Local Modeling Technique Research Articles

A backfitting maximum likelihood estimator for hierarchical and geographically weighted regression modelling, with a case study of house prices in Beijing

Geographically weighted regression (GWR) and its extensions are important local modelling techniques for exploring spatial heterogeneity in regression relationships. However, when dealing with spatial data of overlapping samples – for example, when precise locational information is aggregated to a shared neighbourhood to avoid revealing the addresses of individual survey respondents – GWR-based models can encounter several problems, including obtaining reliable bandwidths. Because data with this characteristic exhibit spatial hierarchical structures, we propose combining hierarchical linear modelling (HLM) with GWR to give a hierarchical and geographically weighted regression (HGWR) model that divides coefficients into sample-level fixed effects, group-level fixed effects, sample-level random effects, and group-level spatially weighted effects. This paper presents a back-fitting likelihood estimator to fit the model, a simulation experiment that suggests that HGWR is better able to capture these effects and the spatial heterogeneity within them than are traditional HLM or GWR models, and a case study looking at predictors of housing price in Beijing, China. The ability of HGWR to tackle both spatial and group-level heterogeneity simultaneously suggests its potential as a promising data modelling tool for handling spatio-temporal big data with spatially hierarchical structures.

Geospatial determinants and spatio-temporal variation of early initiation of breastfeeding and exclusive breastfeeding in Ethiopia from 2011 to 2019, a multiscale geographically weighted regression analysis

BackgroundBreastfeeding offers numerous benefits for infants, mothers, and the community, making it the best intervention for reducing infant mortality and morbidity. The World Health Organization (WHO) recommends initiating breastfeeding within one hour after birth and exclusively breastfeeding for the first six months. This study investigated the trend, spatio-temporal variation, and determinants of spatial clustering of early initiation of breastfeeding (EIBF) and exclusive breastfeeding (EBF) in Ethiopia from 2011 to 2019.MethodsData from the Ethiopian Demographic and Health Survey (EDHS), which was conducted in 2011, 2016, and 2019, were analyzed utilizing a weighted sample of 10,616 children aged 0–23 years for EIBF and 2,881 children aged 0–5 months for EBF. Spatial autocorrelation analysis was used to measure whether EIBF and EBF were dispersed, clustered, or randomly distributed and Kriging interpolation was employed to predict the outcome variables in the unmeasured areas. Spatial scan statistics were used to identify spatial clusters with a high prevalence of cases. Both global and local regression modeling techniques were employed to examine the spatial relationships between the explanatory variables and the dependent variables.ResultsThe trend analysis revealed a notable increase in the prevalence of EIBF from 51.8% in 2011 to 71.9% in 2019. Similarly, the prevalence of EBF increased from 52.7% in 2011 to 58.9% in 2019. Spatial analysis demonstrated significant spatial variation in both EIBF and EBF throughout the country. Cold spots or clusters with a low prevalence of EIBF were observed consistently in the Tigray and Amhara regions, and significant cold spot areas of EBF were observed consistently in the Afar and Somali regions. Multiscale geographically weighted regression analysis revealed significant predictors of spatial variations in EIBF, including the religious affiliation of being a follower of the orthodox religion, parity of 1–2, absence of antenatal care visits, and delivery via cesarean section.ConclusionsDespite the increase in both EIBF and EBF rates over time in Ethiopia, these rates still fall below the national target. To address this issue, the government should prioritize public health programs aimed at improving maternal healthcare service utilization and maternal education. It is essential to integrate facility-level services with community-level services to achieve optimal breastfeeding practices. Specifically, efforts should be made to promote breastfeeding among mothers who have delivered via cesarean section. Additionally, there should be a focus on encouraging antenatal care service utilization and adapting maternal healthcare services to accommodate the mobile lifestyle of pastoralist communities. These steps will contribute to enhancing breastfeeding practices and achieving better outcomes for maternal and child health.

Non-linear memory-based learning for predicting soil properties using a regional vis-NIR spectral library

Visible near-infrared (vis-NIR) spectroscopy has gained widespread recognition as an efficient and reliable approach for the rapid monitoring of soil properties. This technique relies on robust machine learning models that convert soil spectra information to soil properties. In particular, memory-based learning (MBL) has emerged as a powerful local modeling technique for soil spectral analysis. However, conventional MBL algorithms use linear models, disregarding the non-linear relationship between soil properties and vis-NIR spectra. Therefore, we hypothesize that non-linear memory-based learning (N-MBL) models can enhance prediction. This study develops and evaluates the N-MBL algorithm using the Lateritic Red soil spectral library (LRSSL) from Guangdong province in China. This library consists of 742 samples of vis-NIR spectra and corresponding soil properties, including pH, soil organic matter (SOM), total nitrogen (TN), total phosphorus (TP), and total potassium (TK). As a comparison, several commonly used supervised learning methods, such as Partial least squares regression (PLSR), Cubist, Random Forest (RF), Super vector machine (SVM), Convolution neural network (CNN), and local models (MBL), were compared to the proposed N-MBL. The results showed that local models generally outperformed supervised learning methods, particularly when applied to a large soil spectral library with a substantial number of samples (over 500). When comparing the two local models, MBL had more fluctuation of model performance compared to N-MBL as the number of selected nearest neighbors (k) varied between 30 and 250. As k increased, N-MBL showed higher R2 values for SOM and TN prediction than MBL but lower performance for pH and TK prediction. In addition, N-MBL outperformed MBL in predicting TP. In conclusion, N-MBL is a new local algorithm for predicting soil properties from vis-NIR spectra. It has a high potential to improve the accuracy of the prediction of multiple soil properties.

Modelling pre-fatigue, low-velocity impact and post-impact fatigue behaviours of composite helicopter tail structures under multipoint coordinated loading spectrum

This paper aims to numerically study progressive pre-fatigue, low-velocity impact (LVI) and post-impact fatigue (PIF) damage behaviours of a full-scale composite helicopter tail structure under multipoint coordinated loading spectrum. A mixed progressive damage algorithm incorporating residual strength and stiffness degradation rules and failure criteria is developed for progressive fatigue and LVI damage analysis of plain-weave (PW) and unidirectional (UD) composites. Novel global–local​ FE modelling technique is proposed for parallel computation and real-time data transferring of global–local FE models in progressive pre-fatigue, LVI and PIF damage modelling of helicopter composite tail structure. The numerical predictions from this work agree well with experimental data from previous literature, indicating that the mixed algorithm and global–local FE modelling technique can effectively analyse the impact damage tolerance of large full-scale composite aircraft structures.

An investigation of how normalisation and local modelling techniques confound machine learning performance in a mental health study

Machine learning (ML) is increasingly deployed on biomedical studies for biomarker development (feature selection) and diagnostic/prognostic technologies (classification). While different ML techniques produce different feature sets and classification performances, less understood is how upstream data processing methods (e.g., normalisation) impact downstream analyses. Using a clinical mental health dataset, we investigated the impact of different normalisation techniques on classification model performance. Gene Fuzzy Scoring (GFS), an in-house developed normalisation technique, is compared against widely used normalisation methods such as global quantile normalisation, class-specific quantile normalisation and surrogate variable analysis. We report that choice of normalisation technique has strong influence on feature selection. with GFS outperforming other techniques. Although GFS parameters are tuneable, good classification model performance (ROC-AUC > 0.90) is observed regardless of the GFS parameter settings. We also contrasted our results against local modelling, which is meant to improve the resolution and meaningfulness of classification models built on heterogeneous data. Local models, when derived from non-biologically meaningful subpopulations, perform worse than global models. A deep dive however, revealed that the factors driving cluster formation has little to do with the phenotype-of-interest. This finding is critical, as local models are often seen as a superior means of clinical data modelling. We advise against such naivete. Additionally, we have developed a combinatorial reasoning approach using both global and local paradigms: This helped reveal potential data quality issues or underlying factors causing data heterogeneity that are often overlooked. It also assists to explain the model as well as provides directions for further improvement.

Comparing Two Different Development Methods of External Parameter Orthogonalization for Estimating Organic Carbon from Field-Moist Intact Soils by Reflectance Spectroscopy

Visible and near-infrared (Vis–NIR) spectroscopy can provide a rapid and inexpensive estimation for soil organic carbon (SOC). However, with respect to field in situ spectroscopy, external environmental factors likely degrade the model accuracy. Among these factors, moisture has the greatest effect on soil spectra. The external parameter orthogonalization (EPO) algorithm in combination with the Chinese soil spectroscopic database (Dataset A, 1566 samples) was investigated to eliminate the interference of the external parameters for SOC estimation. Two different methods of EPO development, namely, laboratory-rewetting archive soil samples and field-collecting actual moist samples, were compared to balance model performance and analytical cost. Memory-based learning (MBL), a local modeling technique, was introduced to compare with partial least square (PLS), a global modeling method. A total of 250 soil samples from Central China were collected. Of these samples, 120 dry ground samples (Dataset B) were rewetted to different moisture levels to develop EPO P1 matrix. Seventy samples (Dataset C) containing field-moist intact and laboratory dry ground soils were used to establish EPO P2 matrix. The remaining 60 samples (Dataset D) also containing field-moist intact and laboratory dry ground soils were employed to validate the spectral models developed based on Dataset A. Results showed that EPO could correct the effect of external factors on soil spectra. For PLS, the validation statistics were as follows: no correction, validation R2 = 0.02; P1 correction, validation R2 = 0.56; and P2 correction, validation R2 = 0.57. For MBL, the validation results were as follows: no correction, validation R2 = 0.06; P1 correction, validation R2 = 0.65; and P2 correction, validation R2 = 0.69. The P2 consistently yielded better results than P1 did but simultaneously increased the sampling time and economic cost. The use of the P1 matrix and the MBL algorithm was recommended because it could reduce the cost of establishing in situ models for SOC.

An Investigation of How Normalisation and Local Modelling Techniques Confound Machine Learning Performance in a Mental Health Study

An Investigation of How Normalisation and Local Modelling Techniques Confound Machine Learning Performance in a Mental Health Study

The spatial and temporal dynamics of voter preference determinants in four U.S. presidential elections (2008–2020)

AbstractPolitical and social processes that shape people's voting preferences might be linked to geographical location, varying from place to place, and operating at local, regional, and national scales. Here, we use a local modeling technique, multiscale geographically weighted regression (MGWR), to examine spatial and temporal variations in the influences of county‐level socio‐economic factors on voter preference during the 2008–2020 U.S. presidential elections. We argue that the local intercept in the MGWR model is an indicator of the effect of spatial context on voter preference and not only can this be separated from the effect of other socio‐economic factors, but it needs to be in order to prevent misspecification bias in the indicators of these other factors. We also identify strong and consistent divisions across the country in how context shapes election results.

FRF estimation using multiple kernel-based regularisation

Nonparametric kernel-based modelling of dynamical systems offers important advantages over other nonparametric techniques; the estimate is a continuous function, the model complexity is continuously tuneable, and stability, causality and smoothness are imposed on the impulse response estimate. However, for lightly damped systems, most of the existing kernel-based approaches for estimating the impulse- or frequency response function fail because classical kernels are not appropriate for describing lowly damped resonances. Smoothness is imposed on the entire frequency axis with the diagonal correlated or stable spline kernel, with as a result that resonances cannot be captured well. By introducing the superposition of different kernels, carrying prior knowledge about the resonant poles of the system, we make the kernel-based modelling of lightly-damped systems possible with high-accuracy. We use a frequency domain local rational modelling technique as preprocessing step to determine the most dominant poles, and include these as prior knowledge in the kernels. The performance of the new kernel is demonstrated on a highly resonating simulated system and compared to the state of the art nonparametric frequency domain approaches.

Glucose Prediction under Variable-Length Time-Stamped Daily Events: A Seasonal Stochastic Local Modeling Framework.

Accurate glucose prediction along a long-enough time horizon is a key component for technology to improve type 1 diabetes treatment. Subjects with diabetes might benefit from supervision and control systems that accurately predict risks and trigger corrective actions early enough with improved mitigation. However, large intra-patient variability poses big challenges to glucose prediction. In previous works by the authors, clustering and local modeling techniques with seasonal stochastic models proved to be efficient, allowing for good glucose prediction accuracy for long prediction horizons. Continuous glucose monitoring (CGM) data were partitioned into fixed-length postprandial time subseries and clustered with Fuzzy C-Means to collect similar behaviors, enforcing seasonality at each cluster after subseries concatenation. Then, seasonal stochastic models were identified for each cluster and local predictions were integrated into a global prediction. However, free-living conditions do not support the fixed-length partition of CGM data since daily events duration is variable. In this work, a new algorithm is provided to overcome this constraint, allowing better coping with patient’s variability under variable-length time-stamped daily events in supervision and control applications. Besides predicted glucose, two real-time indices are additionally provided—a crispness index, indicating good representation of current glucose behavior by a single model, and a normality index, allowing for the detection of an abnormal glucose behavior (unusual according to registered historical data). The framework is tested in a proof-of-concept in silico study with ten patients over four month training data and two independent two month validation datasets, with and without abnormal behaviors, from the distribution version of the UVA/Padova simulator extended with diverse sources of intra-patient variability.

A Unifying Framework and Comparative Evaluation of Statistical and Machine Learning Approaches to Non-Specific Syndromic Surveillance

Monitoring the development of infectious diseases is of great importance for the prevention of major outbreaks. Syndromic surveillance aims at developing algorithms which can detect outbreaks as early as possible by monitoring data sources which allow to capture the occurrences of a certain disease. Recent research mainly concentrates on the surveillance of specific, known diseases, putting the focus on the definition of the disease pattern under surveillance. Until now, only little effort has been devoted to what we call non-specific syndromic surveillance, i.e., the use of all available data for detecting any kind of infectious disease outbreaks. In this work, we give an overview of non-specific syndromic surveillance from the perspective of machine learning and propose a unified framework based on global and local modeling techniques. We also present a set of statistical modeling techniques which have not been used in a local modeling context before and can serve as benchmarks for the more elaborate machine learning approaches. In an experimental comparison of different approaches to non-specific syndromic surveillance we found that these simple statistical techniques already achieve competitive results and sometimes even outperform more elaborate approaches. In particular, applying common syndromic surveillance methods in a non-specific setting seems to be promising.

A Unifying Framework and Comparative Evaluation of Statistical and Machine Learning Approaches to Non-Specific Syndromic Surveillance

Monitoring the development of infectious diseases is of great importance for the prevention of major outbreaks. Syndromic surveillance aims at developing algorithms which can detect outbreaks as early as possible by monitoring data sources which allow to capture the occurrences of a certain disease. Recent research mainly concentrates on the surveillance of specific, known diseases, putting the focus on the definition of the disease pattern under surveillance. Until now, only little effort has been devoted to what we call non-specific syndromic surveillance, i.e., the use of all available data for detecting any kind of infectious disease outbreaks. In this work, we give an overview of non-specific syndromic surveillance from the perspective of machine learning and propose a unified framework based on global and local modeling techniques. We also present a set of statistical modeling techniques which have not been used in a local modeling context before and can serve as benchmarks for the more elaborate machine learning approaches. In an experimental comparison of different approaches to non-specific syndromic surveillance we found that these simple statistical techniques already achieve competitive results and sometimes even outperform more elaborate approaches. In particular, applying common syndromic surveillance methods in a non-specific setting seems to be promising.

Incorporating Prior Knowledge in Local Parametric Modeling for Frequency Response Measurements: Applied to Thermal/Mechanical Systems

Frequency response function (FRF) identification is a key step in experimental modeling of many applications, including mechatronic systems. Applying these techniques to systems where measurement time is limited leads to a situation where the accuracy of the identified model is deteriorated by transient dynamics. This article aims to develop an identification procedure that mitigates these transient dynamics by employing local parametric modeling techniques. To improve the modeling accuracy, prior knowledge is suitably incorporated in the procedure while at the same time allowing for rational parameterizations that maintain a closed-form solution. The prior knowledge is exploited in a relevant local frequency range using a specific Möbius transformation. Preexisting methods, including the commonly used local polynomial method, are recovered as a special case. The presented framework leads to accurate identification results in a simulation study as well as on experimental measurement data.

Improved frequency response function estimation by Gaussian process regression with prior knowledge

Abstract Kernel-based modelling of dynamical systems offers important advantages such as imposing stability, causality and smoothness on the estimate of the model. Here, we improve the existing frequency domain kernel-based approach for estimating the transfer function of a linear time-invariant system from noisy data. This is done by introducing prior knowledge in the kernel. We use a local rational modelling technique to determine the most significant poles, and include these poles as prior knowledge in the kernel. This results in accurate models for the identification of lightly-damped systems.

Frequency Response Function Measurements of Multivariable Systems via Local Rational Modeling

The frequency response function (FRF) is a fundamental property of a linear time-invariant system that describes the system’s frequency-dependent behavior. Accurately measuring the FRF of multivariable lightly damped systems in a time-efficient manner is difficult due to spectral leakage and long-lasting transient phenomena. In the past, local rational modeling techniques have been introduced that mitigate these difficulties. This article presents an overview of the existing techniques for multivariable systems and proposes a new local rational modeling technique that is both consistent and stochastically efficient in measuring the nonparametric FRF. The proposed technique is successfully validated on simulation examples of a generic multivariable lightly damped system. Its practical applicability is illustrated by characterizing the FRF of an aluminum plate.

Frequency Response Function Measurements via Local Rational Modeling, Revisited

A finite measurement time is at the origin of transient (sometimes called leakage) errors in nonparametric frequency response function (FRF) estimation. If the FRF varies significantly over the frequency resolution of the experiment (= reciprocal of the measurement time), then these transients (leakage) errors cause important bias and variance errors in the FRF estimate. To decrease these errors, several local modeling techniques have been proposed in the literature. This article presents an overview of the existing methods and gives an in-depth bias and variance analysis of the FRF and disturbing noise variance estimates. In addition, a new local modeling approach is described, which combines the small bias error of the local rational approximation with the low noise sensitivity of the local polynomial approximation. It is based on an automatic local model-order selection procedure applied to a specific subclass of rational functions.

Fast character modeling with sketch-based PDE surfaces

Virtual characters are 3D geometric models of characters. They have a lot of applications in multimedia. In this paper, we propose a new physics-based deformation method and efficient character modelling framework for creation of detailed 3D virtual character models. Our proposed physics-based deformation method uses PDE surfaces. Here PDE is the abbreviation of Partial Differential Equation, and PDE surfaces are defined as sculpting force-driven shape representations of interpolation surfaces. Interpolation surfaces are obtained by interpolating key cross-section profile curves and the sculpting force-driven shape representation uses an analytical solution to a vector-valued partial differential equation involving sculpting forces to quickly obtain deformed shapes. Our proposed character modelling framework consists of global modeling and local modeling. The global modeling is also called model building, which is a process of creating a whole character model quickly with sketch-guided and template-based modeling techniques. The local modeling produces local details efficiently to improve the realism of the created character model with four shape manipulation techniques. The sketch-guided global modeling generates a character model from three different levels of sketched profile curves called primary, secondary and key cross-section curves in three orthographic views. The template-based global modeling obtains a new character model by deforming a template model to match the three different levels of profile curves. Four shape manipulation techniques for local modeling are investigated and integrated into the new modelling framework. They include: partial differential equation-based shape manipulation, generalized elliptic curve-driven shape manipulation, sketch assisted shape manipulation, and template-based shape manipulation. These new local modeling techniques have both global and local shape control functions and are efficient in local shape manipulation. The final character models are represented with a collection of surfaces, which are modeled with two types of geometric entities: generalized elliptic curves (GECs) and partial differential equation-based surfaces. Our experiments indicate that the proposed modeling approach can build detailed and realistic character models easily and quickly.

Predicting Spatio-temporal Time Series Using Dimension Reduced Local States

We present a method for both cross-estimation and iterated time series prediction of spatio-temporal dynamics based on local modelling and dimension reduction techniques. Assuming homogeneity of the underlying dynamics, we construct delay coordinates of local states and then further reduce their dimensionality through Principle Component Analysis. The prediction uses nearest neighbour methods in the space of dimension reduced states to either cross-estimate or iteratively predict the future of a given frame. The effectiveness of this approach is shown for (noisy) data from a (cubic) Barkley model, the Bueno-Orovio–Cherry–Fenton model, and the Kuramoto–Sivashinsky model.

Exploring Spatially Non-stationary Relationships in the Determinants of Mineralization in 3D Geological Space

Exploring the spatial relationships between various geological features and mineralization is not only conducive to understanding the genesis of ore deposits but can also help to guide mineral exploration by providing predictive mineral maps. However, most current methods assume spatially constant determinants of mineralization and therefore have limited applicability to detecting possible spatially non-stationary relationships between the geological features and the mineralization. In this paper, the spatial variation between the distribution of mineralization and its determining factors is described for a case study in the Dingjiashan Pb–Zn deposit, China. A local regression modeling technique, geological weighted regression (GWR), was leveraged to study the spatial non-stationarity in the 3D geological space. First, ordinary least-squares (OLS) regression was applied, the redundancy and significance of the controlling factors were tested, and the spatial dependency in Zn and Pb ore grade measurements was confirmed. Second, GWR models with different kernel functions in 3D space were applied, and their results were compared to the OLS model. The results show a superior performance of GWR compared with OLS and a significant spatial non-stationarity in the determinants of ore grade. Third, a non-stationarity test was performed. The stationarity index and the Monte Carlo stationarity test demonstrate the non-stationarity of all the variables throughout the area. Finally, the influences of the degree of non-stationary of all controlling factors on mineralization are discussed. The existence of significant non-stationarity of mineral ore determinants in 3D space opens up an exciting avenue for research into the prediction of underground ore bodies.

Adaptive Tuned Controller Parameters for Non-Linear Tanks

In this article, an adaptive PID controller design is proposes for the nonlinear conical tank process. The modeling of the proposed tank process is obtained from local linear modeling technique. Totally five local linear regions are identified and formed to get nonlinear model of the process. The PID controller is designed for each linear model and combined together to get the adaptive PID controller. The identified adaptive PID is presented to the conical system and the measured results are verified with local PID controllers to show the effectiveness of the proposed one. From the measured results, it is verified that the overall performance of the Adaptive PID controller is significantly better than local PID.