysis method can produce predicted open and close prices with an error rate of 3.18% and 3.21%, respectively. Hence, this method can be used as an alternative for stock price forecasting simultaneously.

On Multivariate Singular Spectrum Analysis and Its Variants

We introduce and analyze a simpler, practically useful variant of multivariate singular spectrum analysis (mSSA), a known time series method to impute (or de-noise) and forecast a multivariate time series. Towards this, we introduce a spatio-temporal factor model to analyze mSSA. This model includes the usual components used to model dynamics in time series analysis, such as trends (low order polynomials), seasonality (finite sum of harmonics), and linear time-invariant systems. We establish that given N time series and T observations per time series, the in-sample prediction error for both imputation and forecasting under mSSA scales as 1/√ min(N, T)T. This is an improvement over: (i) the 1/√T error scaling of SSA, which is the restriction of mSSA to univariate time series; (ii) the 1/min(N, T) error scaling for Temporal Regularized Matrix Factorized (TRMF), a matrix factorization based method for time series prediction. That is, mSSA exploits both the 'temporal' and 'spatial' structure in a multivariate time series. Our experimental results using various benchmark datasets confirm the characteristics of the spatio-temporal factor model and our theoretical findings---our variant of mSSA empirically performs as well or better compared to neural network based time series methods, LSTM and DeepAR.

‘Modelling’ UK tourism demand using fashion retail sales

The United Kingdom (UK) is a world-renowned fashion hub where the economic importance of the tourism sector was recording continuous growth prior to the pandemic. Interestingly, tourism shopping is widely experienced yet seldom discussed from a tourism demand forecasting context. Driven by the potential relevance of tourism shopping and hoping to motivate increased collaboration between the tourism and fashion industries, we analyse whether fashion retail sales can be a leading indicator for inbound tourism demand in the UK. Using the Multivariate Singular Spectrum Analysis leading indicator algorithm, we forecast UK tourism demand and compare the results with six benchmark forecasting models. We find statistically significant evidence for the existence of cross-sector relations between the UK's fashion and tourism industries.

Long-term traffic flow prediction using multivariate SSA forecasting in SDN based networks

Accurate and real-time traffic flow forecasting plays an important role in optimizing traffic routing enabling adaptive and sophisticated applications on the network. Managing and routing enormous traffic flow with dynamic behavior is a highly challenging task. However, arriving at a precise model for traffic forecasting in a short interval of time is not trivial because of the dynamic nature of traffic flow. A novel multivariate time series framework is designed to analyze and forecast the dynamic traffic flow in SDN based networks. The proposed framework adapts the Multivariate Singular Spectrum Analysis (MSSA) forecasting model and incorporates the Randomized Singular Value Decomposition (RSVD) to improve the accuracy of flow prediction. Simulations are conducted to evaluate the effectiveness of the proposed MSSA method. The proposed method predicts the long-term traffic fluctuation from the observed traffic traces. The SDN controller is trained using the traffic traces and future traffic flows are forecasted. The performance evaluation of the proposed method predicts real-time traffic trends accurately with 2.2% MAPE, 9.44 MAE and 13.803 RMSE. The results show that the learning ability of MSSA helps to forecast future network traffic with low prediction errors.

Video-Based Heart Rate Measurement Against Uneven Illuminations Using Multivariate Singular Spectrum Analysis

Spatially uneven illuminations are the dominant interference of video-based heart rate (HR) screening for cooperated subjects in a telehealth service. In this letter, a remote photoplethysmography (rPPG) method is introduced to stably extract pulsatile signals against uneven facial illuminations based on the multivariate singular spectrum analysis (MSSA). This method first divides the facial skins into multiple patches, where the hue channels resistant to light intensity variations are prepared from selected optimal patches. Considering the spatial correlations of heartbeats, the hue signals are then decomposed using the MSSA to reconstruct pulses. Finally, the HR is determined as the one with the highest ratio of energy around the dominant frequency from the first group of MSSA reconstructed signals. Experimental results demonstrate the effectiveness of the proposed method on the in-house BSIPL-rPPG database and the public COHFACE database, where the correlation coefficients of the estimated HRs achieve 0.95 and 0.98, respectively, outperforming those of the comparison methods.

Multivariate singular spectrum analysis of seismicity in the space–time-depth-magnitude domain: insight from eastern Nepal and the southern Tibetan Himalaya

Multivariate singular spectrum analysis of seismicity in the space–time-depth-magnitude domain: insight from eastern Nepal and the southern Tibetan Himalaya

The Synthesis of an Adaptive Filter for Automatic Detection and Time Localization of Premotor EEG Patterns of the Human Brain

An adaptive low-pass filter has been synthesized for automatic patterns detection of arbitrary mental movements in records of multidimensional electroencephalograms (EEG). The filter is based on the multivariate singular spectrum analysis. The effective bandwidth of the filter corresponds to the spectrum of the sought patterns of mental activity on the observed EEG time interval. The use of the synthesized filter provided a reliable automatic search for patterns and the correct determination of their time boundaries. The correctness of the results has been confirmed in experiments with 24 volunteers.

Gate Road Support Deformation Forecasting Based on Multivariate Singular Spectrum Analysis and Fuzzy Time Series

Underground mining engineers and planners in our country are faced with extremely difficult working conditions and a continuous shortage of money. Production disruptions are frequent and can sometimes last more than a week. During this time, gate road support is additionally exposed to rock stress and the result is its progressive deformation and the loss of functionality of gate roads. In such an environment, it is necessary to develop a low-cost methodology to maintain a gate road support system. For this purpose, we have developed a model consisting of two main phases. The first phase is related to support deformation monitoring, while the second phase is related to data analysis. To record support deformations over a defined time horizon we use laser scanning technology together with multivariate singular spectrum analysis to conduct data processing and forecasting. Fuzzy time series is applied to classify the intensity of displacements into several independent groups (clusters).

Harmonic cross-correlation decomposition for multivariate time series.

We introduce harmonic cross-correlation decomposition (HCD) as a tool to detect and visualize features in the frequency structure of multivariate time series. HCD decomposes multivariate time series into spatiotemporal harmonic modes with the leading modes representing dominant oscillatory patterns in the data. HCD is closely related to data-adaptive harmonic decomposition (DAHD) [Chekroun and Kondrashov, Chaos 27, 093110 (2017)10.1063/1.4989400] in that it performs an eigendecomposition of a grand matrix containing lagged cross-correlations. As for DAHD, each HCD mode is uniquely associated with a Fourier frequency, which allows for the definition of multidimensional power and phase spectra. Unlike in DAHD, however, HCD does not exhibit a systematic dependency on the ordering of the channels within the grand matrix. Further, HCD phase spectra can be related to the phase relations in the data in an intuitive way. We compare HCD with DAHD and multivariate singular spectrum analysis, a third related correlation-based decomposition, and we give illustrative applications to a simple traveling wave, as well as to simulations of three coupled Stuart-Landau oscillators and to human EEG recordings.

Does statistical model perform at par with computationally expensive general circulation model for decadal prediction?

Decadal predictions have gained immense importance over the last decade because of their use in near-term adaption planning. Computationally expensive coupled model intercomparison project phase 5 general circulation models (GCMs) are initialized every 5 years and they generate the decadal hindcasts with moderate skill. Here we test the hypothesis that computationally inexpensive data-driven models, such as multi-variate singular spectrum analysis (MSSA), which takes care of trends and oscillations, performs similar to GCMs. We pick up one of the most complex variables having low predictability, Indian summer monsoon rainfall (ISMR) and its possible causal sea surface temperatures (SST). We find that the MSSA approach performs similar to the GCMs in simulating SSTs beyond their nonlinear limits of predictability, which is ∼12 months. These SSTs are used for decadal predictions of ISMR and show improved skills compared to the GCMs. We conclude that data-driven models are possible alternatives to computationally expensive GCMs for decadal predictions.

A state‐dependent linear recurrent formula with application to time series with structural breaks

AbstractAn underlying assumption in Multivariate Singular Spectrum Analysis (MSSA) is that the time series are governed by a linear recurrent continuation. However, in the presence of a structural break, multiple series can be transferred from one homogeneous state to another over a comparatively short time breaking this assumption. As a consequence, forecasting performance can degrade significantly. In this paper, we propose a state‐dependent model to incorporate the movement of states in the linear recurrent formula called a State‐Dependent Multivariate SSA (SD‐MSSA) model. The proposed model is examined for its reliability in the presence of a structural break by conducting an empirical analysis covering both synthetic and real data. Comparison with standard MSSA, BVAR, VAR and VECM models shows the proposed model outperforms all three models significantly.