Nonlinear Principal Component Research Articles

Categorical CVA biplots

Techniques to visualise and understand large amounts of data are of paramount importance. In most settings, this data is usually multivariate, which further stresses the need for effective visualisation techniques. Multivariate visualisation techniques such as canonical variate analysis (CVA) biplots allow for simultaneous lower-dimensional visualisation and data classification by incorporating class-specific data. CVA biplots, however, are currently restricted to numerical data. Through combining concepts from both CVA and non-linear principal component analysis (PCA) biplots, a new biplot construction methodology that improves on the traditional CVA biplot by allowing for categorical variables is proposed. This technique, named CVA(Hr), is showcased using the established mushroom data set, which contains a mix of categorical and ordinal variables. This novel method improves upon existing biplot construction in terms of classification accuracy and class separation.

Black Girls in Mathematics: (Re)envisioning an Inclusive Parent Involvement Measure

Building upon research utilizing Martin’s Mathematical Socialization and Identity Framework, we examine factors related to community and family involvement to advance the current discourse that informs policies. Data from the High School Longitudinal Study (HSLS:09) public-use file provided a sample of 1,029 Black girls for our analyses. We developed a theoretically-sound inclusive measure, as defined by Black girls, titled the Community and Family Involvement Predictive Scale for Mathematics Outcomes utilizing Nonlinear Principal Components Analysis with a Categorical Principal Components Analysis program. Results are an intersectional measure that considers family, peers, and teachers. Implications for policy include a need for federal, state, and district policymakers to consider a wider variety of contexts, specifically for Black girls, in which community and family partnerships are empowered and prioritized in policies focused on parental involvement.

A level-wise spine registration framework to account for large pose changes.

Accurate and efficient spine registration is crucial to success of spine image guidance. However, changes in spine pose cause intervertebral motion that can lead to significant registration errors. In this study, we develop a geometrical rectification technique via nonlinear principal component analysis (NLPCA) to achieve level-wise vertebral registration that is robust to large changes in spine pose. We used explanted porcine spines and live pigs to develop and test our technique. Each sample was scanned with preoperative CT (pCT) in an initial pose and rescanned with intraoperative stereovision (iSV) in a different surgical posture. Patient registration rectified arbitrary spinal postures in pCT and iSV into a common, neutral pose through a parameterized moving-frame approach. Topologically encoded depth projection 2D images were then generated to establish invertible point-to-pixel correspondences. Level-wise point correspondences between pCT and iSV vertebral surfaces were generated via 2D image registration. Finally, closed-form vertebral level-wise rigid registration was obtained by directly mapping 3D surface point pairs. Implanted mini-screws were used as fiducial markers to measure registration accuracy. In seven explanted porcine spines and two live animal surgeries (maximum in-spine pose change of 87.5mm and 32.7 degrees averaged from all spines), average target registration errors (TRE) of 1.70 ± 0.15mm and 1.85 ± 0.16mm were achieved, respectively. The automated spine rectification took 3-5min, followed by an additional 30 secs for depth image projection and level-wise registration. Accuracy and efficiency of the proposed level-wise spine registration support its application in human open spine surgeries. The registration framework, itself, may also be applicable to other intraoperative imaging modalities such as ultrasound and MRI, which may expand utility of the approach in spine registration in general.

Doğrusal Olmayan Temel Bileşenler Analizinin Tanıtımı ve Uygulanabilirliği

Nonlinear principal component analysis (NLPCA) is a descriptive dimension reduction method that examines the relationships between variables and displays the results numerically and visually in multivariate datasets that have a linear or nonlinear relationship between them. In this study, it was aimed to present the basic explanatory information about nonlinear principal components analysis (NLPCA) and to emphasize its usability by performing application. In the study, data obtained from 270 samples for 17 continuous variables concerning 3 pepper varieties were evaluated by Principal components analysis (PCA). With the 4 principal components obtained as a result of PCA, being 3 categorical variables Variety, storage time and Application were analyzed by NLPCA. In the analysis made with PCA, approximately 74% of the total variance was explained and in the analysis made with NLPCA, approximately 58% was explained as well. As a result of the analysis; it was observed that there was a strong relationship between PC1 and storage time and variety, and PC3 and PC2 variables, while the relationship between PC4 and application variables and all variables was low. As a result; by examining the linear and nonlinear relationships between the variables in the multivariate datasets, these relationships intended to be presented in an easily interpreted and easily understandable way in two-dimensional space; it was emphasized that NLPCA can be used alone and/or together with other multivariate analysis methods.

Cytokine-neuroendocrine peripheral signature in the context of the “accelerated ageing” phenomenon in autism spectrum and schizophrenia spectrum disorders

Currently, differentiation between autism spectrum disorders and schizophrenia spectrum disorders in children is a difficult task, because it relies mainly on behavioral and symptomatic characteristics, since these disorders are highly similar. We have previously demonstrated that peripheral indexes of immune and neuroendocrine systems, which we combined into cytokine-neuroendocrine signature, may reflect distinct clinical phenotypes of autism and schizophrenia spectrum disorders. Moreover, a number of researchers discovered the “accelerated ageing” phenomenon in the persons with schizophrenia, which includes deficiencies of cognitive functions and performance as the main symptoms. Here we carried out a search for biological markers of the “accelerated ageing” phenomenon in children with autistic conditions and schizophrenia spectrum disorders. Our aim was to assess the opportunity of applying the cytokine-neuroendocrine signature as biological evidence of “accelerated ageing” phenomenon in children with autism and schizophrenia spectrum disorders, which could be potentially useful for differential diagnosis of these disorders.Thirteen parameters of the cytokine-neuroendocrine signature were assessed in blood plasma using ELISA method in 82 children with autism, 9 children with schizophrenia, 45 normally developing children, 25 subjects in their reproductive age, and 39 elderly persons: cytokines (IL-6, IL- 1β, IFNγ, TNFα, IL-10, IL-4) and neurohormones (oxytocin, dopamine, adrenaline, noradrenaline, adrenocorticotropic hormone, cortisol, and serotonin). The nonlinear principal component analysis (CATPCA algorithm) was used to assess the variants of cytokine-neuroendocrine signature for different diagnostic categories, i.e., “autism spectrum disorders”, “schizophrenia spectrum disorders”, and “healthy ageing”.The “healthy ageing” variant of cytokine-neuroendocrine signature presented a classic phenomenon, referred to as immune senescence presented by pro-inflammatory age-related cytokines — IL-6, IL- 1β, IFNγ. Only the “schizophrenia spectrum disorders” variant of the cytokine-neuroendocrine signature, unlike all the other signature variants, demonstrated high-level similarity with the “healthy ageing” variant (differing in 2 out of 13 indexes): lower levels of IL- 1β and IFNγ, at the same level of IL-6 “gerontological cytokine” index.Evaluation of the cytokine-neuroendocrine signature can be used for differentiation between autistic disorders and schizophrenia spectrum disorders, including predictive diagnostics in children with autism, thus enabling group selection of children at risk for later conversion to schizophrenia.

Clinical pharmacogenomics in action: design, assessment and implementation of a novel pharmacogenetic panel supporting drug selection for diseases of the central nervous system (CNS)

BackgroundPharmacogenomics describes the link between gene variations (polymorphisms) and drug responses. In view of the implementation of precision medicine in personalized healthcare, pharmacogenetic tests have recently been introduced in the clinical practice. However, the translational aspects of such tests have been limited due to the lack of robust population-based evidence.MaterialsIn this paper we present a novel pharmacogenetic panel (iDNA Genomics-PGx–CNS or PGx–CNS), consisting of 24 single nucleotide polymorphisms (SNPs) on 13 genes involved in the signaling or/and the metabolism of 28 approved drugs currently administered to treat diseases of the Central Nervous System (CNS). We have tested the PGx–CNS panel on 501 patient-derived DNA samples from a southeastern European population and applied biostatistical analyses on the pharmacogenetic associations involving drug selection, dosing and the risk of adverse drug events (ADEs).ResultsResults reveal the occurrences of each SNP in the sample and a strong correlation with the European population. Nonlinear principal component analysis strongly indicates co-occurrences of certain variants. The metabolization efficiency (poor, intermediate, extensive, ultra-rapid) and the frequency of clinical useful pharmacogenetic, associations in the population (drug relevance), are also described, along with four exemplar clinical cases illustrating the strong potential of the PGx–CNS panel, as a companion diagnostic assay. It is noted that pharmacogenetic associations involving copy number variations (CNVs) or the HLA gene were not included in this analysis.ConclusionsOverall, results illustrate that the PGx–CNS panel is a valuable tool supporting therapeutic medical decisions, urging its broad clinical implementation.

Non-intrusive quality assessment of noise-suppressed speech using unsupervised deep features

Objective quality assessment aims towards evaluating the perceptual quality of a signal using a machine-based algorithm. Due to different challenges involved in the subjective evaluation of speech quality, it is necessary to develop objective measures. The goal of any non-intrusive quality assessment metric for noise-suppressed speech is to assess the quality of a noise-suppressed signal in the absence of any clean reference signal. As per the ITU-T P.835 recommendations, the quality assessment of noise-suppressed speech involves predicting three quality scores, namely, signal quality, background quality, and overall quality score, and hence, considered in this study. In recent literature, the non-intrusive quality assessment problem is presented as a regression problem, in which the mapping between a set of acoustic features and corresponding quality scores is found using a perceptual model. Recently, we proposed the use of Deep Autoencoder (DAE) features and Subband Autoencoder (SBAE) features for acoustic representation and an Artificial Neural Network (ANN) as a regression model. DAE and SBAE are variants of autoencoder architecture that have bottleneck structure in the hidden layers. Such architecture represents the class of generalized nonlinear Principal Component Analysis (PCA) that guarantees reconstruction of the input features with arbitrary accuracy. Both the features (DAE and SBAE) are extracted using unsupervised deep learning architectures, and they demonstrated better performance than the state-of-the-art spectral feature set, namely, Mel Filterbank Energies (FBEs). In this paper, we present more detailed analysis of previously proposed features, i.e., DAE and SBAE features, and analyze the usefulness of these features in predicting signal as well as background quality scores in addition to the overall quality score. We compare the performance of all the three features with each other as well as with current ITU-T P.563 metric for non-intrusive speech quality assessment. The results of our experiments performed on NOIZEUS database suggest that DAE and SBAE features perform relatively better than the FBEs while predicting signal and overall quality. On the other hand, FBE features perform slightly better than the DAE and SBAE features in predicting the background quality. Moreover, another major contribution of this paper is that we employ an ANN to predict all the three quality scores simultaneously, and present the results. It was observed that using this approach, it is possible to predict all the three scores simultaneously with similar accuracy as that of predicting them individually.

Experimental Investigation on Low-Complexity Adaptive Equalizer Including RSOP Tracking and Phase Recovery for 112 Gb/s PDM-QPSK Transmission System

A low-complexity adaptive equalizer including equalization, rotation of state of polarization (RSOP) tracking, and phase recovery is proposed for coherent optical polarization-division-multiplexing (PDM) quadrature phase-shifting keying (QPSK) transmission system. A conventional N-tap 2 × 2 butterfly finite impulse response filter is simplified to two N-tap filters and a 1-tap 2 × 2 filter. Two N-tap filters could compensate for inter-symbol interference and residual chromatic dispersion based on the same error cost function from the power sum of two polarization coupling constant modulus signals. 1-tap 2 × 2 filter which works on the nonlinear principal component analysis (NPCA) criterion is designed for joint polarization demultiplexing and phase recovery. NPCA is proved to not only void the singularity problem in the constant modulus algorithm (CMA) but also has faster tracking capability. Two kinds of adaptive equalizers using least mean squares NPCA (LMS-NPCA) and recursive least squares NPCA (RLS-NPCA) are compared in our simulation and experiment. In an experiment of 112 Gb/s PDM-QPSK transmission over 50 km standard single-mode fiber, the proposed two schemes have better transmission performance at RSOP speed of 1 Mrad/s and 5 Mrad/s compared to the conventional CMA and Viterbi-Viterbi phase estimation (VVPE) scheme. The reduced complexity of the proposed schemes is more than 40%.

Happiness Inequality Among a Sample of Iranian Older Population

Abstract. This study evaluates the happiness inequality among older Iranians using concentration index analysis. A total of 739 people aged 60–90 years completed the Oxford Happiness Inventory (OHI) questionnaire. The SES variables were constructed using nonlinear principal component analysis (NLPCA) based on all related variables. The multivariate logistic regression analysis showed that persons in the SES quintiles 3–4, urban dwellers, literate, and with no underlying disease had higher odds of happiness than others. Based on the estimated concentration indices, there was inequality in happiness based on SES levels (concentration index [95% confidence Interval]: 0.14 [0.10, 0.19]; p < .05). Our results revealed that happiness in the older population was probably more prevalent among people with higher SES levels.

Modeling and Bioinformatics Identify Responders to G-CSF in Patients With Amyotrophic Lateral Sclerosis.

Objective: Developing an integrative approach to early treatment response classification using survival modeling and bioinformatics with various biomarkers for early assessment of filgrastim (granulocyte colony stimulating factor) treatment effects in amyotrophic lateral sclerosis (ALS) patients. Filgrastim, a hematopoietic growth factor with excellent safety, routinely applied in oncology and stem cell mobilization, had shown preliminary efficacy in ALS.Methods: We conducted individualized long-term filgrastim treatment in 36 ALS patients. The PRO-ACT database, with outcome data from 23 international clinical ALS trials, served as historical control and mathematical reference for survival modeling. Imaging data as well as cytokine and cellular data from stem cell analysis were processed as biomarkers in a non-linear principal component analysis (NLPCA) to identify individual response.Results: Cox proportional hazard and matched-pair analyses revealed a significant survival benefit for filgrastim-treated patients over PRO-ACT comparators. We generated a model for survival estimation based on patients in the PRO-ACT database and then applied the model to filgrastim-treated patients. Model-identified filgrastim responders displayed less functional decline and impressively longer survival than non-responders. Multimodal biomarkers were then analyzed by PCA in the context of model-defined treatment response, allowing identification of subsequent treatment response as early as within 3 months of therapy. Strong treatment response with a median survival of 3.8 years after start of therapy was associated with younger age, increased hematopoietic stem cell mobilization, less aggressive inflammatory cytokine plasma profiles, and preserved pattern of fractional anisotropy as determined by magnetic resonance diffusion tensor imaging (DTI-MRI).Conclusion: Long-term filgrastim is safe, is well-tolerated, and has significant positive effects on disease progression and survival in a small cohort of ALS patients. Developing and applying a model-based biomarker response classification allows use of multimodal biomarker patterns in full potential. This can identify strong individual treatment responders (here: filgrastim) at a very early stage of therapy and may pave the way to an effective individualized treatment option.

Forecasting agricultural product logistics demand by nonlinear principal component analysis and a support vector machine optimised by the grey wolf optimiser

Forecasting agricultural product logistics demand by nonlinear principal component analysis and a support vector machine optimised by the grey wolf optimiser

Fault Detection and Identification Based on Explicit Polynomial Mapping and Combined Statistic in Nonlinear Dynamic Processes

Single traditional multivariate statistical monitoring methods, such as principal component analysis (PCA) and canonical variate analysis (CVA), are less effective in nonlinear dynamic processes. Monitoring approaches based on radial basis kernel function have been intensively applied. However, an infinite dimension nonlinear mapping is redundant and inefficient. To improve the efficiency of traditional methods and consider the nonlinearity and dynamics simultaneously, this paper proposes canonical variate nonlinear principal component analysis (CV-NPCA) based on explicit polynomial mapping and combined statistic for detecting and identifying faults in nonlinear dynamic processes. There are two main contributions of the proposed method. First, explicit second-order polynomial mapping is introduced to combine CVA with PCA to simultaneously decrease the adverse effects of nonlinearity and dynamics. Second, the $Q_{c}$ statistic combining residual vectors with residual components is proposed, and a two-dimensional (2D) contribution plot and the variable with the largest contribution based on the $Q_{c}$ statistic are given for fault identification in the simulation study. Compared with the results of PCA, CVA, kernel principal component analysis (KPCA), nonlinear dynamic principal component analysis (NDPCA) and kernel entropy component analysis (KECA), the proposed method not only has relatively higher fault detection rates and identification rates but also has lower false alarm rates in the numerical simulation process and the benchmark Tennessee Eastman process.

Data-based reduced-order modeling of nonlinear two-time-scale processes

This work focuses on data-based reduced-order modeling of nonlinear processes that exhibit time-scale multiplicity. Using time-series data from all the state variables of a nonlinear process, an approach that involves nonlinear principal component analysis and neural network function approximators is employed to identify the fast and slow process state variables as well as compute a nonlinear slow manifold function approximation in which the fast variables are “slaved” in terms of the slow variables. Subsequently, a nonlinear sparse identification approach is employed to calculate a dynamic model of nonlinear first-order ordinary differential equations that describe the temporal evolution of the slow process states. The method is applied to two chemical process examples, and the advantages of the proposed method over using only sparse identification for the original two-time-scale process are discussed. The approach can be thought of as a data-based analogue of the classical singular perturbation modeling of two-time-scale processes where explicit time-scale separation is assumed (and expressed in terms of a small positive parameter ε multiplying the time derivative of the fast states), and the reduced-order slow subsystem is calculated analytically.

Noise Analysis Method of Radiated EMI based on Non-linear Principal Component Analysis

Aiming at the radiated electromagnetic interference (EMI) noise of electronic equipment, a novel method of radiated EMI noise analysis based on non-linear principal component analysis (NLPCA) algorithm is proposed in this paper. In order to obtain multiple independent common-mode / differential-mode radiated sources, and to find the sources that cause the radiated noises that exceed the limit of standard, NLPCA algorithm is used to process the near-field radiated signals superimposed by multiple radiated sources. The simulation results show that NLPCA can successfully screen out the radiated EMI noises which exceed the limit of standard. Moreover, the experiments are carried out with three models: double-common-mode hybrid sources, double-differential-mode hybrid sources and common-differential-mode hybrid sources. Compared with the traditional independent component algorithm (ICA), the method proposed in this paper can separate the radiated EMI noise sources more accurately and quickly. It can be concluded that the accuracy of NLPCA algorithm is 10% higher than ICA algorithm. This work will contribute to trace the radiated EMI noise sources, and to provide the theoretical basis for the future suppression.

A nonlinear full condition process monitoring method for hot rolling process with dynamic characteristic

As a typical complex industrial process, hot rolling process (HRP) is different from chemical process. Strip steels are produced coil by coil, that means there is a long idle period between coils. The rolling speed is very high and the producing time of each coil is usually a few minutes. Previous researches mostly focus on fault detection in loaded condition and very few attempts have been made to exploit the monitoring of idle condition. In order to monitor the whole process, not only the loaded condition, but also the idle one, a novel nonlinear full condition process monitoring model is developed in this work. First, a dissimilarity index (DI) is defined for condition identification and a support data vector description (SVDD) model is established to monitor the idle condition. Second, t-distributed stochastic neighbor embedding (t-SNE) is used to extract nonlinear principal components (NPC) for slow feature analysis (SFA) and cointegration analysis (CA). Nonlinear cointegration analysis (NCA) can reveal the long-run dynamic relations of nonstationary parts, while nonlinear slow feature analysis (NSFA) can extract the latent temporal dynamic and static variations of stationary ones. Finally, the monitoring performance of the proposed model is verified through a real HRP.

Phenotypic Divergence Analysis in Pigeonpea [Cajanus cajan (L.) Millspaugh] Germplasm Accessions

Pigeonpea (Cajanus cajan (L.) Millspaugh) is an important source of grain protein for low-income countries such as Malawi. Knowledge of the genetic diversity in pigeonpea is essential for an effective breeding program. The study objective was to assess the genetic diversity among diverse pigeonpea accessions to select complementary and unique genotypes for breeding. Eighty-one pigeonpea accessions were evaluated in six environments in Malawi using a 9 × 9 alpha-lattice design with two replications. The cross-tabulation analysis revealed a significant genotype variation on plant growth, flower, and seed traits. The combined analysis of variance identified genotypes MWPLR 14, ICEAP 01170, ICEAP 871091, and ICEAP 01285 as early maturing varieties, while Kachangu, MWPLR 16, TZA 5582, No. 40, and MWPLR 14 were identified as high-yielding genotypes. The correlation analysis revealed a significant positive correlation between grain yield and a hundred seed weight (HSWT) (r = 0.50, p < 0.01), suggesting the usefulness of this trait for selection. The nonlinear principal component analysis identified grain yield (GDY), days to 50% flowering (DTF), days to 75% maturity (DTM), number of pods per plant (NPP), number of racemes per plant (NRP), 100 seed weight (HSWT), leaf hairiness (LH), and number of seeds per pod (NSP) as the most discriminated traits among the test genotypes. The cluster analysis using morphological traits delineated the accessions into three clusters. The selected high-yielding and early-maturing genotypes may be recommended as parental lines for breeding and grain yield improvement in Malawi or similar agro-ecologies.

Data-Driven Incipient Fault Detection via Canonical Variate Dissimilarity and Mixed Kernel Principal Component Analysis

Incipient fault detection plays a crucial role in preventing the occurrence of serious faults or failures in industrial processes. In most industrial processes, linear, and nonlinear relationships coexist. To improve fault detection performance, both linear and nonlinear features should be considered simultaneously. In this article, a novel hybrid linear-nonlinear statistical modeling approach for data-driven incipient fault detection is proposed by closely integrating recently developed canonical variate dissimilarity analysis and mixed kernel principal component analysis (MKPCA) using a serial model structure. Specifically, canonical variate analysis (CVA) is first applied to estimate the canonical variables (CVs) from the collected process data. Linear features are extracted from the estimated CVs. Then, the canonical variate dissimilarity (CVD) which quantifies model residuals in the CVA state-subspace is calculated using the estimated CVs. To explore the nonlinear features, the nonlinear principal components are extracted as nonlinear features through performing MKPCA on CVD. Fault detection indices are formed based on Hotelling's T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> as well as Q statistics from the extracted linear and nonlinear features. Moreover, kernel density estimation is utilized to determine the control limits. The effectiveness of the proposed method is demonstrated by the comparisons with other relevant methods via simulations based on a closed-loop continuous stirred-tank reactor process.

Monthly Rainfall Anomalies Forecasting for Southwestern Colombia Using Artificial Neural Networks Approaches

Improving the accuracy of rainfall forecasting is relevant for adequate water resources planning and management. This research project evaluated the performance of the combination of three Artificial Neural Networks (ANN) approaches in the forecasting of the monthly rainfall anomalies for Southwestern Colombia. For this purpose, we applied the Non-linear Principal Component Analysis (NLPCA) approach to get the main modes, a Neural Network Autoregressive Moving Average with eXogenous variables (NNARMAX) as a model, and an Inverse NLPCA approach for reconstructing the monthly rainfall anomalies forecasting in the Andean Region (AR) and the Pacific Region (PR) of Southwestern Colombia, respectively. For the model, we used monthly rainfall lagged values of the eight large-scale climate indices linked to the El Niño Southern Oscillation (ENSO) phenomenon as exogenous variables. They were cross-correlated with the main modes of the rainfall variability of AR and PR obtained using NLPCA. Subsequently, both NNARMAX models were trained from 1983 to 2014 and tested for two years (2015–2016). Finally, the reconstructed outputs from the NNARMAX models were used as inputs for the Inverse NLPCA approach. The performance of the ANN approaches was measured using three different performance metrics: Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Pearson’s correlation (r). The results showed suitable forecasting performance for AR and PR, and the combination of these ANN approaches demonstrated the possibility of rainfall forecasting in these sub-regions five months in advance and provided useful information for the decision-makers in Southwestern Colombia.

A privacy protection solution based on NLPCA for blockchain supply chain financial system

Many supply chain finance problems can be fundamentally solved by using blockchain. The current technical challenge of applying blockchain in supply chain finance is the lack of systematic privacy protection architecture. Based on the architecture of Julongchain, through the nonlinear principal component analysis in private data feature extraction, this paper proposed a new type of privacy protection architecture based on specific supply chain financial system. This privacy protection solution split privacy data by decision machine, then mixed data using mixed mechanism, finally determined the characteristic weight of privacy data by applying the decentralized decision institution.

Prediction of AOD data by geographical and temporal weighted regression with nonlinear principal component analysis

When predicting aerosol optical depth (AOD) values for geographical weighted regression (GWR) and geographical and temporal weighted regression (GTWR), the input variables are influenced by multiple collinearity. Additionally, too many input variables make the model computationally complex, and too few input variables can reduce the prediction accuracy. In this study, a nonlinear principal component analysis geographical weighted regression method (NLPCA-GWR) and a nonlinear principal component analysis geographical and temporal weighted regression method (NLPCA-GTWR) are proposed. The NLPCA-GWR and NLPCA-GTWR methods use nonlinear principal component analysis (NLPCA) to reduce the dimensionality of several related variables that influence the AOD and to obtain several comprehensive indicators. The obtained comprehensive indicators are used as dependent variables that are input into the GWR and GTWR models to predict AOD values. To test the effectiveness of the NLPCA-GWR and NLPCA-GTWR methods, this paper uses Beijing, Tianjin, and Hebei AOD data from April 2015; air quality data; meteorological data; and geospatial data as experimental data to model and compare the GWR and GTWR methods with the same number of input variables. The results show that the MAE, RMSE, AIC, R2, and $$ {R}_{\mathrm{j}}^2 $$ of the NLPCA-GWR method are 13.58%, 6.99%, 13.86%, 4.07%, and 3.96% higher, respectively, than those of the GWR method. Compared with the GTWR method, the NLPCA-GTWR method improved the MAE, RMSE, AIC, R2, and $$ {R}_{\mathrm{j}}^2 $$ by 6.53%, 2.91%, 2.17%, 1.14%, and 1.14%, respectively.