Functional data clustering via hypothesis testing k-means

Clustering Spatially Correlated Functional Data With Multiple Scalar Covariates

We propose a probabilistic model for clustering spatially correlated functional data with multiple scalar covariates. The motivating application is to partition the 29 provinces of the Chinese mainland into a few groups characterized by the epidemic severity of COVID-19, while the spatial dependence and effects of risk factors are considered. It can be regarded as an extension of mixture models, which allows different subsets of covariates to influence the component weights and the component densities by modeling the parameters of the mixture as functions of the covariates. In this way, provinces with similar spatial factors are a priori more likely to be clustered together. Posterior predictive inference in this model formalizes the desired prediction. Further, the identifiability of the proposed model is analyzed, and sufficient conditions to guarantee "generic" identifiability are provided. An L1 -penalized estimator is developed to assist variable selection and robust estimation when the number of explanatory covariates is large. An efficient expectation-minimization algorithm is presented for parameter estimation. Simulation studies and real-data examples are presented to investigate the empirical performance of the proposed method. Finally, it is worth noting that the proposed model has a wide range of practical applications, e.g., health management, environmental science, ecological studies, and so on.

Smoothing regression and impact measures for accidents of traffic flows

Traffic pattern identification and accident evaluation are essential for improving traffic planning, road safety, and traffic management. In this paper, we establish classification and regression models to characterize the relationship between traffic flows and different time points and identify different patterns of traffic flows by a negative binomial model with smoothing splines. It provides mean response curves and Bayesian credible bands for traffic flows, a single index, and the log-likelihood difference, for traffic flow pattern recognition. We further propose an impact measure for evaluating the influence of accidents on traffic flows based on the fitted negative binomial model. The proposed method has been successfully applied to real-world traffic flows, and it can be used for improving traffic management.

Supervised classification of curves via a combined use of functional data analysis and tree-based methods

Technological advancement led to the development of tools to collect vast amounts of data usually recorded at temporal stamps or arriving over time, e.g. data from sensors. Common ways of analysing this kind of data also involve supervised classification techniques; however, despite constant improvements in the literature, learning from high-dimensional data is always a challenging task due to many issues such as, for example, dealing with the curse of dimensionality and looking for a trade-off between complexity and accuracy. Nowadays, research in functional data analysis (FDA) and statistical learning is very lively to address these drawbacks adequately. This study offers a supervised classification strategy that combines FDA and tree-based procedures. Specifically, we introduce functional classification trees, functional bagging, and functional random forest exploiting the functional principal components decomposition as a tool to extract new features and build functional classifiers. In addition, we introduce new tools to support the understanding of the classification rules, such as the functional empirical separation prototype, functional predicted separation prototype, and the leaves’ functional deviance. Furthermore, we suggest some possible solutions for choosing the number of functional principal components and functional classification trees to be implemented in the supervised classification procedure. This research aims to provide an approach to improve the accuracy of the functional classifier, serve the interpretation of the functional classification rules, and overcome the classical drawbacks due to the high-dimensionality of the data. An application on a real dataset regarding daily electrical power demand shows the functioning of the supervised classification proposal. A simulation study with nine scenarios highlights the performance of this approach and compares it with other functional classification methods. The results demonstrate that this line of research is exciting and promising; indeed, in addition to the benefits of the suggested interpretative tools, we exceed the previously established accuracy records on a dataset available online.

Pooling random forest and functional data analysis for biomedical signals supervised classification: Theory and application to electrocardiogram data

Scientific progress has contributed to creating many devices to gather vast amounts of biomedical data over time. The goal of these devices is generally to monitor people's health conditions, diagnose, and prevent patients' diseases, for example, to discover cardiovascular disorders or predict epileptic seizures. A common way of investigating these data is classification, but these instruments generate signals often characterized by high dimensionality. Learning from these data is definitely a challenging task due to many issues, for example, the trade‐off between complexity and accuracy and the course of dimensionality. This study proposes a supervised classification method based on the joint use of functional data analysis, classification trees, and random forest to deal with massive biomedical data recorded over time. For this purpose, this research suggests different original tools to extract features and train functional classifiers, interpret the classification rules, assess leaves' quality and composition, avoid the classical drawbacks due to the COD, and improve the accuracy of the functional classifiers. Focusing on ECG data as a possible example, the final purpose of this study is to offer an original approach to identify and classify patients at risk using different types of biomedical signals. The results confirm that this line of research is exciting; indeed, the interpretative tools show evidence to be very useful for understanding classification rules. Furthermore, the performance of the proposed functional classifier, in terms of accuracy, is excellent because the latter breaks the previous classification record regarding a well‐known ECG dataset.

A Method of L1-Norm Principal Component Analysis for Functional Data

Recently, with the popularization of intelligent terminals, research on intelligent big data has been paid more attention. Among these data, a kind of intelligent big data with functional characteristics, which is called functional data, has attracted attention. Functional data principal component analysis (FPCA), as an unsupervised machine learning method, plays a vital role in the analysis of functional data. FPCA is the primary step for functional data exploration, and the reliability of FPCA plays an important role in subsequent analysis. However, classical L2-norm functional data principal component analysis (L2-norm FPCA) is sensitive to outliers. Inspired by the multivariate data L1-norm principal component analysis methods, we propose an L1-norm functional data principal component analysis method (L1-norm FPCA). Because the proposed method utilizes L1-norm, the L1-norm FPCs are less sensitive to the outliers than L2-norm FPCs which are the characteristic functions of symmetric covariance operator. A corresponding algorithm for solving the L1-norm maximized optimization model is extended to functional data based on the idea of the multivariate data L1-norm principal component analysis method. Numerical experiments show that L1-norm FPCA proposed in this paper has a better robustness than L2-norm FPCA, and the reconstruction ability of the L1-norm principal component analysis to the original uncontaminated functional data is as good as that of the L2-norm principal component analysis.