Projection Pursuit Regression Research Articles

Clean and accurate soil quality monitoring in mining areas under environmental rehabilitation in the Eastern Brazilian Amazon.

Soil quality monitoring in mining rehabilitation areas is a crucial step to validate the effectiveness of the adopted recovery strategy, especially in critical areas for environmental conservation, such as the Brazilian Amazon. The use of portable X-ray fluorescence (pXRF) spectrometry allows a rapid quantification of several soil chemical elements, with low cost and without residue generation, being an alternative for clean and accurate environmental monitoring. Thus, this work aimed to assess soil quality in mining areas with different stages of environmental rehabilitation based on predictions of soil fertility properties through pXRF along with four machine learning algorithms (projection pursuit regression, PPR; support vector machine, SVM; cubist regression, CR; and random forest, RF) in the Eastern Brazilian Amazon. Sandstone and iron mines in different chronological stages of rehabilitation (initial, intermediate, and advanced) were evaluated, in addition to non-rehabilitated and native forest areas. A total of 81 soil samples (26 from sandstone mine and 55 from iron mine) were analyzed by both traditional wet-chemistry methods and pXRF. The available/exchangeable contents of K, Ca, B, Fe, and Al, in addition to H+Al, cation exchange capacity at pH = 7, Al saturation, soil organic matter, pH, sum of bases, base saturation, clay, and sand were accurately predicted (R2 > 0.70) using pXRF data, with emphasis on the prediction of Fe (R2 = 0.93), clay content (R2 = 0.81), H+Al (R2 = 0.81), and K+ (R2 = 0.85). The best predictive models were developed by RF and CR (86%) and when considering pXRF data + mining area + stage of rehabilitation (73%). The results highlight the potential of pXRF to accurately assess soil properties in environmental rehabilitation areas in the Amazon region (yet scarcely evaluated under this approach), promoting a more agile and cheaper preliminary diagnosis compared to traditional methods.

Reinterpreting fundamental plane correlations with machine learning

Abstract This work explores the relationships between galaxy sizes and related observable galaxy properties in a large volume cosmological hydrodynamical simulation. The objectives of this work are to develop a better understanding of both the correlations between galaxy properties and the influence of environment on galaxy physics in order to build an improved model for the galaxy sizes, building off of the fundamental plane. With an accurate intrinsic galaxy size predictor, the residuals in the observed galaxy sizes can potentially be used for multiple cosmological applications, including making measurements of galaxy velocities in spectroscopic samples, estimating the rate of cosmic expansion, and constraining the uncertainties in the photometric redshifts of galaxies. Using projection pursuit regression, the model accurately predicts intrinsic galaxy sizes and have residuals which have limited correlation with galaxy properties. The model decreases the spatial correlation of galaxy size residuals by a factor of ∼ 5 at small scales compared to the baseline correlation when the mean size is used as a predictor.

Monthly Pork Price Prediction Applying Projection Pursuit Regression: Modeling, Empirical Research, Comparison, and Sustainability Implications

The drastic fluctuations in pork prices directly affect the sustainable development of pig farming, agriculture, and feed processing industries, reducing people’s happiness and sense of gain. Although there have been extensive studies on pork price prediction and early warning in the literature, some problems still need further study. Based on the monthly time series data of pork prices and other 11 influencing prices (variables) such as beef, hog, piglet, etc., in China from January 2000 to November 2023, we have established a project pursuit auto-regression (PPAR) and a hybrid PPAR (H-PPAR) model. The results of the PPAR model study show that the monthly pork prices in the lagged periods one to three have an important impact on the current monthly pork price. The first lagged period has the largest and most positive impact. The second lagged period has the second and a negative impact. We built the H-PPAR model using the 11 independent variables (prices), including the prices of corn, hog, mutton, hen’s egg, and beef in lagged period one, the piglet’s price in lagged period six, and by deleting non-important variables. The results of the H-PPAR model show that the hog price in lagged period one is the most critical factor, and beef price and the other six influencing variables are essential factors. The model’s performance metrics show that the PPAR and H-PPAR models outperform approaches such as support vector regression, error backpropagation neural network, dynamic model average, etc., and possess better suitability, applicability, and reliability. Our results forecast the changing trend of the monthly pork price and provide policy insights for administrators and pig farmers to control and adjust the monthly pork price and further enhance the health and sustainable development of the hog farming industry.

Validity and reliability of deriving the autoregulatory plateau through projection pursuit regression from driven methods.

To compare the construct validity and between-day reliability of projection pursuit regression (PPR) from oscillatory lower body negative pressure (OLBNP) and squat-stand maneuvers (SSMs). Nineteen participants completed 5 min of OLBNP and SSMs at driven frequencies of 0.05 and 0.10 Hz across two visits. Autoregulatory plateaus were derived at both point-estimates and across the cardiac cycle. Between-day reliability was assessed with intraclass correlation coefficients (ICCs), Bland-Altman plots with 95% limits of agreement (LOA), coefficient of variation (CoV), and smallest real differences. Construct validity between OLBNP-SSMs were quantified with Bland-Altman plots and Cohen's d. The expected autoregulatory curve with positive rising and negative falling slopes were present in only ~23% of the data. The between-day reliability for the ICCs were poor-to-good with the CoV estimates ranging from ~50% to 70%. The 95% LOA were very wide with an average spread of ~450% for OLBNP and ~350% for SSMs. Plateaus were larger from SSMs compared to OLBNPs (moderate-to-large effect sizes). The cerebral pressure-flow relationship is a complex regulatory process, and the "black-box" nature of this system can make it challenging to quantify. The current data reveals PPR analysis does not always elicit a clear-cut central plateau with distinctive rising/falling slopes.

Towards Improved Heliosphere Sky Map Estimation with Theseus

The Interstellar Boundary Explorer (IBEX) satellite has been in orbit since 2008 and detects energy-resolved energetic neutral atoms (ENAs) originating from the heliosphere. Different regions of the heliosphere generate ENAs at different rates. It is of scientific interest to take the data collected by IBEX and estimate spatial maps of heliospheric ENA rates (referred to as sky maps) at higher resolutions than before. These sky maps will subsequently be used to discern between competing theories of heliosphere properties that are not currently possible. The data IBEX collects present challenges to sky map estimation. The two primary challenges are noisy and irregularly spaced data collection and the IBEX instrumentation’s point spread function. In essence, the data collected by IBEX are both noisy and biased for the underlying sky map of inferential interest. In this article, we present a two-stage sky map estimation procedure called Theseus. In Stage 1, Theseus estimates a blurred sky map from the noisy and irregularly spaced data using an ensemble approach that leverages projection pursuit regression and generalized additive models. In Stage 2, Theseus deblurs the sky map by deconvolving the PSF with the blurred map using regularization. Unblurred sky map uncertainties are computed via bootstrapping. We compare Theseus to a method closely related to the one operationally used today by the IBEX Science Operation Center (ISOC) on both simulated and real data. Theseus outperforms ISOC in nearly every considered metric on simulated data, indicating that Theseus is an improvement over the current state of the art.

An Exploration of Prediction Performance Based on Projection Pursuit Regression in Conjunction with Data Envelopment Analysis: A Comparison with Artificial Neural Networks and Support Vector Regression

Data envelopment analysis (DEA) is a leading approach in performance analysis and discovering newer benchmarks, and the traditional DEA models cannot forecast the future efficiency of decision-making units (DMUs). Machine learning, such as the artificial neural networks (ANNs), support vector machine/regression (SVM/SVR), projection pursuit regression (PPR), etc., have been viewed as beneficial for managers in predicting system behaviors. PPR is especially suitable for small and non-normal distribution samples, the usual cases in DEA analysis. This paper integrates DEA and PPR to cover the shortcomings we faced while using DEA and DEA-BPNN, DEA-SVR, etc. This study explores the advantages of combining these complementary methods into an integrated performance measurement and prediction model. Firstly, the DEA approach is used to evaluate and rank the efficiency of DMUs. Secondly, we establish two DEA-PPR combined models to describe the DEA efficiency scores (also called the production function) and the DEA-efficient frontier function. The first combined model’s input variables are input–output indicators in the DEA model, and the output variable is the DEA efficiency. In the second model, its input variables are input or output indicators in the DEA model, and the output variable is the optimal input indicator for input-oriented DEA or the output indicator for output-oriented DEA. We conducted positive research on two examples with actual data and virtual small, medium-sized, and large samples. Compared with the DEA-BPNN and DEA-SVR models, the results show that the DEA-PPR combined model has more vital global optimization ability, better convergence, higher accuracy, and a simple topology. The DEA-PPR model can obtain robust results for both small and large cases. The DEA-BPNN and DEA-SVR models cannot obtain robust results for small and medium-sized samples due to overfitting. For large samples, the DEA-PPR model outperforms DEA-BPNN, DEA-SVR, etc. The DEA-PPR combined model possesses better suitability, applicability, and reliability than the DEA-BPNN model, the DEA-SVR model, etc.

Study of stress-strain relationship of hydraulic asphalt concrete at low to intermediate temperatures based on experimental data regression

The conventional principal structural theory modeling is constrained by the underlying assumptions that make the established constitutional model incapable of accurately describing the stress–strain relationship of asphalt concrete. Subsequently, in this study, the traditional modeling idea was changed and the projection pursuit regression (PPR) method was used to analyze triaxial test data obtained from asphalt concrete. The PPR models utilized to calculate deviatoric stress and volumetric strain were developed and the validity and applicability of the PPR model and this method were verified. The results show that the modeling method avoids the problem of inconsistency between a priori model assumptions and objective reality. Asphalt concrete has complex strain softening, strain hardening, shear shrinkage, and shear expansion characteristics. The model employed to calculate deviatoric stress and volumetric strain based on PPR method is superior to the E–B and “Nanshui” models in its capacity to reflect the characteristics of strain softening and shear deformation. The results calculated using the PPR model can accurately describe the stress–strain relationship of asphalt concrete. Studying the stress–strain relationship of asphalt concrete from the perspective of the examination of data breaks through the constraints of traditional modeling ideas, which has certain theoretical significance. The research results can provide a new solution for non-hypothesis modeling of nonlinear data and accurately describing the stress–strain relationship of asphalt concrete.

Bayesian projection pursuit regression

Bayesian projection pursuit regression

Possible Alternatives: Identifying and Quantifying Adulteration in Buffalo, Goat, and Camel Milk Using Mid-Infrared Spectroscopy Combined with Modern Statistical Machine Learning Methods.

Adulteration of higher priced milks with cheaper ones to obtain extra profit can adversely affect consumer health and the market. In this study, pure buffalo milk (BM), goat milk (GM), camel milk (CM), and their mixtures with 5-50% (vol/vol) cow milk or water were used. Mid-infrared spectroscopy (MIRS) combined with modern statistical machine learning was used for the discrimination and quantification of cow milk or water adulteration in BM, GM, and CM. Compared to partial least squares (PLS), modern statistical machine learning-especially support vector machines (SVM), projection pursuit regression (PPR), and Bayesian regularized neural networks (BRNN)-exhibited superior performance for the detection of adulteration. The best prediction models for the different predictive traits are as follows: The binary classification models developed by SVM resulted in differentiation of CM-cow milk, and GM/CM-water mixtures. PLS resulted in differentiation of BM/GM-cow milk and BM-water mixtures. All of the above models have 100% classification accuracy. SVM was used to develop multi-classification models for identifying the high and low proportions of cow milk in BM, GM, and CM, as well as the high and low proportions of water adulteration in BM and GM, with correct classification rates of 94%, 100%, 100%, 99%, and 100%, respectively. In addition, a PLS-based model was developed for identifying the high and low proportions of water adulteration in CM, with correct classification rates of 100%. A regression model for quantifying cow milk in BM was developed using PCA + BRNN, with RMSEV = 5.42%, and RV2 = 0.88. A regression model for quantifying water adulteration in BM was developed using PCA + PPR, with RMSEV = 1.70%, and RV2 = 0.99. Modern statistical machine learning improved the accuracy of MIRS in predicting BM, GM, and CM adulteration more effectively than PLS.

Exploring carbon dioxide emissions forecasting in China: A policy-oriented perspective using projection pursuit regression and machine learning models

Achieving a balance between future greenhouse gas reduction and sustained economic growth is of utmost importance. This study leverages machine learning (ML), specifically projection pursuit regression (PPR), to evaluate the key factors that influence CO2 emission predictions in China. The analysis notably identifies the escalating electricity consumption as a primary influencing factor. Based on empirical findings, it is evident that building electricity consumption will continue to rise steadily until 2050 unless new restrictions or technological advancements are implemented. Relying solely on the reduced carbon intensity of electricity will not enable China to achieve carbon neutrality. Therefore, there is a pressing need for more energy-efficient building retrofits and technologies to reduce power consumption in both residential and commercial properties. This policy-oriented study underscores its practical implications, offering valuable insights to policymakers for developing targeted CO2 reduction strategies that align with sustainable development and climate goals.

Non-hypothetical projection pursuit regression for the prediction of hydration heat of Portland-cement-based cementitious system

In this study, the non-hypothetical projection pursuit regression (NH-PPR) is proposed. The proposed NH-PPR model can predict the hydration heat based on the four cement phases, FA, SL, cement fineness and hydration time. The NH-PPR model is proposed by using the multiple layer iteration method and the non-hypothetical and non-parametric ridge functions to enhance accuracy and solve the problems caused by the parameter selection and the subjective hypothesis. The modeling data set is applied to train model, the testing data set is regressed and fitted into the model, and then the obtained results are compared with the BP model. To further validate the proposed model, another published data set is used to obtain a higher degree of confidence in the prediction. It is shown that the proposed model obtains the better accuracy, stability and versatility, and avoids the parameter selection and subjective hypothesis.

Mechanical strength characteristics of saline soil stabilized by all-solid waste cementitious material based on projection pursuit regression modeling

Mechanical strength characteristics of saline soil stabilized by all-solid waste cementitious material based on projection pursuit regression modeling

Watchdog malicious node detection and isolation using deep learning for secured communication in MANET

Mobile Ad-hoc Networks (MANETs) are wireless networks formed dynamically by connecting or leaving nodes to and from the network without any fixed infrastructure. These categories of wireless networks are susceptible to different attacks based on their dynamic topological structure. Due to this, security is a primary constraint in MANETs to preserve communication between mobile nodes. A Deep Neural Learned Projective Pursuit Regression-based Watchdog Malicious Node Detection and Isolation (DNLPPR-WMNDI) technique is proposed and modelled in this paper to improve the security feature of MANETs. The newly proposed DNLPPR-WMNDI technique initially selects the neighbouring nodes by applying the projection pursuit regression function. In multicasting, the route paths are established through the intermediate node with the help of control commands named RREQ and RREP. After then, Watchdog Malicious Node Detection and Isolation (WMNDI) technique is applied to detect malicious nodes based on the data packet forwarding time. Basically, a malicious node is affected by a node isolation attack. For better communication, a malicious node is isolated from the network and multicast routing is carried out by selecting the next neighbouring node and this improves the communication security. Simulation is done for the developed technique based on different performance metrics.

Estimation of projection pursuit regression via alternating linearization

The projection pursuit regression (PPR) has played an important role in statistical modeling. It can be used both as a data model for statistical interpretation and as an algorithmic model for approximating general non-parametric regressions. Existing estimation methods of PPR usually involve complicated minimization in order to achieve desired efficiency under general settings. This paper presents an algorithm by alternatively linearizing the estimation loss function, referred to as aPPR hereafter, which is easy to implement. The asymptotic theory is also established for both the PPR data model and the algorithmic model. Numerical performance of aPPR in model estimation and model interpretation is demonstrated through simulations and real data analysis.

Metagenomic insights into the potential risks of representative bio/non-degradable plastic and non-plastic debris in the upper and lower reaches of Haihe Estuary, China

As vectors for microorganisms and genetic elements, vast amounts of solid wastes, including plastics and non-plastics, enter oceans through estuaries globally. The heterogeneity of microbiomes developed on different types of plastic and non-plastic matrices and their potential environmental risks in field estuarine regions have not been fully explored. Here, microbial communities, antibiotic resistance genes (ARGs), virulence factors (VFs), and mobile genetic elements (MGEs) on substrate debris (SD) covering non-biodegradable plastics, biodegradable plastics, and non-plastics were first comprehensively characterized based on metagenomic analyzes (substrate identity). These selected substrates were field-exposed at both ends of the Haihe Estuary, China (geographic location). For substrate identity: conspicuously diverse functional gene profiles on different substrates were obtained; the relative gene copies of ARGs, VFs, and MGEs on non-biodegradable plastics were highest at both locations; non-biodegradable plastic matrices recruited the most abundant unique ARGs from ambient waters; the relative abundance of potential bacterial hosts carrying multiple ARGs and VFs (BH-AV) was much higher on non-biodegradable plastic surfaces than on the other two substrates, especially in the coastal water environment. For geographic locations: more abundant specific ARGs, VFs, and MGEs were significantly enriched on SD from the upper estuary; the average relative abundance of identified BH-AV on SD from the upper estuary was 1.99–7.14 folds from the lower estuary. Finally, the results of the Projection Pursuit Regression model verified the higher comprehensive potential risks arising from non-biodegradable plastics (substrate identity) and SD from the upstream of the estuary (geographic location). Based on comparative analysis, our results alert us to pay particular attention to ecological risks triggered by conventional non-biodegradable plastics in rivers and coastal environments and highlight the microbiological risk from terrestrial solid waste to the downstream marine environment.

The potential evaluation of groundwater by integrating rank sum ratio (RSR) and machine learning algorithms in the Qaidam Basin.

Groundwater is a vital resource in arid areas that sustains local industrial development and environmental preservation. Mapping groundwater potential zones and determining high-potential regions are essential for the responsible use of the local groundwater resource. When utilizing machine learning or deep learning algorithms to forecast groundwater potential in arid areas, difficulties such as inaccurate and overfitting predictions might occur due to a shortage of borehole samples. In this study, a database of groundwater conditioning factors with a size of 275,157 × 9 was created in the Qaidam Basin, and 85 known borehole samples were collected. The groundwater potential was evaluated using a combination of rank sum ratio (RSR), projection pursuit regression (PPR) and random forest (RF) algorithms, resulting in four models: PPR, RSR-PPR, RSR-RF, and RF. Results indicated that the groundwater potential was higher in mountainous regions surrounding the Qaidam Basin and decreased progressively towards the central and northwestern regions where most industries and facilities are located. The two primary factors, according to the PPR and RF models, were evapotranspiration (0.246, 0.225) and landform (0.176, 0.294). In terms of their ability to accurately forecast the borehole samples, the four models ranked as follows: RF > RSR-RF > RSR-PPR > PPR. The accuracy of the four models in the low-potential area was 0.73 (PPR), 0.60 (RSR-PPR), 0.87 (RSR-RF), and 0.80 (RF), respectively. However, the RF model showed overfitting due to a lack of samples, especially in high-potential regions, which limits its applicability. The RSR-RF method was applied directly to evaluate the entire factor database, avoiding the risk of overfitting caused by a limited number of training samples. The results demonstrate that the RSR-RF model is effective for classifying groundwater potential types in samples and mapping groundwater potential of the study area. This research presents a novel approach for groundwater potential predictions in areas with insufficient sample sizes, providing a reference for policymakers and researchers.

Water Eutrophication Evaluation Based on the Improved Projection Pursuit Regression Model Under the Hesitant Fuzzy Environment

The water eutrophication restricts the development of economy and society in China, which attracts increasing attention. It also affects the health and ecological environment. The evaluation of water eutrophication is very complicated due to the dynamic variability of the water quality data. This paper adopts the hesitant fuzzy set (HFS) to depict the massive data of samples and uncertain preference information of experts, which reduces the complexity of calculation and avoids the loss of information. After that, we construct the projection index function based on the main factors of water eutrophication. The particle swarm optimization (PSO) algorithm is applied to determine the global optimal projection direction by optimizing the projection index function. Therefore, we construct an improved projection pursuit regression (PPR) model. Finally, the water eutrophication evaluation of several lakes in China is used to demonstrate the improved PPR model. Also, the comparative analysis and contribution rate analysis are conducted to validate its rationality and advantages.

Establishment of a projection-pursuit-regression-based prediction model for the filtration performance of a micro-pressure filtration and cleaning tank for micro-irrigation

Filtration is a key process of a micro-irrigation system. To achieve water conservation, improve the energy efficiency, and meet the low-carbon environmental requirements, this study investigates a new type of pre-pump filtration measure—the micro-pressure filtration and cleaning tank, and the sediment removal (SR), mass of intercepted sediment (Ma), and filtration time (t) are used as evaluation indicators. A uniform orthogonal test was designed to evaluate the influences of the initial sediment concentration, flow rate, and filter area. We carried out simulations using the projection pursuit regression (PPR) method based on physical measurement data, and then NSGA-II (fast elitist non-dominated sorting genetic algorithm) algorithm was used to find the optimal parameter values. The results showed that the order of the factors influencing the SR and Ma of the micro-pressure filtration and cleaning tank was the filter area > initial sediment concentration > flow rate. The order of the factors influencing the filtration time was flow rate > initial sediment concentration > filter area. A PPR prediction model was built based on the filter area, initial sediment concentration, flow rate, and assessment indicators, and the optimal operating conditions were determined (initial sediment concentration: 0.36 kg/m3, flow rate: 7 m3/h, and filter area: 2000 cm2). The research results demonstrated the filtration performance of the micro-pressure filtration and cleaning tank and provide a theoretical basis for the popularization and application of such tanks as well as a reference for sustainable new irrigation technologies.

Projection pursuit adaptation on polynomial chaos expansions

The present work addresses the issue of accurate stochastic approximations in high-dimensional parametric space using tools from uncertainty quantification (UQ). The basis adaptation method and its accelerated algorithm in polynomial chaos expansions (PCE) were recently proposed to construct low-dimensional approximations adapted to specific quantities of interest (QoI). The present paper addresses one difficulty with these adaptations, namely their reliance on quadrature point sampling, which limits the reusability of potentially expensive samples. Projection pursuit (PP) is a statistical tool to find the “interesting” projections in high-dimensional data and thus bypass the curse-of-dimensionality. In the present work, we combine the fundamental ideas of basis adaptation and projection pursuit regression (PPR) to propose a novel method to simultaneously learn the optimal low-dimensional spaces and PCE representation from given data. While this projection pursuit adaptation (PPA) can be entirely data-driven, the constructed approximation exhibits mean-square convergence to the solution of an underlying governing equation and thus captures the supports and probability distributions associated with the physics constraints. The proposed approach is demonstrated on a borehole problem and a structural dynamics problem, demonstrating the versatility of the method and its ability to discover low-dimensional manifolds with high accuracy with limited data. In addition, the method can learn surrogate models for different quantities of interest while reusing the same data set.

Cerebrovascular regulation in patients with vasovagal syncope and autonomic failure due to familial amyloidotic polyneuropathy.

While there is strong evidence for autonomic involvement in cerebrovascular function acutely, long-term role of autonomic nervous system in cerebrovascular function has been controversial. We assessed autoregulation in 10 healthy individuals, nine patients with vasovagal syncope (VVS), and nine with Familial Amyloidotic Polyneuropathy (FAP), in response to head-up tilt test (HUTT). Arterial blood pressure heart rate, cardiac output, and bilateral cerebral blood flow velocity (CBFV) at the M1 segment of middle cerebral artery (transcranial Doppler ultrasound) were recorded during supine rest and 70° HUTT. Autoregulation was quantified using a validated nonlinear and nonparametric approach based on projection pursuit regression. Plasma adrenaline and noradrenaline were also measured at rest and during HUTT. During supine rest and HUTT, plasma noradrenaline content was lower in FAP patients. During HUTT, VVS patients had a hyperadrenergic status; CBFV decreased in all groups, which was greater in FAP patients (p<0.01). Healthy controls responded to HUTT with a reduction in CBFV responses to increases (p=0.01) and decreases (p<0.01) in arterial pressure without any change in the range or effectiveness of autoregulation. VVS patients responded to HUTT with a reduction in falling (p=0.02), but not rising slope (p=0.40). Autoregulatory range (p<0.01) and effectiveness increased (p=0.09), consistent with the rapid increase in levels of catecholamines. In FAP patients, the level of increase in range of autoregulation was significantly related to the magnitude of increase in plasma noradrenaline in response to HUTT (R2=0.26, p=0.05). Autonomic dysfunction affects the cerebral autoregulatory response orthostatic to challenge.