Maximal Information Coefficient Research Articles

Improving the efficiency of machine learning in simulating sedimentary heavy metal contamination by coupling preposing feature selection methods

Sediment cores were collected from Taihu Lake in China. The chronology was determined by radionuclide. Heavy metals and magnetic properties of each core slice were assessed, respectively. The concentrations of most heavy metals in sediments surged at 20 cm from the surface, accompanying the increase in the concentrations of single-domain magnetic particles. This may be resulted from the influence of anthropic activities on the lake's environment after the 1970s. Two feature selection methods, random forest (RF) and maximal information coefficient (MIC), were combined with support vector machine (SVM) model to simulate heavy metals, with the inclusion of selected magnetic and physicochemical parameters. Compared with the modeling results obtained with the full set of parameters, a reasonable simulation performance was obtained with RF and MIC. RF performed better than MIC by increasing the R2 of simulation models for Cd, Cr, Cu, Pb, and Sb. For heavy metals with high ecological risks (As, Cd, Cr, Hg, Pb, Sb), the correlation coefficients for observed and predicted data ranged from 0.73 to 0.97 with only 14–27% of the parameters selected by RF as input variables. The RF-RBF-SVM enabled heavy metal predictions based on the magnetic properties of the lake sediments.

A DES-BDNN based probabilistic forecasting approach for step-like landslide displacement

Accurate and reliable displacement prediction is very important for landslide early warning. However, various uncertainties contained in landslide displacement prediction will greatly affect the prediction accuracy, and reduce the credibility of prediction results. Probability prediction is an efficient way to assess the uncertainties associated landslide displacement and improve the reliability of prediction. This paper proposes a new probabilistic forecasting framework for landslide displacement based on exponential smoothing (DES) and Bayesian deep neural networks (BDNN), which can clearly distinguish the aleatoric uncertainty covered by the evolution of data itself and the epistemic uncertainty reflecting the unsteadiness of intelligent model. Therein, DES predicts the linear part contained in the total displacement, and BDNN predicts the residual nonlinear part. The optimal input features of BDNN model are determined by the maximum information coefficient and Pearson correlation coefficient. The Baishuihe landslide in the Three Gorges Reservoir area was selected to test the effectiveness of the proposed framework with three BDNN models, including Bayesian recurrent neural network (BRNN), Bayesian gated recurrent unit network (BGRU) and Bayesian long short-term memory network (BLSTM). The results suggest that the proposed framework can obtain considerable prediction effect, especially DES-BLSTM and DES-BGRU model. The variational mode decomposition (VMD) and interpolation are used to further optimize the DES-BDNN model from the perspective of reducing the complexity of nonlinear displacement and increasing training datasize. The comparison results show that the improved model can not only obtain high-precision point prediction results, but also accurately infer the total/aleatoric/epistemic uncertainty associated with landslide displacement prediction.

Predictive modeling for soft measurement of loader driveshaft torque based on large-scale distributed data

In view of the harsh working environment, high rotational speed and limited installation space of the loader drive shaft, etc. In this study, a soft measurement method of loader drive shaft torque with distributed sparse least squares support vector machine (DSLS-SVM) algorithm for large-scale data is proposed. Firstly, by analyzing the loader power transmission path, the features for predicting torque are determined. Secondly, irrelevant or redundant features are eliminated using the maximum information coefficient (MIC). Thirdly, the DSLS-SVM algorithm is tuned with the cuckoo search (CS) algorithm to realize the training and testing of the soft measurement model. Finally, to validate the feasibility and reliability, operating data are obtained from new in-service loaders. The test results show that the soft measurement method proposed can effectively characterize the torque under the operating condition, and is suitable for the long-term operating condition monitoring of the loader, which has good application value.

Multivariate Time-Series Prediction in Industrial Processes via a Deep Hybrid Network Under Data Uncertainty

With the rapid progress of the industrial Internet of Things (IIoT), reducing data uncertainty has become a critical issue in predicting the development trends of systems and formulating future maintenance strategies. This article proposes an end-to-end, deep hybrid network-based, short-term, multivariate time-series prediction framework for industrial processes. First, the maximal information coefficient is adopted to extract the nonlinear variate correlation features. Second, a convolutional neural network with a residual elimination module is designed to eliminate data uncertainty. Third, a bidirectional gated recurrent unit network is connected in a time-distributed form to achieve step-ahead prediction. Last, an optimized Bayesian optimization method is adopted to optimize the model's learning rate. A comparison with other state-of-the-art, deep learning-based, time-series prediction methods in the case study illustrates the superiority of the proposed framework in noisy IIoT environments.

Short-Term Forecasting Based on Graph Convolution Networks and Multiresolution Convolution Neural Networks for Wind Power

Accurate prediction of wind power generation is of great significance for the efficient operation of wind farms. However, traditional deep learning-based methods predict the wind power without simultaneously considering the temporal features of wind power and spatial features between variables, which leads to low prediction accuracy. This article proposes a novel wind power forecasting approach based on a graph convolution network (GCN) and a multiresolution convolution neural network (CNN), combining spatial features and temporal features. In this approach, GCN merged with maximum information coefficient (MIC) is proposed to extract the spatial correlation features between input variables, which considers the effects of multiple variables on wind power and provides interpretability for deep learning-based forecasting. On the other hand, multiresolution CNN combines multiscale convolution kernels with a new self-attention mechanism to understand local and long-term temporal features, which enables simultaneous prediction of wind power and other variables. Experiments on a real dataset prove that the proposed method is effective and accurate in short-term wind power forecasting. Comparisons with the other three state-of-the-art methods and ablation experiments also reveal the advantages of the proposed approach.

Comprehensive performance evaluation of high embankments in heavy-haul railways using an improved extension model with attribute reduction algorithm

Effectively evaluating high-embankment deformation and stability is important for heavy-haul railway safety. An improved extension model with an attribute reduction algorithm was proposed for the comprehensive evaluation method. First, a hierarchical evaluation system for high embankments in heavy-haul railways was established using the attribute reduction algorithm, which includes the principal component analysis, maximum information coefficient, coefficient of variation, and improved Dempster-Shafer evidence theory. Furthermore, the improved extension model was used to evaluate high-embankment performance in heavy-haul railways. In this improved extension model, the combination weighting method, an asymmetric proximity function, and the maximum membership principle effectiveness verification were used. Finally, three high embankments in a Chinese heavy-haul railway were studied. The results illustrate that the main influencing factors for high-embankment performance in a heavy-haul railway are annual rainfall, annual temperature, and 21 other indicators. The performance of the three embankments is level III (ordinary), level II (fine), and level III (ordinary), respectively, indicating that these embankments have generally unfavourable performance. The three embankments’ performance matches field measurements, and the proposed method outperforms the Fuzzy-AHP method, cloud model, and gray relational analysis. This study demonstrates the feasibility of the proposed method in assessing the high-embankment performance under heavy axle loads.

Prediction of the Critical Temperature of Superconductors Based on Two-Layer Feature Selection and the Optuna-Stacking Ensemble Learning Model.

The study of superconductors' critical temperature (T c) has been a matter of interest. A method combining a two-layer feature selection (TL) and Optuna-Stacking ensemble learning model is proposed in the study for predicting T c from physicochemical components. Since most machine-learning models require a large amount of prior knowledge to construct the feature vectors associated with T c manually, they may contain redundant or invalid features that adversely affect the analysis and prediction of T c. The TL model combines the advantages of filtered and packed feature selection. In the first layer, feature importance is ranked by "SHapley Additive explain (SHAP)" in combination with CatBoost, followed by maximum mutual information coefficient (MIC) and distance correlation coefficient (DCC) for initial feature selection in terms of feature importance ranking. The second layer uses a cross-validation-based genetic algorithm (cv-GA) to eliminate the remaining redundant/invalid features. The selected features are fed into the Stacking integrated learning model to achieve prediction of Tc, and the multidimensional hyperparametric optimization of the metamodel is achieved by Optuna, an improved Bayesian hyperparametric optimization framework based on the Tree-structured Parzen Estimator (TPE) and pruning strategy. The model has obvious advantages and generality in terms of prediction performance and feature reduction rate, and it also proves to be suitable for high-temperature superconductor T c prediction. It provides an efficient and cost-effective method for data-driven superconductor research.

Evidence Network Inference Recognition Method Based on Cloud Model

Uncertainty is widely present in target recognition, and it is particularly important to express and reason the uncertainty. Based on the advantage of the evidence network in uncertainty processing, this paper presents an evidence network reasoning recognition method based on a cloud fuzzy belief. In this method, a hierarchical structure model of an evidence network is constructed; the MIC (maximum information coefficient) method is used to measure the degree of correlation between nodes and determine the existence of edges, and the belief of corresponding attributes is generated based on the cloud model. In addition, the method of information entropy is used to determine the conditional reliability table of non-root nodes, and the target recognition under uncertain conditions is realized afterwards by evidence network reasoning. The simulation results show that the proposed method can deal with the random uncertainty and cognitive uncertainty simultaneously, overcoming the problem that the traditional method has where it cannot carry out hierarchical recognition, and it can effectively use sensor information and expert knowledge to realize the deep cognition of the target intention.

Stable versus fragile community structures in the correlation dynamics of Chinese industry indices

Correlation dynamics in the stock market is recently gained wide attention, especially its relationship to financial crises. This study examines the correlation dynamics of the Chinese market based on time series data of industry indices. We examine the dynamics of linear and nonlinear dependencies using PCC (Pearson correlation coefficient) and MIC (Maximal information coefficient), respectively. The influence-strength (IS) analysis showed that the former was more closely associated with major events. We analyse the structure of the correlation networks from both the short- and long-term perspectives. For the short-term perspective, we employ IS analysis to extract the time stamps of structural breaks in the correlation structure. The timestamps of critical events in the correlation dynamics usually correspond to major events in the real market, including the 2015 stock market crash in China. We construct a network for each correlation matrix to extract the main correlation structure and detect the community structure. We create the long-term community-based network based on community structure. The long-term community structure of the correlation dynamics has clear economic implications and is thus stable, whereas the short-term community structure is fragile. This study analyses the correlation dynamics in the Chinese market, which is valuable for asset allocation, such as identifying market states and investing in index funds.

Unsupervised Anomaly Detection for Intermittent Sequences Based on Multi-Granularity Abnormal Pattern Mining

In the actual maintenance of manufacturing enterprises, abnormal changes in after-sale parts demand data often make the inventory strategies unreasonable. Due to the intermittent and small-scale characteristics of demand sequences, it is difficult to accurately identify the anomalies in such sequences using current anomaly detection algorithms. To solve this problem, this paper proposes an unsupervised anomaly detection method for intermittent time series. First, a new abnormal fluctuation similarity matrix is built by calculating the squared coefficient of variation and the maximum information coefficient from the macroscopic granularity. The abnormal fluctuation sequence can then be adaptively screened by using agglomerative hierarchical clustering. Second, the demand change feature and interval feature of the abnormal sequence are constructed and fed into the support vector data description model to perform hypersphere training. Then, the unsupervised abnormal point location detection is realized at the micro-granularity level from the abnormal sequence. Comparative experiments are carried out on the actual demand data of after-sale parts of two large manufacturing enterprises. The results show that, compared with the current representative anomaly detection methods, the proposed approach can effectively identify the abnormal fluctuation position in the intermittent sequence of small samples, and also obtain better detection results.

A convolutional Transformer-based truncated Gaussian density network with data denoising for wind speed forecasting

Wind speed forecasting plays an important role in the stable operation of wind energy power systems. However, accurate and reliable wind speed forecasting faces four challenges: how to reduce the data noise; how to find the optimal model inputs; how to describe the complex fluctuations in wind speed; and how to design a suitable loss function to tune the forecasting model. This study proposes a novel forecasting model to address the four challenges mentioned above. First, it uses a wavelet soft threshold denoising method to reduce noise in the original wind speed time series. Second, it uses the maximal information coefficient, which measures the linear and nonlinear relationships between historical wind speed data and forecasted targets, to determine the optimal model inputs. Third, a novel convolutional Transformer-based truncated Gaussian density network is designed to characterize the complex fluctuations in wind speed. The multi-scale information from different convolutional layers is weighted using the self-attention mechanism and then fed into the Transformer network to extract temporal information. The outputs are mapped into the forecasted targets with several fully connected layers. Fourth, considering the non-negativity of wind speed, the truncated Gaussian distribution, which shows a probability of zero when the wind speed is less than zero, is employed to model the uncertainty of wind speed forecasts. This leads to designing a truncated Gaussian distribution-based loss function to train the forecasting model. The forecasting results on three real-world datasets show that the proposed model not only provides accurate deterministic wind speed forecasts but also produces reliable probabilistic wind speed forecasts. The hypothesis testing also illustrates the effectiveness of the proposed model for deterministic and probabilistic wind speed forecasting.

Research on the correlation between three-dimensional morphology and temperature changes in potato slices during drying

Drying is an effective method to reduce potato storage loss. However, potatoes have high porosity with high water content. Shrinkage during drying can lead to folding and cracking of the dried product form. Therefore, this study explored the correlation between the 3D morphology and temperature distribution changes of potato slices during drying, with the aim of providing a reference for the detection of quality changes. An online automatic acquisition device to obtain 3D morphology and temperature information was designed and built. Hot air-drying experiments were conducted on the potato slices. 3D morphology images and temperature images of the potato slices were acquired by 3D and temperature sensors, and the two images were registered using the random sample consensus (RANSAC) algorithm. The region of interest of each image was extracted by algorithms such as threshold segmentation, hole filling and morphological erosion, and the 3D morphology information and temperature information were obtained. The mapping, range and average of each acquisition point were calculated for correlation analysis. Spearman's rank correlation coefficients and Maximum Information Coefficient (MIC) values were selected as measures for the correlation study. The results showed that the Spearman's rank correlation coefficients between average height and average temperature were mostly above 0.7 in absolute value, and the MICs were mostly above 0.9. The average values of the 3D information and temperature information exhibited an extremely strong correlation. This paper gives a new approach to investigate the morphological changes in the drying process by quantifying the relationship between 3D morphology and temperature distribution. This can guide the improvement of potato drying and processing methods.

A Multitask Learning Model for the Prediction of NOx Emissions in Municipal Solid Waste Incineration Processes

Selective non-catalytic reduction (SNCR) is a commercially available technology that can effectively reduce the nitrogen oxides ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\mathrm {NO}}_{x}$ </tex-math></inline-formula> ) emissions in municipal solid waste incineration (MSWI) processes. Real-time measurement of NOx emissions is important to improve the denitration efficiency of SNCR. However, there are commonly time delays to obtain the measurement results from the traditional continuous emission monitoring system (CEMS). In this study, a prediction model based on multitask learning (MTL) is proposed for real-time measurement of NOx emissions. First, time delays are analyzed by using the maximum average cross-correlation function (MACCF) method, and sequences are adjusted according to the time delays, thereby recovering the original data pattern. Second, input variables are selected using a maximal information coefficient (MIC) method to reduce redundant information. Then, an MTL model is constructed for the prediction of NOx emissions. By using the MTL mechanism to share information of related prediction tasks, the potential correlations of industrial time-series data are mined, therefore improving the generalization performance of the model. Also, a self-organizing radial basis function neural network is designed as the module of the MTL model to further improve the prediction accuracy of the model. A strategy for incrementally constructing the MTL model is developed to guarantee the computational efficiency of the model. Finally, the established model is tested using a benchmark dataset and the real industrial data from an MSWI plant. The experimental results show that the proposed MTL model outperforms other state-of-the-art models on computational efficiency and prediction accuracy, demonstrating the potentiality of the MTL model in real-time measurement of NOx emissions in MSWI processes.

A Two-Stage Method for Ultra-Short-Term PV Power Forecasting Based on Data-Driven

To promote the real-time dispatching of a power grid and balanced decision-making of power producers, accuracy and real-time forecasting are two main problems that need to be solved in ultra-short-term photovoltaic (PV) forecasting. Focusing on the problems of slow model training speed and low forecasting accuracy due to the redundancy of training data samples and insufficient long periodic capture of data in complex weather, this paper proposes a two-stage method for ultra-short-term PV power forecasting based on data-driven. In the meteorological analysis stage, the generation power samples similar to the forecast day were extracted by inputting daily meteorological features and using maximal information coefficient (MIC) weighted grey correlation degree to form the corresponding forecast data set. In the power forecasting stage, the temporal convolutional used network (TCN) extracts local features to maintain the sequence of extracted features. Then the bidirectional gating unit (BiGRU) combined with the Skip connection strategy was used to fully learn the long and the short time sequence of photovoltaic sequences, and the attention mechanism was used to pay adaptive attention to the more important historical states. This study experimented on the measured data from a photovoltaic power station in Southeastern China. The experimental results show that this method is effective in photovoltaic power short-term forecasts. In addition, compared with some traditional forecasting models, this method has smaller forecasting errors and higher robustness in the time scales of 15 minutes, 30 minutes, 45 minutes, and 60 minutes.

Bidirectional Minimal Gated Unit-Based Nonlinear Dynamic Soft Sensor Modeling Framework for Quality Prediction in Process Industries

Quality prediction plays a crucial role in improving the product quality and economic benefit for modern process industries. The high-dimensional characteristics of process variables and the nonlinear dynamic behaviors of sequential data make the conventional soft sensor modeling approaches encounter difficulties. Towards this end, a novel nonlinear dynamic soft sensor modeling scheme is designed for quality prediction. It will offer a timely reference for judging product quality and adjusting production plans. Specifically, the maximum information coefficient is introduced for measuring the interdependencies between process and quality variables, and an evaluative criteria is designed for quality-related variable selection. Subsequently, a novel bidirectional minimal gated unit structure is proposed for nonlinear dynamic soft sensor modeling, of which the historical and future temporal information of production and quality features is fully used and integrated for quality prediction. In the end, the effectiveness and practicality of the proposed scheme is demonstrated via a challenging process industry, the hot rolling process. The simulation results indicate that the proposed method is superior to other competitive methods.

Upper Limb Cortical-Muscular Coupling Analysis Based on Time-Delayed Back Maximum Information Coefficient Model.

In musculoskeletal systems, describing accurately the coupling direction and intensity between physiological electrical signals is crucial. The maximum information coefficient (MIC) can effectively quantify the coupling strength, especially for short time series. However, it cannot identify the direction of information transmission. This paper proposes an effective time-delayed back maximum information coefficient (TDBackMIC) analysis method by introducing a time delay parameter to measure the causal coupling. Firstly, the effectiveness of TDBackMIC is verified on simulations, and then it is applied to the analysis of functional cortical-muscular coupling and intermuscular coupling networks to explore the difference of coupling characteristics under different grip force intensities. Experimental results show that functional cortical-muscular coupling and intermuscular coupling are bidirectional. The average coupling strength of EEG → EMG and EMG → EEG in beta band is 0.86 ± 0.04 and 0.81 ± 0.05 at 10% maximum voluntary contraction (MVC) condition, 0.83 ± 0.05 and 0.76 ± 0.04 at 20% MVC, and 0.76 ± 0.03 and 0.73 ± 0.04 at 30% MVC. With the increase of grip strength, the strength of functional cortical-muscular coupling in beta frequency band decreases, the intermuscular coupling network exhibits enhanced connectivity, and the information exchange is closer. The results demonstrate that TDBackMIC can accurately judge the causal coupling relationship, and functional cortical-muscular coupling and intermuscular coupling network under different grip forces are different, which provides a certain theoretical basis for sports rehabilitation.

Population prediction in China based on maximum information coefficient and NAR-BP neural network

Population prediction in China based on maximum information coefficient and NAR-BP neural network

Research on Credit Risk Prediction under Unbalanced Dataset Based on Ensemble Learning

Aiming at the problem of high‐dimensional features and data imbalance in credit risk assessment that affect model prediction results, a credit risk prediction method based on integrated learning is proposed from three levels of features, data and algorithms. First, a hybrid filter and Random Forest feature selection method is used to select features. This method uses the improved Relief algorithm to initially select features, then combines the maximum information coefficient to eliminate redundant features, and uses the Random Forest algorithm to further reduce the feature dimension. Second, on the basis of the Borderline‐SMOTE method, an adaptive idea is introduced to generate a different number of new samples for each minority sample at the boundary, and a new interpolation method is used to make the new sample distribution more reasonable, so as to reduce the sample imbalance. Finally, the Focal Loss is used to improve the loss function of LightGBM, and the sample weight is adjusted through the parameters α and γ in the Focal Loss function so that the model pays more attention to minority samples and difficult‐to‐classify samples, and improves the accuracy of model classification. And use the improved algorithm as the base classifier and then use AdaBoost and random subspace methods to integrate to establish a credit risk prediction model. Through comparative experiments with other methods, the results show that this method effectively improves the G‐mean value and the AUC value and has a better default prediction effect.

Predicting EGFR T790M Mutation in Brain Metastases Using Multisequence MRI-Based Radiomics Signature

Timely identifying T790M mutation for non-small cell lung cancer (NSCLC) patients with brain metastases (BM) is essential to adjust targeted treatment strategies. To develop and validate radiomics models based on multisequence MRI for differentiating patients with T790M resistance from no T790M mutation in BM and explore the optimal sequence for prediction. This retrospective study enrolled 233 patients with proven of BM in NSCLC which included 95 with T790M and 138 without T790M from two hospitals as the training cohort and testing cohort separately. Radiomics features extracted from T2WI, T2 fluid-attenuated inversion recovery (T2-FLAIR), diffusion weighted imaging (DWI) and contrast-enhanced T1-weighted imaging (T1-CE) sequence respectively. The most predictable features were selected based on the maximal information coefficient and Boruta method. Then four radiomics models were built to characterize T790M mutation by random forest classifier. ROC curves, F1 score and DCA curves were constructed to validate the capability and verify the performance of four models. The DWI model showed best performance with AUC and F1 score of 0.886 and 0.789 in the training cohort, 0.850 and 0.743 in the testing cohort. DCA curves also showed higher overall net benefit from the DWI model than from the remaining three models in the testing cohort. Other three models also had some classification power whether in the training or testing cohort, especially T2-FLAIR model. Multisequence MRI-based radiomics has potential to predict the emergence of EGFR T790M resistance mutations especially the radiomics signature based on DWI sequence.

Sphere Gap Breakdown Voltage Prediction Based on ISSA Optimized BP Neural Network and Effective Electric Field Feature Set

Electric field distribution is a determinant factor of air gap breakdown voltage. This paper defined an effective electric field zone between the sphere gaps for feature extraction, and 29 parameters were extracted from this zone to reflect the electric field distribution. A data mining model was established by back propagation neural network (BPNN) for sphere gap breakdown voltage prediction, taking the electric field features as inputs. The maximum information coefficient (MIC) method was used to select features strongly correlated to the breakdown voltage, and a multi‐strategy improved salp swarm algorithm (ISSA) was applied to optimize the BPNN parameters to enhance the prediction performance. The standard sphere gaps provided in IEC 60052 were taken as training set and test set, which were divided according to the electric field nonuniform coefficients. The breakdown voltage prediction results of test sample sphere gaps demonstrate good agreements with the experimental values. With input features selected by the MIC method, the ISSA optimized BPNN model has a mean absolute percentage error of only 0.83% and a maximum relative error of 5.86%. By constructing the nonlinear mapping relationship between the effective electric field features and the insulation strength, this study provides a new approach to predict air gap breakdown voltage. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.