Residual Graph Research Articles

A New Approach to Multiroot Vectorial Problems: Highly Efficient Parallel Computing Schemes

In this article, we construct an efficient family of simultaneous methods for finding all the distinct as well as multiple roots of polynomial equations. Convergence analysis proves that the order of convergence of newly constructed family of simultaneous methods is seventeen. Fractal-based simultaneous iterative algorithms are thoroughly examined. Using self-similar features, fractal-based simultaneous schemes can converge to solutions faster, saving computational time and resources necessary for solving nonlinear equations. Fractals analysis illustrates the newly developed method’s global convergence behavior when compared to single root-finding procedures for solving fractional order polynomials that arise in complex engineering applications. Some real problems from various branches of engineering along with some higher degree polynomials are considered as test examples to show the global convergence property of simultaneous methods, performance and efficiency of the proposed family of methods. Further computational efficiencies, CPU time and residual graphs are also drawn to validate the efficiency, robustness of the newly introduced family of methods as compared to the existing methods in the literature.

Prediction of lncRNA and disease associations based on residual graph convolutional networks with attention mechanism

LncRNAs are non-coding RNAs with a length of more than 200 nucleotides. More and more evidence shows that lncRNAs are inextricably linked with diseases. To make up for the shortcomings of traditional methods, researchers began to collect relevant biological data in the database and used bioinformatics prediction tools to predict the associations between lncRNAs and diseases, which greatly improved the efficiency of the study. To improve the prediction accuracy of current methods, we propose a new lncRNA-disease associations prediction method with attention mechanism, called ResGCN-A. Firstly, we integrated lncRNA functional similarity, lncRNA Gaussian interaction profile kernel similarity, disease semantic similarity, and disease Gaussian interaction profile kernel similarity to obtain lncRNA comprehensive similarity and disease comprehensive similarity. Secondly, the residual graph convolutional network was used to extract the local features of lncRNAs and diseases. Thirdly, the new attention mechanism was used to assign the weight of the above features to further obtain the potential features of lncRNAs and diseases. Finally, the training set required by the Extra-Trees classifier was obtained by concatenating potential features, and the potential associations between lncRNAs and diseases were obtained by the trained Extra-Trees classifier. ResGCN-A combines the residual graph convolutional network with the attention mechanism to realize the local and global features fusion of lncRNA and diseases, which is beneficial to obtain more accurate features and improve the prediction accuracy. In the experiment, ResGCN-A was compared with five other methods through 5-fold cross-validation. The results show that the AUC value and AUPR value obtained by ResGCN-A are 0.9916 and 0.9951, which are superior to the other five methods. In addition, case studies and robustness evaluation have shown that ResGCN-A is an effective method for predicting lncRNA-disease associations. The source code for ResGCN-A will be available at https://github.com/Wangxiuxiun/ResGCN-A.

A residual graph convolutional network for setting initial flow field in computational fluid dynamics simulations

The computational cost of computational fluid dynamics (CFD) simulation is relatively high due to its computational complexity. To reduce the computing time required by CFD, researchers have proposed various methods, including efficient time advancement methods, correction methods for discrete control equations, multigrid methods, reasonable initial field setting methods, and parallel methods. Among these methods, the initial field setting method can provide significant performance improvements, but there is little work on it. Existing CFD industrial software typically uses inflow conditions for the initial flow field or applies empirical methods, which can cause instability in the CFD calculation process and make convergence difficult. With the rapid development of deep learning, researchers are increasingly attempting to replace CFD simulations with deep neural networks and have achieved significant performance improvements. However, these methods still face some challenges. First, they can only predict the computational flow field on regular grids. They cannot directly make predictions for irregular grids such as multi-block grids and unstructured grids, so the final flow field can only be obtained through interpolation and similar methods. Second, although these methods have been claimed to provide high accuracy, there is still a significant gap in performance with CFD and they cannot yet be applied to real scenarios. To address these issues, we propose a Residual Graph Convolutional Network for Initial Flow Field Setting (RGCN-IFS) in CFD simulations. This method converts the grid into a graph structure and uses an improved graph neural network to predict the flow field. In this way, we can predict the flow field on any type of grid. More importantly, this method does not directly replace CFD simulations, but it rather serves in an auxiliary role, providing appropriate initial flow fields for the CFD calculations, improving the convergence efficiency while ensuring calculation accuracy, and directly bridging the accuracy gap between intelligent surrogate models and CFD simulations.

Supervised graph contrastive learning for cancer subtype identification through multi-omics data integration.

Cancer is one of the most deadly diseases in the world. Accurate cancer subtype classification is critical for patient diagnosis, treatment, and prognosis. Ever-increasing multi-omics data describes the characteristics of the patients from different views and serves as complementary information to promote cancer subtype identification. However, omics data generally have different distributions and high dimensions. How to effectively integrate multiple omics data to classify cancer subtypes accurately is a challenge for researchers. This work proposes a method integrating multi-omics data based on supervised graph contrast learning (MCRGCN) to classify cancer subtypes. The method considers the unique feature distribution of each omics data and the interaction of different omics data features to improve the accuracy of cancer subtype classification. To achieve this, MCRGCN first constructs different sample networks based on the multi-omics data of the samples. Then, it puts the omics data and adjacency matrix of the sample into different residual graph convolution models to get multi-omics features of the samples, which are trained with a supervised comparison loss to maintain that the sample features of each omics should be as consistent as possible. Finally, we input the sample features combining multi-omics features into a classifier to obtain the cancer subtypes. We applied MCRGCN to the invasive breast carcinoma (BRCA) and glioblastoma multiforme (GBM) datasets, integrating gene expression, miRNA expression, and DNA methylation data. The results demonstrate that our model is superior to other methods in integrating multi-omics data. Moreover, the results of survival analysis experiments demonstrate that the cancer subtypes identified by our model have significant clinical features. Furthermore, our model can help to identify potential biomarkers and pathways associated with cancer subtypes.

Residual graph transformer for autism spectrum disorder prediction

Brain functional connectivity (FC) based on resting-state functional magnetic resonance imaging (rs-fMRI) has been in vogue to predict Autism Spectrum Disorder (ASD), which is a neuropsychiatric disease up the plight of locating latent biomarkers for clinical diagnosis. Albeit massive endeavors have been made, most studies are fed up with several chronic issues, such as the intractability of harnessing the interaction flourishing within brain regions, the astriction of representation due to vanishing gradient within deeper network architecture, and the poor interpretability leading to unpersuasive diagnosis. To ameliorate these issues, a FC-learned Residual Graph Transformer Network, namely RGTNet, is proposed. Specifically, we design a Graph Encoder to extract temporal-related features with long-range dependencies, from which interpretable FC matrices would be modeled. Besides, the residual trick is introduced to deepen the GCN architecture, thereby learning the higher-level information. Moreover, a novel Graph Sparse Fitting followed by weighted aggregation is proposed to ease dimensionality explosion. Empirically, the results on two types of ABIDE data sets demonstrate the meliority of RGTNet. Notably, the achieved ACC metric reaches 73.4%, overwhelming most competitors with merely 70.9% on the AAL atlas using a five-fold cross-validation policy. Moreover, the investigated biomarkers concord closely with the authoritative medical knowledge, paving a viable way for ASD-clinical diagnosis. Our code is available at https://github.com/CodeGoat24/RGTNet.

A Multi-Scale Residual Graph Convolution Network with hierarchical attention for predicting traffic flow in urban mobility

Accurate prediction of traffic flow is essential for optimizing transportation resource allocation and enhancing urban mobility efficiency. However, traffic data generated daily are vast and complex, involving dynamic and intricate changes in the traffic road network and traffic flow. Therefore, real-time and accurate prediction of traffic flow is a challenging task that requires modeling the intricate spatial–temporal dynamics of traffic data. In this paper, we propose a novel approach for traffic flow prediction, based on a Multi-Scale Residual Graph Convolution Network with hierarchical attention. First, we design a novel encoder–decoder with multi-independent channels to capture traffic flow information from different time scales and diverse temporal dependencies. Second, we employ a coupled graph convolution network with residual graph attention to dynamically learn the varying spatial features among and within traffic stations. Third, we utilize channel attention to fuse the multi-scale spatial–temporal dependencies and accurately predict traffic flow. We evaluate the proposed approach on multiple benchmark datasets, and the experimental results demonstrate its superior performance compared to state-of-the-art approaches in terms of various metrics.

SolPredictor: Predicting Solubility with Residual Gated Graph Neural Network.

Computational methods play a pivotal role in the pursuit of efficient drug discovery, enabling the rapid assessment of compound properties before costly and time-consuming laboratory experiments. With the advent of technology and large data availability, machine and deep learning methods have proven efficient in predicting molecular solubility. High-precision in silico solubility prediction has revolutionized drug development by enhancing formulation design, guiding lead optimization, and predicting pharmacokinetic parameters. These benefits result in considerable cost and time savings, resulting in a more efficient and shortened drug development process. The proposed SolPredictor is designed with the aim of developing a computational model for solubility prediction. The model is based on residual graph neural network convolution (RGNN). The RGNNs were designed to capture long-range dependencies in graph-structured data. Residual connections enable information to be utilized over various layers, allowing the model to capture and preserve essential features and patterns scattered throughout the network. The two largest datasets available to date are compiled, and the model uses a simplified molecular-input line-entry system (SMILES) representation. SolPredictor uses the ten-fold split cross-validation Pearson correlation coefficient R2 0.79±0.02 and root mean square error (RMSE) 1.03±0.04. The proposed model was evaluated using five independent datasets. Error analysis, hyperparameter optimization analysis, and model explainability were used to determine the molecular features that were most valuable for prediction.

RGCNPPIS: A Residual Graph Convolutional Network for Protein-Protein Interaction Site Prediction.

Accurate identification of protein-protein interaction (PPI) sites is crucial for understanding the mechanisms of biological processes, developing PPI networks, and detecting protein functions. Currently, most computational methods primarily concentrate on sequence context features and rarely consider the spatial neighborhood features. To address this limitation, we propose a novel residual graph convolutional network for structure-based PPI site prediction (RGCNPPIS). Specifically, we use a GCN module to extract the global structural features from all spatial neighborhoods, and utilize the GraphSage module to extract local structural features from local spatial neighborhoods. To the best of our knowledge, this is the first work utilizing local structural features for PPI site prediction. We also propose an enhanced residual graph connection to combine the initial node representation, local structural features, and the previous GCN layer's node representation, which enables information transfer between layers and alleviates the over-smoothing problem. Evaluation results demonstrate that RGCNPPIS outperforms state-of-the-art methods on three independent test sets. In addition, the results of ablation experiments and case studies confirm that RGCNPPIS is an effective tool for PPI site prediction.

ResGAT: A Residual Graph Attention Network for Lithology Identification

ResGAT: A Residual Graph Attention Network for Lithology Identification

ST-ReGE: A Novel Spatial-Temporal Residual Graph Convolutional Network for CVD.

Recently, deep learning (DL) has enabled rapid advancements in electrocardiogram (ECG)-based automatic cardiovascular disease (CVD) diagnosis. Multi-lead ECG signals have lead systems based on the potential differences between electrodes placed on the limbs and the chest. When applying DL models, ECG signals are usually treated as synchronized signals arranged in Euclidean space, which is the abstraction and generalization of real space. However, conventional DL models typically merely focus on temporal features when analyzing Euclidean data. These approaches ignore the spatial relationships of different leads, which are physiologically significant and useful for CVD diagnosis because different leads represent activities of specific heart regions. These relationships derived from spatial distributions of electrodes can be conveniently created in non-Euclidean data, making multi-lead ECGs better conform to their nature. Considering graph convolutional network (GCN) adept at analyzing non-Euclidean data, a novel spatial-temporal residual GCN for CVD diagnosis is proposed in this work. ECG signals are firstly divided into single-channel patches and transferred into nodes, which will be connected by spatial-temporal connections. The proposed model employs residual GCN blocks and feed-forward networks to alleviate over-smoothing and over-fitting. Moreover, residual connections and patch dividing enable the capture of global and detailed spatial-temporal features. Experimental results reveal that the proposed model achieves at least a 5.85% and 6.80% increase in F1 over other state-of-the-art algorithms with similar parameters and computations in both PTB-XL and Chapman databases. It indicates that the proposed model provides a promising avenue for intelligent diagnosis with limited computing resources.

CylinGCN: Cylindrical structures segmentation in 3D biomedical optical imaging by a contour-based graph convolutional network

Cylindrical organs, e.g., blood vessels, airways, and intestines, are ubiquitous structures in biomedical optical imaging analysis. Image segmentation of these structures serves as a vital step in tissue physiology analysis. Traditional model-driven segmentation methods seek to fit the structure by constructing a corresponding topological geometry based on domain knowledge. Classification-based deep learning methods neglect the geometric features of the cylindrical structure and therefore cannot ensure the continuity of the segmentation surface. In this paper, by treating the cylindrical structures as a 3D graph, we introduce a novel contour-based graph neural network for 3D cylindrical structure segmentation in biomedical optical imaging. Our proposed method, which we named CylinGCN, adopts a novel learnable framework that extracts semantic features and complex topological relationships in the 3D volumetric data to achieve continuous and effective 3D segmentation. Our CylinGCN consists of a multiscale 3D semantic feature extractor for extracting inter-frame multiscale semantic features, and a residual graph convolutional network (GCN) contour generator that combines the semantic features and cylindrical topological priors to generate segmentation contours. We tested the CylinGCN framework on two types of optical tomographic imaging data, small animal whole body photoacoustic tomography (PAT) and endoscopic airway optical coherence tomography (OCT), and the results show that CylinGCN achieves state-of-the-art performance. Code will be released at https://github.com/lzc-smu/CylinGCN.git.

Dynamic Generative Residual Graph Convolutional Neural Networks for Electricity Theft Detection

Dynamic Generative Residual Graph Convolutional Neural Networks for Electricity Theft Detection

Ocean Wind Speed Prediction Based on the Fusion of Spatial Clustering and an Improved Residual Graph Attention Network

Accurately predicting wind speed is crucial for the generation efficiency of offshore wind energy. This paper proposes an ultra-short-term wind speed prediction method using a graph neural network with a multi-head attention mechanism. The methodology aims to effectively explore the spatio-temporal correlations present in offshore wind speed data to enhance the accuracy of wind speed predictions. Initially, the offshore buoys are organized into a graphical network. Subsequently, in order to cluster the nodes with comparable spatio-temporal features, it clusters the nearby nodes around the target node. Then, a multi-head attention mechanism is incorporated to prioritize the interconnections among distinct regions. In the construction of the graph neural network, a star topology structure is formed by connecting additional nodes to the target node at the center. The effectiveness of this methodology is validated and compared to other time series-based approaches through comparative testing. Metrics such as Mean Absolute Error, Mean Squared Error, Root Mean Squared Error, and R yielded values of 0.364, 0.239, 0.489, and 0.985, respectively. The empirical findings indicate that graph neural networks utilizing a multi-head attention mechanism exhibit notable benefits in the prediction of offshore wind speed, particularly when confronted with intricate marine meteorological circumstances.

Incidence and predictors of treatment interruption among patients on anti-tuberculosis treatment in Nekemte public healthcare facilities, Oromia, Western Ethiopia.

Tuberculosis treatment interruption increases the risk of poor treatment outcomes and the occurrence of drug resistant Tuberculosis. However, data on the incidence and predictors of tuberculosis treatment interruption are still scarce in Ethiopia, as well as in the study area. Therefore, this study aimed to assess the incidence and predictors of treatment interruption among patients on tuberculosis treatment in Nekemte public healthcare facilities, Oromia region, Western Ethiopia, from July 1, 2017, to June 30, 2021. A retrospective cohort study design was conducted among 800 patients enrolled in anti-tuberculosis treatment during the study period. Data were collected from patient cards who were enrolled in treatment from July 1, 2017 to June 30, 2021. Epidata version 3.2 was used for data entry, and STATA version 14 was used for analysis. A multivariable Cox regression model with a 95% confidence interval (CI) and adjusted hazard ratio (AHR) was used to identify the significant predictors at a p value < 0.05. Finally, the log likelihood ratio, and a Cox-Snell residual graph was used to check the adequacy of the model. A total of 800 patients were followed for a median time of 2.3 (95% CI: 2.20-2.36) months, and with a maximum follow-up time of 11.7 months. The overall incidence rate of treatment interruption was 27.4 per 1000 (95% CI: 22.8-32.8) person-month observations. Age 18-34 years (AHR = 1.8, 95% CI: 1.02-3.18), male (AHR = 1.63, 95% CI: 1.1-2.42), rural residence (AHR = 3, 95% CI: 1.98-4.64), presence of comorbidity (AHR = 10, 95% CI: 5.47-18.27) and lack of treatment supporters on the treatment follow-up (AHR = 2.82, 95% CI: 1.9-4.41) were found to be significant predictors of treatment interruption. A high incidence rate of interruption was observed among TB patients in public health facilities in Nekemte town. Health facilities should provide supportive care for patients with co-morbidities and consider interventions that target middle-aged patients from rural areas that reduce treatment interruptions.

Residual GCB-Net: Residual Graph Convolutional Broad Network on Emotion Recognition

Electroencephalogram (EEG) data is commonly applied in the emotion recognition research area. It can accurately reflect the emotional changes of the human body by applying graphical-based algorithms or models. EEG signals are non-linear signals. Biological tissues’ adjustment and adaptive ability will inevitably affect electrophysiological signals, making EEG have the typical non-linear characteristics. Graph Convolutional Broad Network (GCB-net) extracted features from non-linear signals and abstract features via stacked CNN. It adopted the broad concept and enhanced the feature by the broad learning system (BLS), obtaining sound results. However, it performed poorly with increasing network depth, and the accuracy of some features decreased with BLS. This paper proposed a Residual Graph Convolutional Broad Network (Residual GCB-net), which promotes the performance on a deeper-layer network and extracts higher-level information. It substitutes the original convolutional layer with residual learning blocks, which solves the deep learning network degradation and extracts more features in deeper networks. In SEED data set, GCB-Res net could obtain the best accuracy (94.56%) on the all-frequency band of differential entropy (DE) and promote much on another feature. In Dreamer, it obtained the best accuracy (91.55%) on the dimension of Arousal. The result demonstrated the excellent classification performance of Residual GCB-net in EEG emotion recognition.

MIPA-ResGCN: a multi-input part attention enhanced residual graph convolutional framework for sign language recognition

Sign language (SL) is used as primary mode of communication by individuals who experience deafness and speech disorders. However, SL creates an inordinate communication barrier as most people are not acquainted with it. To solve this problem, many technological solutions using wearable devices, video, and depth cameras have been put forth. The ubiquitous nature of cameras in contemporary devices has resulted in the emergence of sign language recognition (SLR) using video sequence as a viable and unobtrusive substitute. Nonetheless, the utilization of SLR methods based on visual features, commonly known as appearance-based methods, presents notable computational complexities. In response to these challenges, this study introduces an accurate and computationally efficient pose-based approach for SLR. Our proposed approach comprises three key stages: pose extraction, handcrafted feature generation, and feature space mapping and recognition. Initially, an efficient off-the-shelf pose extraction algorithm is employed to extract pose information of various body parts of a subject captured in a video. Then, a multi-input stream has been generated using handcrafted features, i.e., joints, bone lengths, and bone angles. Finally, an efficient and lightweight residual graph convolutional network (ResGCN) along with a novel part attention mechanism, is proposed to encode body's spatial and temporal information in a compact feature space and recognize the signs performed. In addition to enabling effective learning during model training and offering cutting-edge accuracy, the proposed model significantly reduces computational complexity. Our proposed method is assessed on five challenging SL datasets, WLASL-100, WLASL-300, WLASL-1000, LSA-64, and MINDS-Libras, achieving state-of-the-art (SOTA) accuracies of 83.33 %, 72.90 %, 64.92 %, 100± 0 %, and 96.70± 1.07 %, respectively. Compared to previous approaches, we achieve superior performance while incurring a lower computational cost.

Cloud-Graph: A feature interaction graph convolutional network for remote sensing image cloud detection

Convolutional neural networks (CNNs) have made significant progress in the field of cloud detection in remote sensing images thanks to their powerful feature representation capabilities. Existing methods typically aggregate low-level features containing details and high-level features containing semantics to make full use of both features to accurately detect cloud regions. However, CNNs are still limited in their ability to reason about the relationships between features, while not being able to model context well. To overcome this problem, this paper designs a novel feature interaction graph convolutional network model that extends the feature fusion process of convolutional neural networks from Euclidean space to non-Euclidean space. The algorithm consists of three main components: remote sensing image feature extraction, feature interaction graph reasoning, and high-resolution feature recovery. The algorithm constructs a feature interaction graph reasoning (FIGR) module to fully interact with low-level and high-level features and then uses a residual graph convolutional network to infer feature higher-order relationships. The network model effectively alleviates the problem of a semantic divide in the feature fusion process, allowing the aggregated features to fuse valuable details and semantic information. The algorithm is designed to better detect clouds with complex cloud layers in remote sensing images with complex cloud shape, size, thickness, and cloud-snow coexistence. Validated on publicly available 38-Cloud and SPARCS datasets and the paper’s own Landsat-8 cloud detection dataset with higher spatial resolution, the proposed method achieves competitive performance under different evaluation metrics. Code is available at https://github.com/HaiLei-Fly/CloudGraph.

A vulnerability detection algorithm based on residual graph attention networks for source code imbalance (RGAN)

It is essential to detect potential vulnerabilities in software to ensure its safety. As software systems become more complex, traditional static vulnerability detection methods perform poorly. Currently, deep learning-based vulnerability detection models only extract source code vulnerability features using sequences or graphs. Sequential neural networks ignore structural information in the code, such as control flow diagrams and data flow diagrams. Additionally, graph neural networks cannot accurately extract features due to the lack of effective methods for extracting nodes’ features and aggregating global information. To address the above issue, we propose a vulnerability detection algorithm based on residual graph attention networks for source code imbalance (RGAN). Firstly, a local feature extraction module (PE-BL-A module) is designed. Using the sequence neural network, the module extracts various useful features, including node features in a control flow diagram based on local semantic features. Secondly, we present the Residual Graph Attention Network module (RGAT). To learn and update node features along the control flow direction, the module uses a graph attention network with residual connections. In this module, a mean biaffine attention pooling mechanism is proposed that can extract total graph vulnerability features more effectively. Thirdly, a dynamic cross-entropy loss function is designed. Using this function, it can handle sample imbalances during training. Finally, experiments conducted on several benchmark datasets demonstrate that the proposed model achieves state-of-the-art results.

MC-RGN: Residual Graph Neural Networks based on Markov Chain for sequential recommendation

Sequential recommendation aims to predict the next item the user will interact with based on his/her historical interaction sequences. Existing sequential recommendation methods mainly use self-attention to capture the preferences with individual user–item historical interaction sequences, while ignoring the group preferences that are exhibited by all user–item interaction sequences. Besides, like general recommendation, data sparsity remains the main factor detrimentally affecting recommendation performance. To remedy the damage of data sparsity and improve the recommendation performance, we employ Residual connections and Graph Neural Networks based on Markov Chain to propose MC-RGN, which incorporates group preferences into a single user–item historical sequence. To demonstrate the effectiveness of the proposed method, extensive experiments were conducted on four real-world datasets, MovieLens, Sports, Yelp and Beauty. Experimental results showed that the proposed method achieved an average improvement of 14.32% on Hit@10 and 27.17% on NDCG@10 compared to the baseline models. To showcase whether the proposed method alleviates the negative impact of data sparsity on recommendation performance, we compared the recommendation performance decline of the SASRec and the proposed method under various levels of data sparsity. The results indicate that the proposed method notably reduced the damage caused by data sparsity (0.07% vs 20.94%, 2.37% vs 23.70%, 6.51% vs 27.01%, and 22.78% vs 28.42% at data usage ratios of 80%, 60%, 40%, and 20%, respectively). Finally, our proposed model is available via https://github.com/crx1729/MC-RGN.

PREDICTING SURFACE FOREST FUELS ON THE CERRADO IN CANTÃO STATE PARK FROM AIRBORNE RGB SENSOR IMAGES

Forest fuel quantification in a typical Cerrado area is difficult due to the high costs and long field times associated with collecting data. In search of alternatives that facilitate data collection, indirect estimation has been studied, resulting in local equations for predicting the load based on easily obtainable variables. In this context, we sought to develop local equations to estimate the load of forest fuel, in a Cerrado area, in the Cantão Park State – Tocantins. As a function of variables measured in the field and digital variables from the processing of RGB digital images (Red, Green and Blue) acquired through aerial surveys. With the processing of digital images, the following variables were extracted: mean height in the digital model (hMDA) and point density in the three-dimensional model (DPM). After the aerial survey, field sampling was carried out, collecting the following variables: mean height in the field (hc), number of individuals (Qti) and Total Fuel Material (MCT). Subsequently, equations were fitted, adopting the entire sample set. The model selection criterion was based on R²aj, Syx% and residual graph, in which adjusted coefficient of determination (R²aj) from 0.12 to 0.83 and residual standard error (Syx%) of 19.4 were obtained at 44%. It was observed that the use of control points performed by the MDA reduces the occurrence of errors, the correlations between the analyzed variables indicate the importance of considering multiple factors when performing analyzes and predictions in the study areas.