Semiparametric mixture regression for asynchronous longitudinal data using multivariate functional principal component analysis

Cardiovascular diseases (CVDs) are one of the primary reasons for death worldwide. These diseases often occur due to the occlusion of coronary arteries, thereby leading to insufficient blood and oxygen supply that damages cardiac muscle cells. Electrocardiogram (ECG) signals which reflect heart electrical activity are being used for diagnosing various cardiac diseases. Typically, a standard ECG consists of 12 channels referred to as leads which enable practitioners to monitor heartbeats through different channels where each heartbeat lasts approximately 600 ms. The majority of studies focus on the classification and early diagnosis of arrhythmias. Although the current studies on change-point methods have acquired massive accuracy in detecting potential shifts during a multi-channel process, they lack flexibility in manually assigning more weights to the channels, which are of more importance for experts. This could be addressed by implementing the weighted multivariate functional principal component analysis (WMFPCA). The objective of this study is to develop a novel change-point detection method to monitor long-term cardiovascular treatment. A third-order tensor structure was employed to represent the 12-lead ECG data in three dimensions (beats × samples × leads). Exploiting intra-beat, inter-beat, and inter-lead correlations along with channel significance in the third-order tensor, the WMFPCA is incorporated into Hotelling's statistic to construct monitoring schemes. Simulation results show that the proposed approach outperforms the existing methods in monitoring multi-channel processes. Finally, applying the suggested model on a real-world dataset containing Myocardial Infarction (MI) subjects verifies the model.

We address the problem of performing dimension reduction on multivariate functional data observed on different domains in an endogenously stratified sampling context. The aim is to propose a new multivariate functional principal component analysis \(MFPCA) approach for data sampled by a stratification of a population according to a binary variable of interest. This estimation strategy is derived from a direct relationship between univariate and multivariate FPCA for finite Karhunen-Loève decompositions. The proposed methodology yields encouraging results and can be applied to data with measurement errors. Computational results on simulated data highlight the good performance of the proposed methodology compared to the classical MFPCA, which ignores the type of data sampling. A real-life application considering breast cancer cells data is also presented.

The paper entitled \(\textit{Multivariate Functional Principal Component Analysis for Endogenously Stratified Data}\) has been published in the journal Afrika Statistika, Vol. 17 (4), 2023, pp. 3321–3366 (DOI: 10.16929/as/2022.3321.308). The authors have identified the need for substantial modifications, including additions, deletions, and revisions. This erratum is published to address these necessary corrections and updates.

Modern metro systems in big cities have accumulated large amounts of passenger transit transaction data via the deployment of automatic fare collection (AFC) devices, which could facilitate a thorough analysis of passenger flow dynamics. To discover the underlying passenger flow patterns over all stations in an entire metro system, this paper proposes a multivariate functional principal component analysis (MFPCA) method. The functional integrity of a single daily passenger flow profile at each station is explicitly utilized, and the complex correlation among a multitude of daily passenger flow profiles from all stations is comprehensively modeled. Moreover, to simultaneously improve the interpretability of eigenvectors and mitigate the sensitivity to outliers, the MFPCA is formulated as a minimization problem with both a sparsity and a robustness penalty term. A computationally efficient algorithm is developed accordingly to obtain the eigenvectors. The superiority of our proposed sparse and robust MFPCA (SRMFPCA) is validated using a Hong Kong Mass Transit Railway (MTR) dataset. The derived sparse and smooth eigenvectors can be well interpreted as empirically meaningful passenger flow patterns. The results of our method can be further used as solid foundations for station clustering, correlation analysis and outlier identification.

Functional principal component analysis (FPCA) is a commonly used nonparametric degradation modeling technique. A basic requirement of FPCA is that different units must share the same scale in X-axis. A FPCA-based degradation modeling method has been specially designed for truncated degradation signals whose amplitudes are truncated at the failure threshold. This method formulates the degradation time as a function of state level by axis rotation. Since the degradation signals of different units are truncated at the same failure threshold level, the axis rotation strategy ensures the same scale in X-axis. However, in cases of noisy signals, one state level may correspond to multiple time points, which means that the time function depending on state level does not exist. In addition, this method assumes that the noise term as well as the functional principal component (FPC) scores follow the Gaussian distribution, which restricts the flexibility in real practice. Aiming at the above two issues, this paper develops a new degradation modeling method based on the FPCA. The proposed method formulates the degradation model on the definition of first pass time (FPT), which ensures the existence of the time function depending on state level. The noise term and the FPC scores are not restricted to the Gaussian distribution. A particle filtering based updating algorithm is developed to deal with the non-Gaussian state estimation issue of the FPC scores according to the online condition monitoring signals. The effectiveness of the proposed method is verified using an experiment of milling cutter wear.

The standard paradigm in Affective Computing involves acquiring one/several markers (e.g., physiological signals) of emotions and training models on these to predict emotions. However, due to the internal nature of emotions, labelling/annotation of emotional experience is done manually by humans using specially developed annotation tools. To effectively exploit the resulting subjective annotations for developing affective systems, their quality needs to be assessed. This entails, (i) evaluating the variations in annotations, across different subjects and emotional stimuli, to detect spurious/unexpected patterns; and (ii) developing strategies to effectively combine these subjective annotations into a ground truth annotation. This article builds on our previous work by presenting a novel Functional Data Analysis based approach to assess the quality of annotations. Specifically, the bivariate annotation time-series are transformed into functions, such that each resulting functional annotation then becomes a sample element for analysis like Multivariate Functional Principal Component Analysis (MFPCA) that evaluate variation across all annotations. The resulting scores from MFPCA provide interesting insights into annotation patterns and facilitate the use of multivariate statistical techniques to address both (i) and (ii). Given the presented efficacy of these methods, we believe they offer an exciting new approach to assessing the quality of annotations.

Postural synergies allow a rich set of hand configurations to be represented in lower dimension space compared to the original joint space. In our previous works, we have shown that this can be extended to trajectories thanks to the multivariate functional principal component analysis, obtaining a set of basis functions able to represent grasping movements learned from human demonstration. In this article, we introduce a human cognition-inspired approach for generalizing and improving robot grasping skills in this motion synergies subspace. The use of a reinforcement learning (RL) algorithm allows the robot to explore the surrounding space and improve its capability to reach and grasp objects. The learning method is the policy improvement with path integrals, running in the policy space. Bootstrapped with synergy coefficients obtained from neural networks, the policy reward is based on a force closure grasp quality index computed at the end of the task, measuring how a firm is the grip. We finally show that combining neural networks and RL allows the robot manipulator to have a good initial estimate of the grasping configuration and faster convergence to an optimal grasp with respect to a database approach, the latter a less general solution in presence of new objects.

In this paper, we propose a generalized functional linear regression model for a binary outcome indicating the presence/absence of a cardiac disease with multivariate functional data among the relevant predictors. In particular, the motivating aim is the analysis of electrocardiographic traces of patients whose pre-hospital electrocardiogram (ECG) has been sent to 118 Dispatch Center of Milan (the Italian free-toll number for emergencies) by life support personnel of the basic rescue units. The statistical analysis starts with a preprocessing of ECGs treated as multivariate functional data. The signals are reconstructed from noisy observations. The biological variability is then removed by a nonlinear registration procedure based on landmarks. Thus, in order to perform a data-driven dimensional reduction, a multivariate functional principal component analysis is carried out on the variance-covariance matrix of the reconstructed and registered ECGs and their first derivatives. We use the scores of the Principal Components decomposition as covariates in a generalized linear model to predict the presence of the disease in a new patient. Hence, a new semi-automatic diagnostic procedure is proposed to estimate the risk of infarction (in the case of interest, the probability of being affected by Left Bundle Brunch Block). The performance of this classification method is evaluated and compared with other methods proposed in literature. Finally, the robustness of the procedure is checked via leave-j-out techniques.

With the emergence of numerical sensors in many aspects of every- day life, there is an increasing need in analyzing multivariate functional data. This work focuses on the clustering of such functional data, in order to ease their modeling and understanding. To this end, a novel clustering technique for multivariate functional data is presented. This method is based on a func- tional latent mixture model which fits the data in group-specific functional subspaces through a multivariate functional principal component analysis. A family of parsimonious models is obtained by constraining model parameters within and between groups. An EM algorithm is proposed for model inference and the choice of hyper-parameters is addressed through model selection. Nu- merical experiments on simulated datasets highlight the good performance of the proposed methodology compared to existing works. This algorithm is then applied to the analysis of the pollution in French cities for one year.

Methods and tools for implementing regularized multivariate functional principal component analysis ('ReMFPCA') for multivariate functional data whose variables might be observed over different dimensional domains. 'ReMFPCA' is an object-oriented interface leveraging the extensibility and scalability of R6. It employs a parameter vector to control the smoothness of each functional variable. By incorporating smoothness constraints as penalty terms within a regularized optimization framework, 'ReMFPCA' generates smooth multivariate functional principal components, offering a concise and interpretable representation of the data. For detailed information on the methods and techniques used in 'ReMFPCA', please refer to Haghbin et al. (2023) &lt;<a href="https://doi.org/10.48550%2FarXiv.2306.13980" target="_top">doi:10.48550/arXiv.2306.13980</a>&gt;.

Disruptions in gait function are common after concussion in adolescents; however, the neuromotor control deficits driving these gait disruptions are not well known. Fifteen concussed (age mean [SD]): 17.4 [0.6], 13 females, days since injury: 26.3 [9.9]) and 17 uninjured (age: 18.0 [0.7], 10 females) adolescents completed 3 trials each of single-task gait and dual-task gait (DT). During DT, participants simultaneously walked while completing a serial subtraction task. Gait metrics and variability in instantaneous mean frequency in lower extremity muscles were captured by inertial sensors and surface electromyography, respectively. A 2-way analysis of covariance was used to compare gait metrics across groups and conditions. Functional principal components analysis was used to identify regions of variability in instantaneous mean frequency curves. Functional principal component scores were compared across groups using a Welch statistic. Both groups displayed worse performance on gait metrics during DT condition compared to single-task, with no differences between groups (P < .001). Concussed adolescents displayed significantly greater instantaneous mean frequency, indicated by functional principal component 1, in the tibialis anterior, biceps femoris, and semitendinosus (P < .05) during single-task and DT compared with uninjured adolescents. Our observations suggest that concussed adolescents display inefficient motor unit recruitment lasting longer than 2weeks following injury, regardless of the addition of a secondary task.

In this article, we present a nonparametric approach to predict the evolution of multistream longitudinal data. Our approach first decomposes each stream into a linear combination of eigenfunctions and their corresponding functional principal component (FPC) scores. A Gaussian process prior for the FPC scores is then induced based on a functional semimetric that introduces a similarity measure across streams. Finally, an empirical Bayesian updating strategy is derived to update the established prior using real-time stream data. Empirical evidence shows that the proposed framework outperforms state-of-the-art approaches and can effectively account for heterogeneity as well as achieve high predictive accuracy.

This paper presents an approach to generating asynchro nous schedules of various concurrency levels and describes novel net-based scheduling and allocation optimization tec hniques for asynchronous high-level synthesis. The asynch ronous schedules are optimized through the sets of concurr ent variable and statement pairs. Experimental results and a comparison of the net-based techniques with the best seq uential scheduling and allocation techniques are presented.

PurposeThe purpose of this paper is to analyze and forecast the Chinese term structure of interest rates using functional principal component analysis (FPCA).Design/methodology/approachThe authors propose an FPCA-K model using FPCA. The forecasting of the yield curve is based on modeling functional principal component (FPC) scores as standard scalar time series models. The authors evaluate the out-of-sample forecast performance using the root mean square and mean absolute errors.FindingsMonthly yield data from January 2002 to December 2016 are used in this paper. The authors find that in the full sample, the first two FPCs account for 98.68 percent of the total variation in the yield curve. The authors then construct an FPCA-K model using the leading principal components. The authors find that the FPCA-K model compares favorably with the functional signal plus noise model, the dynamic Nelson-Siegel models and the random walk model in the out-of-sample forecasting.Practical implicationsThe authors propose a functional approach to analyzing and forecasting the yield curve, which effectively utilizes the smoothness assumption and conveniently addresses the missing-data issue.Originality/valueTo the best knowledge, the authors are the first to use FPCA in the modeling and forecasting of yield curves.

Background: A shift towards the dynamic measurement of physiologic resilience and improved technology incorporated into experimental paradigms in aging research is producing high-resolution data. Identifying the most appropriate analysis method for this type of data is a challenge. In this work, the functional principal component analysis (fPCA) was employed to demonstrate a data-driven approach to the analysis of high-resolution data in aging research.Methods: Cerebral oxygenation during standing was measured in a large cohort [The Irish Longitudinal Study on Aging (TILDA)]. FPCA was performed on tissue saturation index (TSI) data. A regression analysis was then conducted with the functional principal component (fPC) scores as the explanatory variables and transition time as the response.Results: The mean ± SD age of the analysis sample was 64 ± 8 years. Females made up 54% of the sample and overall, 43% had tertiary education. The first PC explained 96% of the variance in cerebral oxygenation upon standing and was related to a baseline shift. Subsequent components described the recovery to before-stand levels (fPC2), drop magnitude and initial recovery (fPC3 and fPC4) as well as a temporal shift in the location of the minimum TSI value (fPC5). Transition time was associated with components describing the magnitude and timing of the nadir.Conclusions: Application of fPCA showed utility in reducing a large amount of data to a small number of parameters which summarize the inter-participant variation in TSI upon standing. A demonstration of principal component regression was provided to allow for continued use and development of data-driven approaches to high-resolution data analysis in aging research.