Optimal Kernel Function Research Articles

Optimal Kernel Function for High Speed Rail Received Signal Level Dataset

Optimal Kernel Function for High Speed Rail Received Signal Level Dataset

A dataset of downscaled monthly precipitation at 1 km resolution in Guangxi, China and ASEAN regions from 2001 to 2020

Located in the southeastern Asia, Guangxi, China and the ASEAN regions have a subtropical monsoon climate with abundant rainfall and frequent floods, which has a great impact on social and economic activities. The precipitation data with high precision and high spatial and temporal resolution are of great significance for industrial and agricultural production, water conservancy development, drought and flood monitoring and prevention, and ecological environment protection. In this paper, we used the Global Precipitation Measurement Mission precipitation data (GPM IMERG) from 2001 to 2020 as the dependent variable in combination with the enhanced vegetation index (EVI), surface evapotranspiration (ET), land surface temperature (LST) from MODIS data and elevation (ELV) from ASTER data as explanatory variables. Then we introduced a geographically weighted regression (GWR) model to construct an annual scale model, depicting the spatial variation of 10-km satellite precipitation with the influence of geographical environmental conditions. Five types of kernel functions were adopted in our GWR model, including the gaussian, exponential, bisquare, tricube, and boxcar kernel function. The optimal kernel function was selected based on the correlation coefficient, the root means square error and bias. Thus, we established the dataset of downscaled monthly precipitation in Guangxi, China and ASEAN regions from 2001 to 2020 by extrapolating the GWR model with input variables at 1 km resolution. The dataset of 1-km monthly precipitation from 2001 to 2020 was also generated by the proportional coefficient method. Moreover, ground observation data from 2,679 stations during 2001–2020 were used for verification. The correlation coefficient, root mean square error and deviation were 0.792, 74.610mm and -0.122%, respectively. The results show that this dataset can reflect the precipitation spatial and temporal distribution and its variations at 1-km resolution in detail, and could be potentially promising for ecological environment, hydrological management, flood prediction and other relevant fields.

Forecasting interval‐valued returns of crude oil: A novel kernel‐based approach

AbstractThis paper proposes a novel kernel‐based generalized random interval multilayer perceptron (KG‐iMLP) method for predicting high‐volatility interval‐valued returns of crude oil. The KG‐iMLP model is constructed by utilizing the distance based on a kernel function, which outperforms the conventional Euclidean distance. Additionally, the optimal kernel function is estimated using the variance–covariance matrix of the prediction error, contributing to a better understanding of the overall characteristics of interval‐valued data. The introduction of the kernel function renders the algorithms used for estimating machine learning parameters ineffective. Therefore, this paper further proposes a backward distance of accumulative error propagation algorithm to estimate both the kernel function and model parameters, which provides a feasible approach for utilizing kernel function in interval neural networks. In the empirical analysis of weekly and daily returns of WTI crude oil, the superior predictive performance of the proposed method is demonstrated, enabling stable and accurate predictions for both point values and interval values. The model exhibits consistent outstanding performance across different network structures, showcasing the potential of KG‐iMLP for crude oil price forecasting.

A deterministic and probabilistic hybrid model for wind power forecasting based improved feature screening and optimal Gaussian mixed kernel function

Forecasting wind power is crucial to ensuring the electricity system runs steadily. However, wind power forecasting is hampered by the randomness and volatility of wind power data. In this paper, a deterministic and probabilistic decomposition ensemble model based on improved feature screening and optimal Gaussian mixed kernel function is proposed, which mainly includes feature screening, feature learning, intelligent weighted integration and interval prediction modules. First, an improved feature screening (IFS) is proposed to capture the optimal features of the original wind power data, eliminating the interference of redundant features. Then an optimized deep neural network is suggested to learn the outcomes of IFS and further explore the temporal correlation of these features. Then, considering the difference of the contribution of each feature component, the final result is obtained by integrating the preliminary forecast results using intelligent weighted integration (IWI). Finally, an optimal mixed kernel-based Gaussian process regression model is developed for interval prediction, which improves the adaptability of the model. The data sets of two wind farms in Inner Mongolia were used for empirical testing. On the two datasets, the model's root mean square error (RMSE) is 1.1845 and 1.7354, respectively, both of which are lower than the comparison model. The model has the lowest coverage width criterion (CWC) of 0.1499 and 0.1460 on the two datasets, respectively.

Black-box modeling of ship maneuvering motion using multi-output least-squares support vector regression based on optimal mixed kernel function

Black-box modeling has been widely used to predict ship maneuvering motion. A novel black-box modeling approach using optimal mixed kernel multi-output least-squares support vector regression (MMLSSVR) based on the artificial hummingbird algorithm (AHA) is proposed in this paper. To improve the performance of the MMLSSVR model, a mixed kernel function that combines a radial basis function and a polynomial kernel function to capture both global and local properties is proposed. The optimal hyper-parameters of the mixed kernel function are determined by the AHA, which employs the linear combination of the mean square error and the determinant of error covariance as the objective function to balance between prediction accuracy and stability. The performance of the proposed method is evaluated using SR108 large container ship data. The experimental results demonstrate that the proposed MMLSSVR model achieves desirable prediction accuracy and strong generalizability for ship maneuvering motion modeling.

Seismic fault identification in coal mines based on the self-organizing map-gray wolf optimizer-support vector machine algorithm

Accurate fault identification in coal mines is important to improve mine safety and economic benefits. We compare various intelligent algorithms for data preprocessing and optimization and analyze the construction methods of seismic attribute data sets and the performance of intelligent optimization algorithms using fault identification accuracy as the discrimination index to find a better combined model for seismic fault identification. First, the training data set is constructed by mining the fault and nonfault information revealed by the roadway. The distribution characteristics of the seismic attribute data indicate similarities among them, and they are nonlinearly separable. Directly using the attributes to construct the data set, the accuracy of fault identification using the support vector machine (SVM) model is 78.41%. Principal component analysis (PCA) and self-organizing mapping (SOM) neural networks are used to extract effective information and then combined with the SVM classification model, and the accuracy of fault identification is 83.82% and 87.47%, respectively. Compared with the original data and PCA dimensionality reduction data, the accuracy of fault detection is improved by 9.06% and 3.66%, respectively, indicating that SOM can effectively improve the accuracy of fault detection by eliminating similar attributes and reducing the weight of redundant information. Then, through a fixed attribute data set, genetic algorithm (GA), particle swarm optimization (PSO), and gray wolf optimizer (GWO) intelligent optimization algorithms are used to find the optimal kernel function parameter and penalty parameter of the SVM classifier. The accuracy rate of the SOM-GWO-SVM model reaches 91.12%, compared with the SOM-PSO-SVM and SOM-GA-SVM, and the model accuracy is increased by 5.2% and 5.61%, respectively. Compared with PSO and GA, the GWO algorithm has a better global search ability. The identification result of the SOM-GWO-SVM model is closest to the actual fault exposure, especially for the identification of “short” faults and associated faults, which has obvious advantages over the traditional manual interpretation in terms of efficiency and accuracy.

On the partition noise in chosen particle weighted methods and its consequences for weakly-compressible flow models

The Meshless Finite Volume (MFV) method, which is a member of the particle weighted methods (PWM) family, is analysed in the context of the so-called partition noise problem. This issue is inherent to PWM-type discretisation which is based on compact support kernel functions and particle sampling. The partition noise exhibits itself as spurious oscillations observed in the solution; they are caused by unphysical source terms in the discretised equations and approximate local volumes computation. Unfortunately, decreasing the discrete length scale which controls the spatial resolution reduces the partition noise only weakly (and never completely). When choosing numerical schemes, a special care is required since in naive implementations the partition noise may even lead to loss of stability. However, even when stability is assured, PWM does not fulfil the assumptions of the Lax equivalence theorem (i.e. the discretised equations are not consistent), therefore convergence in the classical meaning cannot be guaranteed.As an example of a problematic use of MFV, we investigate its application to the solution of fluid flow equations at low Mach numbers, aiming to mimic truly incompressible flow conditions. Taken here as isothermal Euler equations, they are the basis of the so-called weakly-compressible (WC) flow models. Such modelling does not involve any elliptic-type equation and, due to the algorithmic and computational reasons, seems to be well-suited for particle methods. The WC flow model imposes, however, a serious challenge for PWM since: (i) the method is not gauge invariant and the disparity between the speed of sound and the convective velocity scale causes a significant spurious source of momentum; (ii) the inaccuracy in the local volumes approximation leads to errors in the computed density which are comparable to physically relevant slight variations, inherent to the WC approach. We propose specific numerical and modelling measures: controlled relaxation of initial particle distribution, particle volumes computation using an optimal kernel function, a choice of gradient limiting techniques and a carefully chosen background pressure. Although these improvements significantly increase the accuracy (however at remarkably increased computational cost), the theoretical 2nd-order convergence is achieved only at lower spatial resolutions when the truncation errors dominate. The accuracy of mesh-based methods is achieved in PWM only for the pressure field; the errors in the velocity field are much larger and convergence is at most 1st-order. We point some contradictory requirements of the model equations and the numerical method. One of the conclusions is that it is doubtful to construct a convergent truly Lagrangean method of PWM type at reasonable computational cost. The present findings also apply to conservative variants of the weakly-compressible Smoothed Particle Hydrodynamics which, being first order consistent in the best case, suffers from the partition noise even more severely than the considered MFV approach which is theoretically second order consistent. The conclusions pose a question about a rationale for the use of WC-PWM approach in chosen applications, in particular free surface and interfacial flows.

Prediction of concrete strength using MCMC and GPR methods

Concrete strength prediction is a complex nonlinear regression task that involves multiple ingredients and age as key factors. In order to achieve accurate predictions, the Markov Chain Monte Carlo (MCMC) and Gaussian Process Regression (GPR) techniques are employed. The dataset, sourced from Kaggle repositories, comprises a comprehensive collection of 1030 data points. Alongside the existing features (content of ingredients, age and strength), we introduce new ones, including water-cement ratio, sand ratio, and water-binder ratio, to enhance the model's credibility. To determine the optimal kernel function, the dataset is partitioned into training and testing subsets. Notably, the MCMC method yields an R2 of 0.41, while GPR demonstrates a significantly improved R2 of 0.89. Further investigation is warranted to refine the model's fit and optimize its predictive capacity.

Memory-dependent derivative grey Bernoulli model and its application in electricity generation forecast

PurposeThis paper aims to develop a novel grey Bernoulli model with memory characteristics, which is designed to dynamically choose the optimal memory kernel function and the length of memory dependence period, ultimately enhancing the model's predictive accuracy.Design/methodology/approachThis paper enhances the traditional grey Bernoulli model by introducing memory-dependent derivatives, resulting in a novel memory-dependent derivative grey model. Additionally, fractional-order accumulation is employed for preprocessing the original data. The length of the memory dependence period for memory-dependent derivatives is determined through grey correlation analysis. Furthermore, the whale optimization algorithm is utilized to optimize the cumulative order, power index and memory kernel function index of the model, enabling adaptability to diverse scenarios.FindingsThe selection of appropriate memory kernel functions and memory dependency lengths will improve model prediction performance. The model can adaptively select the memory kernel function and memory dependence length, and the performance of the model is better than other comparison models.Research limitations/implicationsThe model presented in this article has some limitations. The grey model is itself suitable for small sample data, and memory-dependent derivatives mainly consider the memory effect on a fixed length. Therefore, this model is mainly applicable to data prediction with short-term memory effect and has certain limitations on time series of long-term memory.Practical implicationsIn practical systems, memory effects typically exhibit a decaying pattern, which is effectively characterized by the memory kernel function. The model in this study skillfully determines the appropriate kernel functions and memory dependency lengths to capture these memory effects, enhancing its alignment with real-world scenarios.Originality/valueBased on the memory-dependent derivative method, a memory-dependent derivative grey Bernoulli model that more accurately reflects the actual memory effect is constructed and applied to power generation forecasting in China, South Korea and India.

Research on New Word Recognition Based on Weibo Information and SVM

In order to effectively recognize Weibo new words, this paper proposes a Weibo new word recognition method based on Weibo information and SVM. Firstly, positive and negative samples are extracted from the Weibo corpus and the training corpus annotated with part of speech. Next, the word features of these samples are vectorized and trained through support vector machines to obtain support vectors for new word classification. Finally, it is vectorized and inputted into the trained support vector machine classifier to obtain the recognized Weibo new words. By comparing the experimental results, the optimal fusion feature combination and SVM kernel function are obtained.

A Multi-Antenna Spectrum Sensing Method Based on CEEMDAN Decomposition Combined with Wavelet Packet Analysis

In many practical communication environments, the presence of uncertain and hard-to-estimate noise poses significant challenges to cognitive radio spectrum sensing systems, especially when the noise distribution deviates from the Gaussian distribution. This paper introduces a cutting-edge multi-antenna spectrum sensing methodology that synergistically integrates complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), wavelet packet analysis, and differential entropy. Signal feature extraction commences by employing CEEMDAN decomposition and wavelet packet analysis to denoise signals collected by secondary antenna users. Subsequently, the differential entropy of the preprocessed signal observations serves as the feature vector for spectrum sensing. The spectrum sensing module utilizes the SVM classification algorithm for training, while incorporating elite opposition-based learning and the sparrow search algorithm with genetic variation to determine optimal kernel function parameters. Following successful training, a decision function is derived, which can obviate the need for threshold derivation present in conventional spectrum sensing methods. Experimental validation of the proposed methodology is conducted and comprehensively analyzed, conclusively demonstrating its remarkable efficacy in enhancing spectrum sensing performance.

Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. In this work, we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets. Inspired by the weighted essentially non-oscillatory (WENO) scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. As a continuum model, our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene. Our tests show that the proposed data-driven model is robust and generalizable, in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

Pattern Discovery and Multi-Slot-Ahead Forecast of Network Traffic: A Revisiting to Gaussian Process

The forecast of network traffic with arbitrary predicting horizon is a key enabler of smart management in next-generation networks, as sufficient amount of time can be provided for the proactive manipulation of network resources to maintain high quality transmission. Nevertheless, the evolving characteristic of network traffic challenges the current learning-based and data-driven algorithms on both prediction accuracy and computational complexity. In this work, we explore special properties of network traffic, which are further encoded into the Gaussian Process (GP)-based online learning framework, so as to better comprehend and predict future network traffic from a Bayesian perspective. Specifically, we proceed by three steps, 1). Observing network traffic is evolving, to explore and exploit the dynamic traffic patterns at different times and time-scales, we try to approximate the optimal kernel function of GP by utilizing a mixture of Gaussian to encode the dominant and several nondominant patterns. 2). As network traffic at different time-scales share several common patterns, we adopt Process Convolution (PConv) to fully exploit correlations among multiple subsequent time-slots, so as to facilitate network traffic forecast with large predicting horizon. 3). To promote the tracking capability of the proposed GP-PConv framework without significantly increasing the number of hyper-parameters to train, we slightly modify the GP-based prediction through Lyapunov optimization, which brings performance improvements both in terms of accuracy and computational complexity. Finally, we demonstrate the superiority of the proposed algorithm through simulation.

Blasting vibration hazard classification and prediction research

This paper explores the hazard classification method of blasting vibration on nearby buildings. The ratio of the self-vibration frequency f0 of the protected buildings to the main vibration frequency f of blasting vibration and the ratio of the actual measured peak blasting vibration velocity to the permissible vibration velocity of blasting safety regulations are used as two indicators of the blasting vibration hazard classification method, the blasting vibration hazard index calculation formula was proposed, and the blasting vibration hazard was classified into four levels according to the blasting vibration hazard index. An open pit mine blasting project was used for monitoring, the collected data were processed by random forest method. After processing, bursting heart distance, the total explosive quantity required for one blast, the hole distance meter delay, and the row distance meter delay was selected as the input parameters; the optimal kernel function parameter gamma and c were applied to the SVR (Support Vector Regression) model by changing the search step to expand the parameter search, and improved GS-SVR (Grid Search-Support Vector Regression) model was constructed, through which peak blasting vibration velocity and vibration frequency values were predicted. The results show: improved GS-SVR is effective in predicting peak blasting vibration velocity, with the lowest relative error of 0.15% and the average error of 7.96%; the minimum relative error for the prediction of vibration frequency is 0.03% and the average error is 2.54%. The measured data in the literature of related scholars verified that the blasting vibration hazard classification method is scientific and feasible. It can provide reference and reference for blasting vibration hazard classification and prediction of similar blasting projects.

Automated recognition of asymmetric gait and fatigue gait using ground reaction force data.

Introduction: The purpose of this study was to evaluate the effect of running-induced fatigue on the characteristic asymmetry of running gait and to identify non-linear differences in bilateral lower limbs and fatigued gait by building a machine learning model. Methods: Data on bilateral lower limb three-dimensional ground reaction forces were collected from 14 male amateur runners before and after a running-induced fatigue experiment. The symmetry function (SF) was used to assess the degree of symmetry of running gait. Statistical parameter mapping (Paired sample T-test) algorithm was used to examine bilateral lower limb differences and asymmetry changes pre- and post-fatigue of time series data. The support vector ma-chine (SVM) algorithm was used to recognize the gait characteristics of both lower limbs before and after fatigue and to build the optimal algorithm model by setting different kernel functions. Results: The results showed that the ground reaction forces were asymmetrical (SF > 0.5) both pre-and post-fatigue and mainly concentrated in the medial-lateral direction. The asymmetry of the medial-lateral direction increased significantly after fatigue (p < 0.05). In addition, we concluded that the polynomial kernel function could make the SVM model the most accurate in classifying left and right gait features (accuracy of 85.3%, 82.4%, and 82.4% in medial-lateral, anterior-posterior and vertical directions, respectively). Gaussian radial basis kernel function was the optimal kernel function of the SVM algorithm model for fatigue gait recognition in the medial-lateral and vertical directions (accuracy of 54.2% and 62.5%, respectively). Moreover, polynomial was the optimal kernel function of the anterior-posterior di-rection (accuracy = 54.2%). Discussion: We proved in this study that the SVM algorithm model depicted good performance in identifying asymmetric and fatigue gaits. These findings can provide implications for running injury prevention, movement monitoring, and gait assessment.

Improved Regularized Multi-class Logistic Regression for Gene Classification with Optimal Kernel PCA and HC Algorithm.

A significant challenge in high-dimensional and big data analysis is related to the classification and prediction of the variables of interest. The massive genetic datasets are complex. Gene expression datasets are enriched with useful genes that are associated with specific diseases such as cancer. In this study, we used two gene expression datasets from the Gene Expression Omnibus and preprocessed them before classification. We used optimal kernel principal component analysis in which the optimal kernel function was chosen for dataset dimensionality reduction and extraction of the most important features. The gene sets with a high validity index were collected using a combined hieratical clustering and optimal kernel principal component analysis (KHC-RLR) algorithm. Logistic regression is one of the most common methods for classification, and it has been shown to be a useful classification approach for gene expression data analysis. In this study, we used multi-class logistic regression to classify the collected gene sets. We found that ordinary logistic regression caused a major overfitting problem; therefore, we used regularized multi-class logistic regression to classify the gene sets. The proposed KHC-RLR algorithm showed a high performance and satisfied accuracy measures.

Online Multikernel Learning Method via Online Biconvex Optimization.

Random feature-based online multikernel learning (RF-OMKL) is a promising low-complexity framework for machine learning optimization from continuous streaming data. Nonetheless, it is still an open problem to find an efficient algorithm with an analytical performance guarantee due to the challenge of an underlying online biconvex optimization (OBO). The state-of-the-art method named expert-based online multikernel learning (EoKle) tackled this problem approximately with the lens of expert-based online learning, in which multiple kernels (or experts) optimize their own kernel functions separately and the best sole one is determined via Hedge algorithm. It is asymptotically optimal as to the best sole kernel function in hindsight. We propose collaborative expert-based online multikernel learning (CoKle) by devising a collaborative Hedge (CoHedge) algorithm, in which kernel functions separately optimized as in EoKle are combined in an asymptotically optimal way. It is proved that CoKle is asymptotically optimal as to the best combination of each optimal kernel function in hindsight. Remarkably, this is the first method with a theoretical performance guarantee for expert-based RF-OMKL. Despite its effectiveness, CoKle is inherently suboptimal due to the individual optimization of kernel functions. We address this by presenting an OBO-based method (named BoKle) and partially prove its asymptotic optimality for RF-OMKL. Thus, BoKle can outperform the suboptimal expert-based methods such as CoKle and EoKle. Finally, we demonstrate the superiority of BoKle via experiments with real datasets.

Recognition of Corrosion State of Water Pipe Inner Wall Based on SMA-SVM under RF Feature Selection

To solve the problem of low detection accuracy of water supply pipeline internal wall damage, a random forest algorithm with simplified features and a slime mold optimization support vector machine detection method was proposed. Firstly, the color statistical characteristics, gray level co-occurrence matrix, and gray level run length matrix features of the pipeline image are extracted for multi-feature fusion. The contribution of the fused features is analyzed using the feature simplified random forest algorithm, and the feature set with the strongest feature expression ability is selected for classification and recognition. The global search ability of the slime mold optimization algorithm is used to find the optimal kernel function parameters and penalty factors of the support vector machine model. Finally, the optimal parameters are applied to support the vector machine model for classification prediction. The experimental results show that the recognition accuracy of the classification model proposed in this paper reaches 94.710% on the data sets of different corrosion forms on the inner wall of the pipeline. Compared with the traditional Support Vector Machines (SVM) classification model, the SVM model based on differential pollination optimization, the SVM model based on particle swarm optimization, and the back propagation (BP) neural network classification model, it is improved by 4.786%, 3.023%, 4.030%, and 0.503% respectively.

A Multi-View Deep Metric Learning approach for Categorical Representation on mixed data

It is an important and challenging task to represent the categorical values in mixed data as numerical vectors with intrinsic features, by revealing the complex coupling relationships between the categorical values, attributes and samples. The majority of extant studies expose only one particular coupling relationship in depth, or fuse multiple coupling relationships by using shallow learning based on kernels. The former may not fully mine the essential features of the categorical data. The latter typically has some limitations, for example, difficulty in expanding the spatial structure and difficulty in determining the optimal kernel function. Therefore, this paper proposes a Multi-view Deep Metric Learning for Categorical Representation on mixed data (MvDML-CR). Specifically, first, based on the principle of information complementarity, multiple coupled views are extracted from the complex interaction relationships of the categorical data. Then, in each coupled view, a new proxy loss function is designed to build a deep metric learning sub-model with strong separability, which represents the categorical values as numerical vectors with discrimination. Last, we employ the Hilbert–Schmidt independence criterion to maximize the dependency between the views, and then fuse the sub-models trained in the different views to enhance the complementarity and consistency of the categorical representations. Extensive experiments on 34 mixed datasets with diversified characteristics demonstrate that the classification performance of MvDML-CR is significantly improved, compared with the state-of-the-art competitors.

Targeting Sustainable Transportation Development: The Support Vector Machine and the Bayesian Optimization Algorithm for Classifying Household Vehicle Ownership

Predicting household vehicle ownership (HVO) is a crucial component of travel demand forecasting. Furthermore, reliable HVO prediction is critical for achieving sustainable transportation development objectives in an era of rapid urbanization. This research predicted the HVO using a support vector machine (SVM) model optimized using the Bayesian Optimization (BO) algorithm. BO is used to determine the optimal SVM parameter values. This hybrid model was applied to two datasets derived from the US National Household Travel Survey dataset. Thus, two optimized SVM models were developed, namely SVMBO#1 and SVMBO#2. Using the confusion matrix, accuracy, receiver operating characteristic (ROC), and area under the ROC, the outcomes of these two hybrid models were examined. Additionally, the results of hybrid SVM models were compared with those of other machine learning models. The results demonstrated that the BO algorithm enhanced the performance of the standard SVM model for predicting the HVO. The BO method determined the Gaussian kernel to be the optimal kernel function for both datasets. The performance of the SVM#1 model was improved by 4.27% and 5.16% for the training and testing phases, respectively. For SVM#2 model, the performance of this model was improved by 1.20% and 2.14% for the training and testing phases, respectively. Moreover, the BO method enhanced the AUC of the SVM models used to predict the HVO. The hybrid SVM models also outperformed other machine learning models developed in this study. The findings of this study showed that SVM models hybridized with the BO algorithm can effectively predict the HVO and can be employed in the process of travel demand forecasting.