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--A novel iterative learning algorithm is proposed to improve the classic orthogonal forward regression (OFR) algorithm in an attempt to produce an optimal solution under a purely OFR framework without using any other auxiliary algorithms. The new algorithm searches for the optimal solution on a global solution space while maintaining the advantage of simplicity and computational efficiency. Both a theoretical analysis and simulations demonstrate the validity of the new algorithm.

Measurement of the ground reaction forces (GRF) during walking is typically limited to laboratory settings, and only short observations using wearable pressure insoles have been reported so far. In this study, a new proxy measurement method is proposed to estimate the vertical component of the GRF (vGRF) from wearable accelerometer signals. The accelerations are used as the proxy variable. An orthogonal forward regression algorithm (OFR) is employed to identify the dynamic relationships between the proxy variables and the measured vGRF using pressure-sensing insoles. The obtained model, which represents the connection between the proxy variable and the vGRF, is then used to predict the latter. The results have been validated using pressure insoles data collected from nine healthy individuals under two outdoor walking tasks in non-laboratory settings. The results show that the vGRFs can be reconstructed with high accuracy (with an average prediction error of less than 5.0%) using only one wearable sensor mounted at the waist (L5, fifth lumbar vertebra). Proxy measures with different sensor positions are also discussed. Results show that the waist acceleration-based proxy measurement is more stable with less inter-task and inter-subject variability than the proxy measures based on forehead level accelerations. The proposed proxy measure provides a promising low-cost method for monitoring ground reaction forces in real-life settings and introduces a novel generic approach for replacing the direct determination of difficult to measure variables in many applications.

A new parametric approach is proposed for nonlinear and nonstationary system identification based on a time-varying nonlinear autoregressive with exogenous input (TV-NARX) model. The TV coefficients of the TV-NARX model are expanded using multiwavelet basis functions, and the model is thus transformed into a time-invariant regression problem. An ultra-orthogonal forward regression (UOFR) algorithm aided by mutual information (MI) is designed to identify a parsimonious model structure and estimate the associated model parameters. The UOFR-MI algorithm, which uses not only the observed data themselves but also weak derivatives of the signals, is more powerful in model structure detection. The proposed approach combining the advantages of both the basis function expansion method and the UOFR-MI algorithm is proved to be capable of tracking the change of TV parameters effectively in both numerical simulations and the real EEG data.

Functional connectivity and effective connectivity of the human brain, representing statistical dependence and directed information flow between cortical regions, significantly contribute to the study of the intrinsic brain network and its functional mechanism. Many recent studies on electroencephalography (EEG) have been focusing on modeling and estimating brain connectivity due to increasing evidence that it can help better understand various brain neurological conditions. However, there is a lack of a comprehensive updated review on studies of EEG‐based brain connectivity, particularly on visualization options and associated machine learning applications, aiming to translate those techniques into useful clinical tools. This article reviews EEG‐based functional and effective connectivity studies undertaken over the last few years, in terms of estimation, visualization, and applications associated with machine learning classifiers. Methods are explored and discussed from various dimensions, such as either linear or nonlinear, parametric or nonparametric, time‐based, and frequency‐based or time‐frequency‐based. Then it is followed by a novel review of brain connectivity visualization methods, grouped by Heat Map, data statistics, and Head Map, aiming to explore the variation of connectivity across different brain regions. Finally, the current challenges of related research and a roadmap for future related research are presented.

A new Ultra Least Squares (ULS) criterion is introduced for system identification. Unlike the standard least squares criterion which is based on the Euclidean norm of the residuals, the new ULS criterion is derived from the Sobolev space norm. The new criterion measures not only the discrepancy between the observed signals and the model prediction but also the discrepancy between the associated weak derivatives of the observed and the model signals. The new ULS criterion possesses a clear physical interpretation and is easy to implement. Based on this, a new Ultra Orthogonal Forward Regression (UOFR) algorithm is introduced for nonlinear system identification, which includes converting a least squares regression problem into the associated ultra least squares problem and solving the ultra least squares problem using the orthogonal forward regression method. Numerical simulations show that the new UOFR algorithm can significantly improve the performance of the classic OFR algorithm.Key words: orthogonal forward regression, system identification, ultra least squares, ultra orthogonal forward regression, ultra orthogonal least squares. IntroductionSystem identification plays a more and more important role in revealing the unknown mechanisms and rules underlying complex phenomena (Schmidt & Lipson, 2009). System identification includes the detection of the model structure and estimation of the associated parameters. A system identification problem can often be thought of as an optimization problem where the optimal model is searched from a large predefined candidate model dictionary given a criterion. The criterion is 2 used to evaluate the performance of each model by measuring the discrepancy between the observed data and the model predictions. The candidate model dictionary is often chosen to be large enough to include the unknown correct model. Hence an exhaustive search algorithm is often infeasible in these kinds of applications because of the large solution space. Even an evolutionary algorithm which can greatly reduce the search process can still be very computationally intensive.Hence an algorithm which can efficiently find the optimal solution is desired. However, a fast algorithm often dictates an optimal substructure; otherwise the search may converge to a suboptimal solution. Many efforts have been made to improve the search process under a certain specific loss function or performance index, for example, the simulated annealing algorithm, particle swarm optimisation, and so on. In this paper, a different and new methodology will be introduced.Instead of improving the search method, a new and effective criterion will be introduced to describe the objective of the regression more accurately. Under the new criterion, the solution space has a better structure and a fast algorithm is more likely to find the optimal solution.System identification aims to identify a model from observed data based on a criterion. A good criterion results in not only better parameter estimation but also a good search pa...