Sparse and Robust Multivariate Functional Principal Component Analysis for Passenger Flow Pattern Discovery in Metro Systems

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.

The drastic increase of metro passengers in recent years inevitably causes the overcrowdedness in the metro systems. Accurately predicting passenger flows at metro stations is critical for efficient metro system management, which helps alleviate such overcrowdedness. Compared to the prevalent next-step prediction, multi-step passenger flow prediction could prominently increase the prediction duration and reveal finer-grained passenger flow variations, which better helps metro system management. Thus, in this paper, we address the problem of <i>multi-step metro station passenger (MSP) flow prediction</i>. In light of MSP flows&#x2019; unique spatial-temporal characteristics, we propose <i>STP-TrellisNets+</i>, which for the first time augments the newly-emerged temporal convolutional framework <i>TrellisNet</i> for multi-step MSP flow prediction. The temporal module of STP-TrellisNets+ (named <i>CP-TrellisNetsED</i>) employs a Closeness TrellisNet followed by a <i>Periodicity TrellisNets-based Encoder-Decoder (P-TrellisNetsED)</i> to jointly capture the short- and long-term temporal correlation of MSP flows. In parallel to CP-TrellisNetsED, its spatial module (named <i>GC-TrellisNetsED</i>) adopts a novel transfer flow-based metric to characterize the spatial correlation among MSP flows, and implements another TrellisNetsED on multiple <i>diffusion graph convolutional networks (DGCNs)</i> in time-series order to capture the dynamics of such spatial correlation. Extensive experiments with two large-scale real-world automated fare collection datasets demonstrate that STP-TrellisNets+ outperforms the state-of-the-art baselines.

Metro systems play an important role in meeting the demand for urban transportation in large cities. The understanding of passenger route choice is critical for public transit management. The wide deployment of automated fare collection (AFC) systems opens up a new opportunity. However, only each trip's tap-in and tap-out time stamp and stations can be directly obtained from AFC system records; the train and route chosen by a passenger are unknown, information necessary to solve our problem. While existing methods work well in some specific situations, they hardly work for complicated situations. In this paper, we propose a solution that needs no additional equipment or human involvement than the AFC systems. We develop a probabilistic model that can estimate from empirical analysis how the passenger flows are dispatched to different routes and trains. We validate our approach using a large-scale data set collected from the Shenzhen Metro system. The measured results provide us with useful input when building the passenger path choice model.

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.

SummaryThe transitional phase of menopause induces significant hormonal fluctuations, exerting a profound influence on the long-term well-being of women. In an extensive longitudinal investigation of women’s health during mid-life and beyond, known as the Study of Women’s Health Across the Nation (SWAN), hormonal biomarkers are repeatedly assessed, following an asynchronous schedule compared to other error-prone covariates, such as physical and cardiovascular measurements. We conduct a subgroup analysis of the SWAN data employing a semiparametric mixture regression model, which allows us to explore how the relationship between hormonal responses and other time-varying or time-invariant covariates varies across subgroups. To address the challenges posed by asynchronous scheduling and measurement errors, we model the time-varying covariate trajectories as functional data with reduced-rank Karhunen–Loéve expansions, where splines are employed to capture the mean and eigenfunctions. Treating the latent subgroup membership and the functional principal component (FPC) scores as missing data, we propose an Expectation-Maximization algorithm to effectively fit the joint model, combining the mixture regression for the hormonal response and the FPC model for the asynchronous, time-varying covariates. In addition, we explore data-driven methods to determine the optimal number of subgroups within the population. Through our comprehensive analysis of the SWAN data, we unveil a crucial subgroup structure within the aging female population, shedding light on important distinctions and patterns among women undergoing menopause.

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;.

Accurate and reliable short-term passenger flow prediction is crucial for optimizing operational organization and enhancing intelligent management in urban rail transit. However, passenger flow remains relatively stable during off-peak periods, while intense fluctuations during peak hours increase the complexity and uncertainty of prediction, posing challenges for comprehensive and accurate short-term forecasting. To accurately capture the complex dynamic changes in peak-hour passenger flow and reduce the emphasis on the stable characteristics of off-peak periods, this study proposes a composite model. Initially, we construct a passenger flow dataset by processing passenger card swipe information from the Automatic Fare Collection (AFC) system. Temporal features are extracted from the data using a Bidirectional Long Short-Term Memory (BiLSTM) neural network. Furthermore, we introduce a Causal Temporal Pattern Attention (CTPA) mechanism enhanced with dilated causal convolution to optimize temporal feature weights specifically for peak and off-peak passenger flow periods. The optimized features from the regression BiLSTM and CTPA modules are integrated, and multi-step passenger flow predictions are obtained through a fully connected layer. During the training process of the BiLSTM-CTPA model, we utilize the Bayesian Optimization (BO) algorithm to optimize key hyperparameters such as the number of hidden layers, neurons, batch size, learning rate, regularization, and iterations, thereby enhancing training efficiency. Experimental results demonstrate that compared to the baseline model, our approach achieves lower Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). In conclusion, the model presented in this paper provides robust data support for the daily operation and management of urban rail transit.

The metro hub of large city is the main collecting and distributing center of passengers in urban rail transit, with high hidden danger of passenger flow congestion. The purpose of the paper is to propose an evaluation method of passenger pressure state in metro hub based on AFC (Automatic Fare Collection) data. Firstly, drawing on the concept of PSR (Press-State-Response) framework to build the index of passenger flow saturation, the passenger flows and capacity of facilities in the metro hub was calculated based on AFC data and survey data to extract the index, and the evaluation of passenger pressure state at bottleneck position was realized. Secondly, based on the saturation of passenger flow, the objective weight of each bottleneck position was determined by entropy weight method and the comprehensive evaluation model of passenger pressure state in the metro hub was established. Finally, based on AFC data of Dongzhimen metro hub within a week in Beijing, passenger pressure states of bottleneck positions and overall metro hub were evaluated respectively, to verify the effectiveness of the method.

With the large-scale construction of China's high-speed railway network, the demand for passenger flow is growing and varies in different seasons. Therefore, refinement operational requirements are increasingly prominent. However, the passenger flow itself has time-varying characteristics, and the division of passenger flow seasons and periods is divided by manual methods and experience subjectively. As a result, it is difficult to adjust it dynamically with the passenger flow changing dynamically. There are few studies on the seasons and periods of the division about high-speed railway passenger flow at home and abroad. In this study, the seasonal and period division methods of high-speed railway passenger flow were studied, the dynamic characteristics of passenger flow were analyzed, and the annual passenger flow fluctuation was considered. Then, the high-speed railway passenger flow was divided into seasons by using the firefly affinity propagation algorithm. Meanwhile, the high-speed railway passenger flow was divided into periods by employing the orderly clustering algorithm with the consideration of the daily passenger flow fluctuation.

Urban rail transit is developing rapidly, and new lines are constantly being opened and connected to the existing road network. Accurately grasping the passenger flow after the opening of the new line can provide a reference for the operation and management of urban rail transit stations. In order to predict the daily passenger flow after the opening of the new line, based on the passenger flow of the existing line stations, combined with the distribution of job-resident population, the new line stations and the existing line stations are matched by station classification, and a neural network model is established to predict the daily passenger flow after the new line is opened. The passenger flow provides a reference for the passenger flow management for the opening of new rail transit lines in the future.