Spatio-temporal Graph Convolutional Network Research Articles

Passenger spatiotemporal distribution prediction in airport terminals based on physics-guided spatio-temporal graph convolutional network and its effect on indoor environment prediction

The airport as an important transportation hub plays a leading role in promoting sustainable cities and new-type urbanization. To boost safe, environmental-friendly and technologically advanced airports, the passenger travel behavior as a core that decides the resource allocation, system tuning and capacity dispatching, must be grasped. Previous research in passenger distribution prediction focused on physics-based methods or only mining temporal dynamics. In this work, a refined passenger distribution prediction was modeled based on a learning-based method embedding physical prior knowledge, and then its effects on indoor environment prediction were analyzed. Among them, based on insect intelligent building architecture, a virtual spatial graph was defined in Guangzhou Baiyun International Airport Terminal 2, then a Wi-Fi positioning system was constructed; Next, a physics-guided spatio-temporal graph convolutional network, considering both the spatial dependencies and the passenger arrival pattern extracted from cost-free flight schedules, was developed for domestic and international passenger distribution predictions with R2 over 0.87 and 0.76 respectively; Lastly, the contributions of predicted occupant densities to the indoor environment prediction were evaluated with results showing that the average R2 for indoor temperature, relative humidity and CO2 concentration prediction was enhanced by 0.4 %∼91.5 %, 0.2 %∼29.7 % and 0.4 %∼45.4 % respectively as the prediction horizon broadening.

Simultaneous forecasting of wind speed for multiple stations based on attribute-augmented spatiotemporal graph convolutional network and tree-structured parzen estimator

The global increase in energy demand and environmental concerns have made the development of wind energy increasingly important. Accurate wind speed prediction is crucial for maximizing the benefits of wind energy. In order to further improve the accuracy of multi-site wind speed prediction, this study adopts an evolutionary algorithm-based deep learning model that fully considers the spatiotemporal relationships among multiple station's wind speed data. Firstly, the mutual information (MI) method is used to select variables with stronger correlations to wind speed as auxiliary input factors. Then, an improved version of Attribute-Augmented Spatiotemporal Graph Convolutional Network (IASTGCN) is employed to process data from multiple stations, taking into account both temporal and spatial factors. Additionally, an MI-based wind speed data relationship matrix between multiple stations is calculated to replace the original distance relationship matrix in the model, enabling the model to better capture and utilize the relationships between stations. Next, the Tree-structured Parzen Estimator (TPE) is used to optimize the hyperparameters of the model. This ultimately achieves multi-site multi-step wind speed prediction. Experimental results demonstrate that the proposed model outperforms baseline models and models that only consider either temporal or spatial factors in various scenarios, exhibiting better predictive performance.

A novel spatiotemporal graph convolutional network framework for functional connectivity biomarkers identification of Alzheimer’s disease

BackgroundFunctional connectivity (FC) biomarkers play a crucial role in the early diagnosis and mechanistic study of Alzheimer’s disease (AD). However, the identification of effective FC biomarkers remains challenging. In this study, we introduce a novel approach, the spatiotemporal graph convolutional network (ST-GCN) combined with the gradient-based class activation mapping (Grad-CAM) model (STGC-GCAM), to effectively identify FC biomarkers for AD.MethodsThis multi-center cross-racial retrospective study involved 2,272 participants, including 1,105 cognitively normal (CN) subjects, 790 mild cognitive impairment (MCI) individuals, and 377 AD patients. All participants underwent functional magnetic resonance imaging (fMRI) and T1-weighted MRI scans. In this study, firstly, we optimized the STGC-GCAM model to enhance classification accuracy. Secondly, we identified novel AD-associated biomarkers using the optimized model. Thirdly, we validated the imaging biomarkers using Kaplan–Meier analysis. Lastly, we performed correlation analysis and causal mediation analysis to confirm the physiological significance of the identified biomarkers.ResultsThe STGC-GCAM model demonstrated great classification performance (The average area under the curve (AUC) values for different categories were: CN vs MCI = 0.98, CN vs AD = 0.95, MCI vs AD = 0.96, stable MCI vs progressive MCI = 0.79). Notably, the model identified specific brain regions, including the sensorimotor network (SMN), visual network (VN), and default mode network (DMN), as key differentiators between patients and CN individuals. These brain regions exhibited significant associations with the severity of cognitive impairment (p < 0.05). Moreover, the topological features of important brain regions demonstrated excellent predictive capability for the conversion from MCI to AD (Hazard ratio = 3.885, p < 0.001). Additionally, our findings revealed that the topological features of these brain regions mediated the impact of amyloid beta (Aβ) deposition (bootstrapped average causal mediation effect: β = -0.01 [-0.025, 0.00], p < 0.001) and brain glucose metabolism (bootstrapped average causal mediation effect: β = -0.02 [-0.04, -0.001], p < 0.001) on cognitive status.ConclusionsThis study presents the STGC-GCAM framework, which identifies FC biomarkers using a large multi-site fMRI dataset.

A fish appetite assessment method based on improved ByteTrack and spatiotemporal graph convolutional network

The appetite of fish significantly influences aquaculture efficiency and fish welfare. However, accurately assessing fish appetite has posed a challenging problem. Currently, the study of fish feeding behaviour relies primarily on the overall information obtained from images of fish schools, often overlooking the distinctive behavioural traits of individual fish. Analysing the behaviour of individual fish is hindered by challenges such as intraclass variation and cross-occlusion within real aquaculture environments. To address these challenges, this paper introduces a novel method for assessing appetite based on individual fish behaviour. The ByteTrack model was improved to enable stable tracking of each fish within a school under complex conditions. Additionally, this paper employs the spatiotemporal graph convolutional neural network (ST-GCN) to extract the movement characteristics of individual fish, facilitating accurate appetite assessment. The experimental results demonstrate that the proposed method achieves 98.47% accuracy in appetite assessment, surpassing the performance of other state-of-the-art methods. This paper provides a new opportunity and effective means for analysing fish behaviour and appetite in intricate environments.

A novel dynamic spatio-temporal graph convolutional network for wind speed interval prediction

It is crucial to predict the wind speed for the utilization of renewable wind energy and the operation of transmission lines with increased capacity. The intermittency and stochastic fluctuations of wind speed pose a significant challenge for the high-quality wind speed prediction, and a novel wind speed interval prediction (WSIP) model is constructed in this study by employing the residual estimation (RE)-oriented dynamic spatio-temporal graph convolutional network (DSTGCN) approach. Firstly, a dynamic adjacency matrix is designed to obtain time-varying global spatial weight allocations among each wind speed node. Then, the spatio-temporal features are extracted by using gated recurrent units (GRUs) and GCNs to construct the wind speed graph networks. Moreover, the RE-oriented strategy incorporating the pinball loss is designed to provide a guidance the parameter training of the constructed model, thus eliminating the quantile crossings problem. As a result, the deterministic point prediction of the wind speed is expanded to the quantile-based probabilistic interval prediction. Finally, the experimental results are presented to demonstrate the validity and superiority of proposed scheme in both qualitative and quantitative performance.

Dynamic Spatiotemporal Correlation Graph Convolutional Network for Traffic Speed Prediction

Accurate and real-time traffic speed prediction remains challenging due to the irregularity and asymmetry of real-traffic road networks. Existing models based on graph convolutional networks commonly use multi-layer graph convolution to extract an undirected static adjacency matrix to map the correlation of nodes, which ignores the dynamic symmetry change of correlation over time and faces the challenge of oversmoothing during training iterations, making it difficult to learn the spatial structure and temporal trend of the traffic network. To overcome the above challenges, we propose a novel multi-head self-attention gated spatiotemporal graph convolutional network (MSGSGCN) for traffic speed prediction. The MSGSGCN model mainly consists of the Node Correlation Estimator (NCE) module, the Time Residual Learner (TRL) module, and the Gated Graph Convolutional Fusion (GGCF) module. Specifically, the NCE module aims to capture the dynamic spatiotemporal correlations between nodes. The TRL module utilizes a residual structure to learn the long-term temporal features of traffic data. The GGCF module relies on adaptive diffusion graph convolution and gated recurrent units to learn the key spatial features of traffic data. Experimental analysis on a pair of real-world datasets indicates that the proposed MSGSGCN model enhances prediction accuracy by more than 4% when contrasted with state-of-the-art models.

Multi-faceted spatio-temporal network for weather-aware air traffic flow prediction in multi-airport system

As one of the core modules for air traffic flow management, Air Traffic Flow Prediction (ATFP) in the Multi-Airport System (MAS) is a prerequisite for demand and capacity balance in the complex meteorological environment. Due to the challenge of implicit interaction mechanism among traffic flow, airspace capacity and weather impact, the Weather-aware ATFP (Wa-ATFP) is still a nontrivial issue. In this paper, a novel Multi-faceted Spatio-Temporal Graph Convolutional Network (MSTGCN) is proposed to address the Wa-ATFP within the complex operations of MAS. Firstly, a spatio-temporal graph is constructed with three different nodes, including airport, route, and fix to describe the topology structure of MAS. Secondly, a weather-aware multi-faceted fusion module is proposed to integrate the feature of air traffic flow and the auxiliary features of capacity and weather, which can effectively address the complex impact of severe weather, e.g., thunderstorms. Thirdly, to capture the latent connections of nodes, an adaptive graph connection constructor is designed. The experimental results with the real-world operational dataset in Guangdong-Hong Kong-Macao Greater Bay Area, China, validate that the proposed approach outperforms the state-of-the-art machine-learning and deep-learning based baseline approaches in performance. The case study of convective weather scenarios further proves the adaptability of the proposed approach.

FeSTGCN: A frequency-enhanced spatio-temporal graph convolutional network for traffic flow prediction under adaptive signal timing

FeSTGCN: A frequency-enhanced spatio-temporal graph convolutional network for traffic flow prediction under adaptive signal timing

Exploring a spatiotemporal hetero graph-based long short-term memory model for multi-step-ahead flood forecasting

Operational flood prevention platforms and systems rely upon the advance notice provided by flood forecasts to formulate efficient measures for flood mitigation. Capturing complex spatial heterogeneity and correlation of hydro-meteorological variables is fundamentally challenging for artificial neural networks. This challenge becomes even more significant when the complexity involved introduces systematic biases and time-lag phenomena in flood forecasts. For the first time, this study proposed a Spatiotemporal Hetero Graph-based Long Short-term Memory (SHG-LSTM) model for multi-step-ahead flood forecasting. The case study focused on the Jianxi basin in China. 25,341 hydro-meteorological data, with a temporal resolution of three hours, collected during flood events were divided into training and test datasets for model construction purpose. The model was fed with 3-h streamflow and precipitation data from 23 gauge stations, covering a time span of the preceding 21 h, for generating flood forecasts at 1 up to 7 horizons. To make a comparative analysis, both LSTM and the Spatiotemporal Graph Convolutional Network (S-GCN) were constructed. This study conducted multiple rounds of model training with varying initial parameters to assess the accuracy, stability, and reliability of the LSTM, S-GCN, and SHG-LSTM models. The results demonstrated that the SHG-LSTM model outperformed LSTM and S-GCN models, with an average reduction in the volume error (VE) of 6.5% and 11.1%, respectively, a decrease in the Mean Absolute Error (MAE) of 6.7% and 8.1%, respectively, and a reduction in the Root Mean Square Error (RMSE) of 5.0% and 12.9%, respectively. Furthermore, the SHG-LSTM model not only could efficiently overcome the under-prediction bottleneck, but also could largely mitigate the time-lag phenomenon in flood forecasts, even during the testing stages. These findings indicate that the proposed SHG-LSTM model can provide a general framework for modelling the spatial heterogeneity and correlation of hydro-meteorological variables and achieve accurate and reliable flood forecasts, thereby enhancing the model’s applicability in flood prevention platforms and systems.

Spatial-temporal deep learning model based on Similarity Principle for dock shared bicycles ridership prediction

Demand prediction plays a critical role in traffic research. The key challenge of traffic demand prediction lies in modeling the complex spatial dependencies and temporal dynamics. However, there is no mature and widely accepted concept to support the solution of the above challenge. Essentially, a prediction model combined with similar objects in temporal and spatial dimensions could obtain better performance. This paper proposes a concept called the Similarity-based Principle (SP), which is applied to improve the prediction performance of deep learning models in complex traffic scenarios. For the temporal components, the long-term temporal dynamics in contemporaneous historical data for ridership are extracted by the Stacked Autoencoder (SAE) method. For the spatial components, the activity-based spatial geographic information (ABG-information) is used to capture the spatial correlation of the traffic network, which is reflected in the daily activities of humans. Specifically, the SP is applied to a Spatio-temporal Graph Convolutional Neural Network (STGCNN) model. In the case study, the Similarity-based Principle Spatio-temporal Graph Convolutional Neural Network (SP-STGCNN) model predicts demand for bicycle sharing in San Francisco. The results show that the SP effectively improves the model's performance. The prediction accuracy is enhanced by up to 10.34% compared with STGCNN. For spatial relationships, the model using the geographic information attribute performs better than that using the road information attribute and the distance attribute. It is proved that the construction of the Spatio-temporal model-based similarity principle can improve the performance.

Vessel trajectory prediction based on spatio-temporal graph convolutional network for complex and crowded sea areas

In order to improve the navigation ability of vessels and ensure the safety of maritime traffic, vessel trajectory prediction plays a crucial role in the intelligent navigation and collision avoidance. Especially for complex and crowded waters, autonomous vessels must have high situational awareness to detect other vessels, and predict their future trajectories and assess collision risks. In this work, a deep attention-aware spatio-temporal graph convolutional network based on AIS data (DAA-SGCN) is proposed to predict the future trajectories of vessels. It mainly includes three modules: motion information encoding of vessel trajectories, the spatio-temporal feature extraction module and the trajectory prediction module. The LSTM is used to extract the motion features of vessels, the spatio-temporal graph is constructed based on deep attention mechanism. The spatial social interaction features are extracted by ST-GCN, and the temporal correlation are extracted by RT-CNN, to obtain the high-level spatio-temporal features of vessel trajectories. Then, the feature embedding is fed into the trajectory prediction module to predict the future trajectories of vessels. On the basis of a large number of experiments, the prediction performance of the DAA-SGCN compared to the optimal baseline model is improved by about 74% and 69% in ADE and FDE metrics.

Enhancing four-axis machining center accuracy through interactive fusion of spatiotemporal graph convolutional networks and an error-controlled digital twin system

Mitigating thermal errors constitutes a crucial method for enhancing the machining accuracy of four-axis machining centers. At the heart of effective thermal error control lie the thermal error control platform and a resilient thermal error prediction model. It is imperative to note that thermal errors exhibit intricate dynamic and nonlinear spatiotemporal dependencies. However, prevailing thermal error prediction models tend to primarily focus on temporal features or employ simplistic spatiotemporal characteristics, resulting in diminished accuracy and robustness. Furthermore, the present thermal error compensation system is plagued by a lack of user-friendliness, stemming from its suboptimal execution efficiency. In response to the aforementioned challenges, an innovative approach: the interactive fusion spatiotemporal graph convolutional network is proposed. This novel model is specifically designed to capture the intricate dynamic spatiotemporal dependencies inherent in thermal errors. The interactive fusion spatiotemporal graph convolutional network model consists of three essential components: a bilinear temporal convolutional network, a multi-layer spatiotemporal module, and a linear module. These components work in harmony to comprehensively extract both global and local spatiotemporal features. Subsequently, a mapping relationship between thermal errors and compensation components is established, laying the foundation for theoretical advancements in thermal error compensation within the realm of four-axis machining centers. A digital twin system framework tailored for error control is devised, which leverages cloud-edge computing to enable dynamic control and real-time monitoring of thermal errors. To assess the effectiveness of this digital twin system framework and the interactive fusion spatiotemporal graph convolutional network model, a series of rigorous experiments were conducted. The oriented to error-controlled digital twin system coupled with the interactive fusion spatiotemporal graph convolutional network model yielded exceptional machining accuracy, resulting in minimal geometric disparities of [−3.0 μm, 3.0 μm] for the central hole diameter D and [−3.5 μm, 4.0 μm] for the hole distance H.

Fault Diagnosis of Gearbox Based on Refined Topology and Spatio-Temporal Graph Convolutional Network

Fault Diagnosis of Gearbox Based on Refined Topology and Spatio-Temporal Graph Convolutional Network

Research on a Resource Modeling and Power Prediction Method Based on Virtual Aggregation

Distributed resources at a grid’s end cannot upload operational power data to local centers due to data transmission and privacy issues. This leaves the centers with incomplete information, thus impacting decision making. This paper presents a virtual aggregation-based model for such scenarios. We define four virtual aggregate types based on resource response characteristics. Using characteristic coefficients, we identify these aggregates’ categories and proportions from bus power. To address blind source separation in single-channel power signals, we apply the Ensemble Empirical Mode Decomposition-Fast Independent Component Analysis (EEMD-FastICA) method. This helps extract and analyze bus power, thereby deriving power curves for different aggregates. Moreover, we use a graph convolutional network to explore how factors like date, time, weather, and pricing intertwine with aggregate power. We develop a predictive model with an advanced SpatioTemporal Graph Convolutional Network (STGCN), thus facilitating proactive power forecasting for virtual aggregates. Case studies show our method’s efficacy in extracting power curves under limited information, with the STGCN ensuring accurate, forward-looking predictions.

MEC Server Sleep Strategy for Energy Efficient Operation of an MEC System

Optimizing the energy consumption of an MEC (Multi-Access Edge Computing) system is a crucial challenge for operation cost reduction and environmental conservation. In this paper, we address an MECS (MEC Server) sleep control problem that aims to reduce the energy consumption of the system while providing users with a reasonable service delay by adjusting the number of active MECSs according to the load imposed on the system. To tackle the problem, we identify two crucial issues that influence the design of an effective sleep control technique and propose methods to address each of these issues. The first issue is accurately predicting the system load. Changes in system load are spatio-temporally correlated among MECSs. By leveraging such correlation information with STGCN (Spatio-Temporal Graph Convolutional Network), we enhance the prediction accuracy of task arrival rates for each MECS. The second issue is rapidly selecting MECSs to sleep when the load distribution over an MEC system is given. The problem of choosing sleep MECS is a combinatorial optimization problem with high time complexity. To address the issue, we employ a genetic algorithm and quickly determine the optimal sleep MECS with the predicted load information for each MECS. Through simulation studies, we verify that compared to the LSTM (Long Short-Term Memory)-based method, our method increases the energy efficiency of an MEC system while providing a compatible service delay.

A Spatiotemporal Graph Neural Network with Graph Adaptive and Attention Mechanisms for Traffic Flow Prediction

This study addresses the complex challenges associated with road traffic flow prediction and congestion management through the enhancement of the attention-based spatiotemporal graph convolutional network (ASTGCN) algorithm. Leveraging toll data and real-time traffic flow information from Orange County, California, the algorithm undergoes refinement to adeptly capture abrupt changes in road traffic dynamics and identify instances of acute congestion. The optimization of the graph structure is approached from both macro and micro perspectives, incorporating key factors such as road toll information, node connectivity, and spatial distances. A novel graph self-learning module is introduced to facilitate real-time adjustments, while an attention mechanism is seamlessly integrated into the spatiotemporal graph convolution module. The resultant model, termed AASTGNet, exhibits superior predictive accuracy compared to existing methodologies, with MAE, RMSE, and MAPE values of 8.6204, 14.0779, and 0.2402, respectively. This study emphasizes the importance of incorporating tolling schemes in road traffic flow prediction, addresses static graph structure limitations, and adapts dynamically to temporal variations and unexpected road events. The findings contribute to advancing the field of traffic prediction and congestion management, providing valuable insights for future research and practical applications.

Multi-layer parallel-perceptual-fusion spatiotemporal graph convolutional network for cross-domain, poor thermal information prediction in cloud-edge control services

Thermal error, which has spatiotemporal behavior, severely reduces machining accuracy of high-accuracy machine tools and should be controlled in real time. The deep learning is used to establish spatiotemporal thermal error model with large-sample thermal information as input. But the acquisition of large-sample thermal information is extremely difficult and costly. So, in the actual application, thermal error is predicted with poor thermal information as input, and then the robustness is weak because the cross-domain and poor spatiotemporal thermal information prediction is still a severe challenge. In this study, the transfer learning model of multi-layer parallel-perceptual-fusion spatiotemporal graph convolutional network is proposed without deepening network depth, instead, its width is expanded. Specifically, the adjacency matrix is constructed to consider the spatial information by defining the distance between each two sensors, and then the graph convolutional network is integrated into long short-term memory and gated recurrent unit to propose graph convolutional long short-term memory and graph convolutional gated recurrent unit with constructed adjacency matrix as input, respectively. The graph convolutional long short-term memory and graph convolutional gated recurrent unit are superimposed to propose the multi-layer parallel-perceptual-fusion spatiotemporal graph convolutional network. To improve the robustness, the adjacency matrix is retrained, and the transfer learning model of multi-layer parallel-perceptual-fusion spatiotemporal graph convolutional network is proposed and applied to forecast thermal error, and its prediction accuracy is 94.926%. Spatiotemporal characteristics of temperature and thermal error are fully captured by transfer learning model of graph convolutional long short-term memory and graph convolutional gated recurrent unit. Finally, the transfer learning model of multi-layer parallel-perceptual-fusion spatiotemporal graph convolutional network is embedded into thermal error control service architecture based on cloud-edge collaboration. With implementation of thermal error control service architecture based on cloud-edge collaboration, machining error of machine tools is reduced by more than 80%.

Sports-ACtrans Net: research on multimodal robotic sports action recognition driven via ST-GCN.

Accurately recognizing and understanding human motion actions presents a key challenge in the development of intelligent sports robots. Traditional methods often encounter significant drawbacks, such as high computational resource requirements and suboptimal real-time performance. To address these limitations, this study proposes a novel approach called Sports-ACtrans Net. In this approach, the Swin Transformer processes visual data to extract spatial features, while the Spatio-Temporal Graph Convolutional Network (ST-GCN) models human motion as graphs to handle skeleton data. By combining these outputs, a comprehensive representation of motion actions is created. Reinforcement learning is employed to optimize the action recognition process, framing it as a sequential decision-making problem. Deep Q-learning is utilized to learn the optimal policy, thereby enhancing the robot's ability to accurately recognize and engage in motion. Experiments demonstrate significant improvements over state-of-the-art methods. This research advances the fields of neural computation, computer vision, and neuroscience, aiding in the development of intelligent robotic systems capable of understanding and participating in sports activities.

Predicting the daily number of patients for allergic diseases using PM10 concentration based on spatiotemporal graph convolutional networks.

Air pollution causes and exacerbates allergic diseases including asthma, allergic rhinitis, and atopic dermatitis. Precise prediction of the number of patients afflicted with these diseases and analysis of the environmental conditions that contribute to disease outbreaks play crucial roles in the effective management of hospital services. Therefore, this study aims to predict the daily number of patients with these allergic diseases and determine the impact of particulate matter (PM10) on each disease. To analyze the spatiotemporal correlations between allergic diseases (asthma, atopic dermatitis, and allergic rhinitis) and PM10 concentrations, we propose a multi-variable spatiotemporal graph convolutional network (MST-GCN)-based disease prediction model. Data on the number of patients were collected from the National Health Insurance Service from January 2013 to December 2017, and the PM10 data were collected from Airkorea during the same period. As a result, the proposed disease prediction model showed higher performance (R2 0.87) than the other deep-learning baseline methods. The synergic effect of spatial and temporal analyses improved the prediction performance of the number of patients. The prediction accuracies for allergic rhinitis, asthma, and atopic dermatitis achieved R2 scores of 0.96, 0.92, and 0.86, respectively. In the ablation study of environmental factors, PM10 improved the prediction accuracy by 10.13%, based on the R2 score.

Application of 3D recognition algorithm based on spatio-temporal graph convolutional network in basketball pose estimation

In recent years, human motion recognition in computer vision has become a hot research direction in this field. Based on 2D human motion recognition technology, real-time extraction of motion features from 2D planes is used to recognize human movements. This method can only learn the position contour and color information of the image. It cannot directly reflect the motion situation, which results in low recognition accuracy and efficiency. In response to this issue, this study proposes a combination method of motion recognition and 3D pose estimation to recognize and classify basketball movements. First, the 2D skeleton model is obtained by extracting the feature information in the video action, which is converted into a 3D model, and the model is replaced by the time-space convolutional network to establish a human action recognition model. The experiment showed that when the number of iterations reached 6, the accuracy of the spatio-temporal graph convolutional network algorithm model reached 92%. Comparing the accuracy rates of different algorithm models, the average accuracy rates of convolutional neural network, long short memory network, graph convolution, long short model of action recognition and graph convolution model of action recognition were 61.6%, 65.4%, 72.5%, 76.8% and 90.3% respectively. The results show that the proposed 3D recognition algorithm can accurately recognize different basketball movements. This study can provide reference for basketball coaches and athletes in basketball training.