Multidimensional Input Data Research Articles

Enhanced Short-Term Load Forecasting: Error-Weighted and Hybrid Model Approach

To tackle the challenges of high variability and low accuracy in short-term electricity load forecasting, this study introduces an enhanced prediction model that addresses overfitting issues by integrating an error-optimal weighting approach with an improved ensemble forecasting framework. The model employs a hybrid algorithm combining grey relational analysis and radial kernel principal component analysis to preprocess the multi-dimensional input data. It then leverages an ensemble of an optimized deep bidirectional gated recurrent unit (BiGRU), an enhanced long short-term memory (LSTM) network, and an advanced temporal convolutional neural network (TCN) to generate predictions. These predictions are refined using an error-optimal weighting scheme to yield the final forecasts. Furthermore, a Bayesian-optimized Bagging and Extreme Gradient Boosting (XGBoost) ensemble model is applied to minimize prediction errors. Comparative analysis with existing forecasting models demonstrates superior performance, with an average absolute percentage error (MAPE) of 1.05% and a coefficient of determination (R2) of 0.9878. These results not only validate the efficacy of our proposed strategy, but also highlight its potential to enhance the precision of short-term load forecasting, thereby contributing to the stability of power systems and supporting societal production needs.

Spaceborne particle identification platform and its application based on convolutional neural network

The identification of particle types in space radiation particle detection is a problem of great concern in scientific research and engineering applications. At present, the particle types are mainly identified by the difference in energy deposition of particles in the sensor, the difference in waveform in the sensor, the flight time and energy of particles, and the difference in the deflection path of particles in the electric field, such as traditional telescope detectors, particle pulse waveform analysis, flight time TOF system and electrostatic analyzer. However, the current on-orbit particle identification logic is relatively simple and the identification accuracy is limited. Convolutional neural networks have powerful target classification capabilities and are good at capturing and extracting target feature details, which can improve the accuracy of particle energy measurement and identification. Based on the environment commonly used in space environment detection payloads, this paper proposes a method for building an on-orbit convolutional neural network particle identification platform to achieve particle type identification. The platform first constructs a multi-dimensional input data set, completes the model training and weight derivation with the help of the software platform, and completes the waveform inference and data set expansion through the hardware platform. The established identification platform is used to train and test the neutron and gamma waveform data obtained in actual tests, and the accuracy of the identification of the software and hardware platforms is analyzed, completing the verification of the platform. The establishment and application of this platform provides a new idea and method for particle measurement and identification in future space environment detection, and has strong engineering practice significance.

Short-Term Electrical Load Forecasting Based on IDBO-PTCN-GRU Model

Accurate electrical load forecasting is crucial for the stable operation of power systems. However, existing forecasting models face limitations when handling multidimensional features and feature interactions. Additionally, traditional metaheuristic algorithms tend to become trapped in local optima during the optimization process, negatively impacting model performance and prediction accuracy. To address these challenges, this paper proposes a short-term electrical load forecasting method based on a parallel Temporal Convolutional Network–Gated Recurrent Unit (PTCN-GRU) model, optimized by an improved Dung Beetle Optimization algorithm (IDBO). This method employs a parallel TCN structure, using TCNs with different kernel sizes to extract and integrate multi-scale temporal features, thereby overcoming the limitations of traditional TCNs in processing multidimensional input data. Furthermore, this paper enhances the optimization performance and global search capability of the traditional Dung Beetle Optimization algorithm through several key improvements. Firstly, Latin hypercube sampling is introduced to increase the diversity of the initial population. Next, the Golden Sine Algorithm is integrated to refine the search behavior. Finally, a Cauchy–Gaussian mutation strategy is incorporated in the later stages of iteration to further strengthen the global search capability. Extensive experimental results demonstrate that the proposed IDBO-PTCN-GRU model significantly outperforms comparison models across all evaluation metrics. Specifically, the mean absolute error (MAE), mean absolute percentage error (MAPE), and root mean square error (RMSE) were reduced by 15.01%, 14.44%, and 14.42%, respectively, while the coefficient of determination (R2) increased by 2.13%. This research provides a novel approach to enhancing the accuracy of electrical load forecasting.

High-percentage new energy distribution network line loss frequency division prediction based on wavelet transform and BIGRU-LSTM.

The access of new energy improves the flexibility of distribution network operation, but also leads to more complex mechanism of line loss. Therefore, starting from the nonlinear, fluctuating and multi-scale characteristics of line loss data, and based on the idea of decomposition prediction, this paper proposes a new method of line loss frequency division prediction based on wavelet transform and BIGRU-LSTM (Bidirectional Gated Recurrent Unit-Long Short Term Memory Network).Firstly, the grey relation analysis and the improved NARMA (Nonlinear Autoregressive Moving Average) correlation analysis method are used to extract the non-temporal and temporal influencing factors of line loss, and the corresponding feature data set is constructed. Then, the historical line loss data is decomposed into physical signals of different frequency bands by using wavelet transform, and the multi-dimensional input data of the prediction network is formed with the above characteristic data set. Finally, the BIGRU-LSTM prediction network is built to realize the probabilistic prediction of high-frequency and low-frequency components of line loss. The effectiveness and applicability of the method proposed in this paper were verified through numerical simulation. By dividing the line loss data into different frequency bands for frequency prediction, the mapping relationship between different line loss components and influencing factors was accurately matched, thereby improving the prediction accuracy.

Bayesian hierarchical model for bias-correcting climate models

Abstract. Climate models, derived from process understanding, are essential tools in the study of climate change and its wide-ranging impacts. Hindcast and future simulations provide comprehensive spatiotemporal estimates of climatology that are frequently employed within the environmental sciences community, although the output can be afflicted with bias that impedes direct interpretation. Post-processing bias correction approaches utilise observational data to address this challenge, although they are typically criticised for not being physically justified and not considering uncertainty in the correction. This paper proposes a novel Bayesian bias correction framework that robustly propagates uncertainty and models underlying spatial covariance patterns. Shared latent Gaussian processes are assumed between the in situ observations and climate model output, with the aim of partially preserving the covariance structure from the climate model after bias correction, which is based on well-established physical laws. Results demonstrate added value in modelling shared generating processes under several simulated scenarios, with the most value added for the case of sparse in situ observations and smooth underlying bias. Additionally, the propagation of uncertainty to a simulated final bias-corrected time series is illustrated, which is of key importance to a range of stakeholders, such as climate scientists engaged in impact studies, decision-makers trying to understand the likelihood of particular scenarios and individuals involved in climate change adaption strategies where accurate risk assessment is required for optimal resource allocation. This paper focuses on one-dimensional simulated examples for clarity, although the code implementation is developed to also work on multi-dimensional input data, encouraging follow-on real-world application studies that will further validate performance and remaining limitations. The Bayesian framework supports uncertainty propagation under model adaptations required for specific applications, providing a flexible approach that increases the scope of data assimilation tasks more generally.

Tactics analysis and evaluation of women football team based on convolutional neural network

In order to realize the process of player feature extraction and classification from multi-frequency frame-changing football match images more quickly, and complete the tactical plan that is more conducive to the game, this paper puts forward a method for analyzing and judging the tactics of women’s football team based on Convolutional Neural Network (CNN). By extracting the players’ performance in recent training and competition from continuous video frame data, a multi-dimensional vector input data sample is formed, and CNN is used to analyze the players’ hidden ability before the game and the players’ mistakes in different positions on the field to cope with different football schedules. Before the formal test, 10 games of 2021–2022 UEFA Women’s Champions League were randomly selected and intercepted to train the CNN model. The model showed excellent accuracy in the classification of image features of various football moves and goal angles, and the overall classification accuracy of each category exceeded 95%. The accuracy of classifying a single match is above 88%, which highlights the reliability and stability of the model in identifying and classifying women’s football matches. On this basis, the test results show that: according to the analysis of players’ personal recessive ability before the game, after model image recognition and comparison, the difference between the four scores of players’ personal recessive ability with CNN mode and the manual score of professional coaches was smaller, and the numerical difference was within the minimum unit value, and the numerical calculation results were basically the same. According to the analysis of players’ mistakes in different positions on the field, CNN was used to monitor the real-time mistakes. It was found that the two players in the forward position made the highest mistakes, and they were replaced by substitute players at 73.44 min and 65.28 min after the team scored and kept the ball, respectively. After the substitute players played, the team’s forward position mistake rate decreased obviously. The above results show that CNN technology can help players get personal recessive ability evaluation closer to professional evaluation in a shorter time, and help the coaching team to analyze the real-time events better. The purpose of this paper is to help the women’s football team complete the pre-match tactical training, reduce the analysis time of players’ mistakes in the game, deal with different opponents in the game and improve the winning rate of the game.

Robust Generalized Scalar-on-Tensor Regression

High-dimensional (HD) data, such as images and profiles, are commonly collected from complex systems and contain significant explanatory and predictive information for effective systems monitoring and control. Therefore, developing accurate and robust predictive models based on HD data is crucial. In literature, various methods, including linear scalar-on-tensor regression, are developed to model a complex system based on HD data. However, existing estimation techniques ignore the presence of outliers and are prone to biased estimations. This paper proposes a robust scalar-on-tensor regression framework that handles multi-dimensional HD input data when the data contain outliers. Our proposed estimation method is constructed using maximum Lq-likelihood estimation instead of the classical maximum likelihood estimation. The asymptotic analysis under the Gaussian distribution assumption and the guideline on choosing the tuning parameter of our proposed method is provided. Several simulations and case studies evaluate the proposed method’s efficacy compared to several benchmark methods in the literature.

A novel approach for large‐scale environmental data partitioning on cloud and on‐premises storage for compute continuum applications

SummaryCloud‐based services have proved useful in several research fields, such as engineering, health science, and astrophysics, to mention a few examples. The computational environmental science community developed a strong need for cloud facilities to store, process, and manage data from observations and numerical models for simulations and forecasts. Weather forecast models and global sensor networks deal with multidimensional geo‐referenced data∖sets. However, environmental data consumer applications usually require a relatively small amount of multidimensional input data slice to analyze a specific area or time interval. Hence, reducing data dimension for information retrieval is mandatory. This paper presents a twofold solution: a technique to load and retrieve the sliced multidimensional data set on different cloud services such as Amazon Web Service (AWS), Google Cloud Platform, and Microsoft Azure. The experimental results performed on these cloud services highlight that the proposed method can significantly speed up the process of loading and retrieving the data slices compared to working with the entire data set in bulk or OPeNDAP server.

A multi-sensor mapping Bi-LSTM model of bridge monitoring data based on spatial-temporal attention mechanism

The premise of intelligent structural health monitoring is to build a digital benchmark model representing the multi-sensor mapping relationship. Previously, researchers have used machine learning methods such as Long-and-Short-Term-Memory (LSTM) networks for modeling multi-sensor mapping relationships. However, the typical LSTM networks treat multi-dimensional input data equally, ignoring the possible correlations of different periods and sensor placements. Consequently, they can hardly obtain an accurate model for long-time series and multidimensional datasets. To address the issues, by introducing a two-layer attention mechanism in the temporal and spatial dimensions, an improved Bi-direction LSTM neural network model embedding the attention mechanism is proposed. The model focuses on grasping the non-stationary response process and the spatial correlation of multi-sensors. The accuracy and efficiency of the proposed approach are verified through two case studies. In addition, based on the visualization of attention weight assignments, the spatial–temporal attention distribution is studied to give an engineering interpretation.

A Theoretical Energy Loss Calculation Method for Transformer District Based on Improved Convolutional Neural Networks

Energy saving and emission reduction are important in the industrial field, and the transmitting loss of electric energy has been getting wide attention. The development of advanced metering infrastructures and information technology has enabled a massive accumulation of electricity data. Therefore, data-driven method is prospective to be applied to the calculation and analysis of energy loss. In order to establish an efficient data-driven theoretical energy loss calculation method for the transformer district, the following researches are carried out in this article: 1) In order to determine the input variables for the calculation model, the optimal types and number of input variables are determined through sample preclassification, grey correlation analysis and the 10-fold cross-validation method; 2) The structure of the convolutional neural networks is improved for accurately revealing the nonlinear relationship between multidimensional input data and theoretical energy loss; 3) A sample expansion method for transformer district based on generative adversarial networks is proposed, and the effect of the size of samples on the theoretical energy loss calculation in transformer district is analyzed. The simulations show that the proposed method results in acceptable calculation accuracy, training efficiency, and generalization ability.

A novel flood risk mapping approach with machine learning considering geomorphic and socio-economic vulnerability dimensions

Quantifying flood hazards by employing hydraulic/hydrodynamic models for flood risk mapping is a widely implemented non-structural flood management strategy. However, the unavailability of multi-domain and multi-dimensional input data and expensive computational resources limit its application in resource-constrained regions. The fifth and sixth IPCC assessment reports recommend including vulnerability and exposure components along with hazards for capturing risk on human-environment systems from natural and anthropogenic sources. In this context, the present study showcases a novel flood risk mapping approach that considers a combination of geomorphic flood descriptor (GFD)-based flood susceptibility and often neglected socio-economic vulnerability components. Three popular Machine Learning (ML) models, namely Decision Tree (DT), Random Forest (RF), and Gradient-boosted Decision Trees (GBDT), are evaluated for their abilities to combine digital terrain model-derived GFDs for quantifying flood susceptibility in a flood-prone district, Jagatsinghpur, located in the lower Mahanadi River basin, India. The area under receiver operating characteristics curve (AUC) along with Cohen's kappa are used to identify the best ML model. It is observed that the RF model performs better compared to the other two models on both training and testing datasets, with AUC score of 0.88 on each. The socio-economic vulnerability assessment follows an indicator-based approach by employing the Charnes-Cooper-Rhodes (CCR) model of Data Envelopment Analysis (DEA), an efficient non-parametric ranking method. It combines the district's relevant socio-economic sensitivity and adaptive capacity indicators. The flood risk classes at the most refined administrative scale, i.e., village level, are determined with the Jenks natural breaks algorithm using flood susceptibility and socio-economic vulnerability scores estimated by the RF and CCR-DEA models, respectively. It was observed that >40 % of the villages spread over Jagatsinghpur face high and very high flood risk. The proposed novel framework is generic and can be used to derive a wide variety of flood susceptibility, vulnerability, and subsequently risk maps under a data-constrained scenario. Furthermore, since this approach is relatively data and computationally parsimonious, it can be easily implemented over large regions. The exhaustive flood maps will facilitate effective flood control and floodplain planning.

Remaining Useful Life Prediction of Aeroengines Based on Multi-Head Attention Mechanism

Aeroengines are the core components of an aircraft; therefore, their health determines flight safety. Currently, owing to their complex structure and problems associated with their various detection parameters, predicting the remaining useful life (RUL) of aeroengines is very important to ensure their safety and reliability. In this paper, we propose a new hybrid method based on convolutional neural networks (CNN), timing convolutional neural networks (TCN), and the multi-head attention mechanism. Firstly, an CNN-TCN model is established for multi-dimensional features, in which two layers of the CNN extract features of multi-dimensional input data, and the TCN process the timing features. Subsequently, the outputs of multiple CNN-TCNs are weighted using the multi-head attention mechanism, and the results are stitched together. Next, we compare the root mean square error (RMSE) and scores of various RUL prediction methods to show the superiority of the proposed method. The results showed that compared with previous research results, the RMSE and Score of FD001 decreased by 10.87% and 42.57%, respectively, whereas those of FD003 decreased by 14.13% and 58.15%, respectively.

Tensor Wiener Filter

In signal processing and data analytics, Wiener filter is a classical powerful tool to transform an input signal to match a desired or target signal by a linear time-invariant (LTI) filter. The input signal of a Wiener filter is one-dimensional while its associated least-squares solution, namely Wiener-Hopf equation, involves a two-dimensional data-array, or correlation matrix. However, the actual match should often be carried out between a multi-dimensional filtered signal-sequence, which is the output of a multi-channel filter characterized as a linear-time-invariant MIMO (multi-input and multi-output) system, and a multi-dimensional desired signal-sequence simultaneously. In the presence of such a multi-channel filter, the solution to the corresponding Wiener filter, which we call MIMO Wiener-Hopf equation now, involves a correlation tensor. Therefore, we call this optimal multi-channel filter Tensor Wiener Filter (TWF). Due to lack of the pertinent mathematical framework of needed tensor operations, TWF has never been investigated so far. Now we would like to make the first-ever attempt to establish a new mathematical framework for TWF, which relies on the inverse of the correlation tensor. We propose the new parallel block-Jacobi tensor-inversion algorithm for this tensor inversion. A typical application of the new TWF approach is illustrated as a multi-channel linear predictor (MCLP) built upon a multi-channel autoregressive (MCAR) filter with multi-dimensional input data. Numerical experiments pertaining to seismic data, optical images, and macroeconomic time-series are conducted in comparison with other existing methods. The memory- and computational-complexities corresponding to our proposed parallel block-Jacobi tensor-inversion algorithm are also studied in this paper.

GlyphCreator: Towards Example-based Automatic Generation of Circular Glyphs

Circular glyphs are used across disparate fields to represent multidimensional data. However, although these glyphs are extremely effective, creating them is often laborious, even for those with professional design skills. This paper presents GlyphCreator, an interactive tool for the example-based generation of circular glyphs. Given an example circular glyph and multidimensional input data, GlyphCreator promptly generates a list of design candidates, any of which can be edited to satisfy the requirements of a particular representation. To develop GlyphCreator, we first derive a design space of circular glyphs by summarizing relationships between different visual elements. With this design space, we build a circular glyph dataset and develop a deep learning model for glyph parsing. The model can deconstruct a circular glyph bitmap into a series of visual elements. Next, we introduce an interface that helps users bind the input data attributes to visual elements and customize visual styles. We evaluate the parsing model through a quantitative experiment, demonstrate the use of GlyphCreator through two use scenarios, and validate its effectiveness through user interviews.

Prediction of dissolved oxygen concentration in aquaculture based on attention mechanism and combined neural network.

As an essential water quality parameter in aquaculture ponds, dissolved oxygen (DO) affects the growth and development of aquatic animals and their feeding and absorption. However, DO is easily influenced by external factors. It is not easy to make scientific and accurate predictions of DO concentration trends, especially in long-term predictions. This paper uses a one-dimensional convolutional neural network to extract the features of multidimensional input data. Bidirectional long and short-term memory neural network propagated forward and backward twice and thoroughly mined the before and after attribute relationship of each data of dissolved oxygen sequence. The attention mechanism focuses the model on the time series prediction step to improve long-term prediction accuracy. Finally, we built an integrated prediction model based on convolutional neural network (CNN), bidirectional long and short-term memory neural network (BiLSTM) and attention mechanism (AM), which is called CNN-BiLSTM-AM model. To determine the accuracy of the CNN-BiLSTM-AM model, we conducted short-term (30 minutes, one hour) and long-term (6 hours, 12 hours) experimental validation on real datasets monitored at two aquaculture farms in Yantai City, Shandong Province, China. Meanwhile, the performance was compared and visualized with support vector regression, recurrent neural network, long short-term memory neural network, CNN-LSTM model and CNN-BiLSTM model. The results show that compared with other comparative models, the proposed CNN-BiLSTM-AM model has an excellent performance in mean absolute error, root means square error, mean absolute percentage error and determination coefficient.

Mode of use by mobile phone and change of time of simple audio-motor reaction for users of mobile communication. Age related features of ipsilateral and contralateral effects

By analysing the time of a simple auditory-motor reaction with mono-presentation of an audio signal, the effect of the electromagnetic radiation of a mobile phone on the human auditory system is evaluated. Regularities in the frequency of occurrence of ipsi and contralateral effects in mobile users of different age groups are obtained. This study has no analogues in either Russian or foreign publications and is currently exclusive. The purpose was to study age-related features of the severity of ipsi and contralateral effects, depending on the mode of use of the mobile phone. To record the ipsi- and contralateral effects, we used the differences in the average values of a simple auditory-motor reaction between the left and right ears with mono-presentation of the sound signal of 573 respondents of different age groups. The obtained values were compared with the control group data for each age group (491 respondents). If the difference was greater than in the control group, the ipsilateral or contralateral effect was recorded. The severity of the effect was evaluated taking into account the lateral preferences of each participant in the experiments (to which ear the mobile phone is most often held) and the mode of use of the mobile phone. Statistical processing of the results was carried out using the non-parametric Mann-Whitney test and the method of descriptive statistics: prevalence indicator (Pr) (relative frequency of manifestation of a particular attribute in the sample). The comparison of the severity of ipsi and contralateral effects for different age groups allowed us to establish the following patterns. It was found that, in general, the manifestation of the contralateral effect decreases with age, and the ipsilateral effect increases. However, this change is not linear. It is shown that the features of the manifestation of the contralateral and ipsilateral effect for each age group depend both on the time of daily use of a mobile phone and on the total duration of use of a mobile phone. We believe that when studying multidimensional input data, an individual approach is necessary. The presented results confirm the negative effect of the radiation of mobile phones on the auditory system, primarily of our younger generation. Given the special vulnerability of children to physical environmental factors and the depth of penetration of EMR MT into the brain of a child, we believe that from a radiobiological point of view, there is already a need to develop a special SanPiN (sanitary rules and norms) for all available modern low-intensity sources of electromagnetic radiation, including Wi-Fi.

Analysis of COVID-19 Infections on a CT Image Using DeepSense Model.

In this paper, a data mining model on a hybrid deep learning framework is designed to diagnose the medical conditions of patients infected with the coronavirus disease 2019 (COVID-19) virus. The hybrid deep learning model is designed as a combination of convolutional neural network (CNN) and recurrent neural network (RNN) and named as DeepSense method. It is designed as a series of layers to extract and classify the related features of COVID-19 infections from the lungs. The computerized tomography image is used as an input data, and hence, the classifier is designed to ease the process of classification on learning the multidimensional input data using the Expert Hidden layers. The validation of the model is conducted against the medical image datasets to predict the infections using deep learning classifiers. The results show that the DeepSense classifier offers accuracy in an improved manner than the conventional deep and machine learning classifiers. The proposed method is validated against three different datasets, where the training data are compared with 70%, 80%, and 90% training data. It specifically provides the quality of the diagnostic method adopted for the prediction of COVID-19 infections in a patient.

A Content-Based Method for Sybil Detection in Online Social Networks via Deep Learning

Online social networks (OSNs) are generally susceptible to Sybil attack, which causes a series of cybersecurity problems and privacy violations. Malicious attackers can create massive Sybils and further utilize those fake identities to launch various Sybil attacks. Therefore, Sybil detection in OSNs has become an urgent security research problem for both academia and industries. The existing content-based methods to detect Sybils base on the combination of manual-design features and machine learning algorithms, which requires lots of professional experiences and human effort. These methods divide the Sybil detection problem into two piece-wise sub-problems, which prevents us from getting the optimal solution. In this work, we propose a novel content-based method to detect Sybils. The proposed method is an end-to-end classification model that extracts features directly from the input data, and then output the classification results in a unified framework. The proposed method includes three main parts: first, the self-normalizing convolutional neural network (CNN) is adopted to extract lower features from the multi-dimensional input data; second, the bidirectional self-normalizing LSTM network (bi-SN-LSTM) is developed to extract higher features from the compressed feature map sequence; third, the dense layer and softmax classifier are stacked to output the classification results. Unlike the traditional bidirectional long short-term memory network (bi-LSTM), the proposed bi-SN-LSTM network utilizes SELU as the activation function of its recurrent step, which provides unbounded changes to the state value. Through the case study of the real-world dataset, the comparison experiments demonstrate that our method significantly outperforms other state-of-the-art methods.

Prediction of Creaky Speech by Recurrent Neural Networks Using Psychoacoustic Roughness

The use of a psychoacoustic roughness model as a predictor of creaky voice is reported. We found that the roughness temporal profile of vocalic segments can predict the presence of creakiness in speech. Using a simple bi-directional Recurrent Neural Network ( rnn ), we were able to predict the presence of creakiness in vocalic segments from only roughness traces with an accuracy similar to that obtained with rnn s trained on at least 12-dimensional input data (including amplitude difference between the first two harmonics, residual peak prominence, etc.). Training rnn s with the combination of roughness and multidimensional input data improved the performance of the predictor, but not significantly. Likewise, augmenting the dataset by time derivatives of the input features did not improve the predictor's performance. The proposed roughness-based predictor eases interpretation and comparison of creakiness among corpora and suggests that roughness prediction models could be successfully used for classification of creaky intervals in speech.

Standing-wave-decomposition Gaussian process

We propose a Standing Wave Decomposition (SWD) approximation to Gaussian Process regression (GP). GP involves a costly matrix inversion operation, which limits applicability to large data analysis. For an input space that can be approximated by a grid and when correlations among data are short-ranged, the kernel matrix inversion can be replaced by analytic diagonalization using the SWD. We show that this approach applies to uni- and multi-dimensional input data, extends to include longer-range correlations, and the grid can be in a latent space and used as inducing points. Through simulations, we show that our approximate method applied to the squared exponential kernel outperforms existing methods in predictive accuracy per unit time in the regime where data are plentiful. Our SWD-GP is recommended for regression analyses where there is a relatively large amount of data and/or there are constraints on computation time.