Mathematics

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25 pages, 4726 KiB

Open AccessArticle

PFA-Nipals: An Unsupervised Principal Feature Selection Based on Nonlinear Estimation by Iterative Partial Least Squares

by Emilio Castillo-Ibarra, Marco A. Alsina, Cesar A. Astudillo and Ignacio Fuenzalida-Henríquez

Mathematics 2023, 11(19), 4154; https://doi.org/10.3390/math11194154 - 3 Oct 2023

Cited by 1 | Viewed by 1280

Abstract

Unsupervised feature selection (UFS) has received great interest in various areas of research that require dimensionality reduction, including machine learning, data mining, and statistical analysis. However, UFS algorithms are known to perform poorly on datasets with missing data, exhibiting a significant computational load [...] Read more.

Unsupervised feature selection (UFS) has received great interest in various areas of research that require dimensionality reduction, including machine learning, data mining, and statistical analysis. However, UFS algorithms are known to perform poorly on datasets with missing data, exhibiting a significant computational load and learning bias. In this work, we propose a novel and robust UFS method, designated PFA-Nipals, that works with missing data without the need for deletion or imputation. This is achieved by considering an iterative nonlinear estimation of principal components by partial least squares, while the relevant features are selected through minibatch K-means clustering. The proposed method is successfully applied to select the relevant features of a robust health dataset with missing data, outperforming other UFS methods in terms of computational load and learning bias. Furthermore, the proposed method is capable of finding a consistent set of relevant features without biasing the explained variability, even under increasing missing data. Finally, it is expected that the proposed method could be used in several areas, such as machine learning and big data with applications in different areas of the medical and engineering sciences. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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19 pages, 4905 KiB

Open AccessArticle

IC-SNN: Optimal ANN2SNN Conversion at Low Latency

by Cuixia Li, Zhiquan Shang, Li Shi, Wenlong Gao and Shuyan Zhang

Mathematics 2023, 11(1), 58; https://doi.org/10.3390/math11010058 - 23 Dec 2022

Cited by 6 | Viewed by 2305

Abstract

The spiking neural network (SNN) has attracted the attention of many researchers because of its low energy consumption and strong bionics. However, when the network conversion method is used to solve the difficulty of network training caused by its discrete, too-long inference time, [...] Read more.

The spiking neural network (SNN) has attracted the attention of many researchers because of its low energy consumption and strong bionics. However, when the network conversion method is used to solve the difficulty of network training caused by its discrete, too-long inference time, it may hinder the practical application of SNN. This paper proposes a novel model named the SNN with Initialized Membrane Potential and Coding Compensation (IC-SNN) to solve this problem. The model focuses on the effect of residual membrane potential and rate encoding on the target SNN. After analyzing the conversion error and the information loss caused by the encoding method under the low time step, we propose a new initial membrane potential setting method and coding compensation scheme. The model can enable the network to still achieve high accuracy under a low number of time steps by eliminating residual membrane potential and encoding errors in the SNN. Finally, experimental results based on public datasets CIFAR10 and CIFAR100 also demonstrate that the model can still achieve competitive classification accuracy in 32 time steps. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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18 pages, 3040 KiB

Open AccessArticle

OTNet: A Small Object Detection Algorithm for Video Inspired by Avian Visual System

by Pingge Hu, Xingtong Wang, Xiaoteng Zhang, Yueyang Cang and Li Shi

Mathematics 2022, 10(21), 4125; https://doi.org/10.3390/math10214125 - 4 Nov 2022

Cited by 1 | Viewed by 2468

Abstract

Small object detection is one of the most challenging and non-negligible fields in computer vision. Inspired by the location–focus–identification process of the avian visual system, we present our location-focused small-object-detection algorithm for video or image sequence, OTNet. The model contains three modules corresponding [...] Read more.

Small object detection is one of the most challenging and non-negligible fields in computer vision. Inspired by the location–focus–identification process of the avian visual system, we present our location-focused small-object-detection algorithm for video or image sequence, OTNet. The model contains three modules corresponding to the forms of saliency, which drive the strongest response of OT to calculate the saliency map. The three modules are responsible for temporal–spatial feature extraction, spatial feature extraction and memory matching, respectively. We tested our model on the AU-AIR dataset and achieved up to 97.95% recall rate, 85.73% precision rate and 89.94 F₁ score with a lower computational complexity. Our model is also able to work as a plugin module for other object detection models to improve their performance in bird-view images, especially for detecting smaller objects. We managed to improve the detection performance by up to 40.01%. The results show that our model performs well on the common metrics on detection, while simulating visual information processing for object localization of the avian brain. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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17 pages, 2172 KiB

Open AccessArticle

Application of HMM and Ensemble Learning in Intelligent Tunneling

by Yongbo Pan and Xunlin Zhu

Mathematics 2022, 10(10), 1778; https://doi.org/10.3390/math10101778 - 23 May 2022

Cited by 2 | Viewed by 1786

Abstract

The cutterhead torque and thrust, reflecting the obstruction degree of the geological environment and the behavior of excavation, are the key operating parameters for the tunneling of tunnel boring machines (TBMs). In this paper, a hybrid hidden Markov model (HMM) combined with ensemble [...] Read more.

The cutterhead torque and thrust, reflecting the obstruction degree of the geological environment and the behavior of excavation, are the key operating parameters for the tunneling of tunnel boring machines (TBMs). In this paper, a hybrid hidden Markov model (HMM) combined with ensemble learning is proposed to predict the value intervals of the cutterhead torque and thrust based on the historical tunneling data. First, the target variables are encoded into discrete states by means of HMM. Then, ensemble learning models including AdaBoost, random forest (RF), and extreme random tree (ERT) are employed to predict the discrete states. On this basis, the performances of those models are compared under different forms of the same input parameters. Moreover, to further validate the effectiveness and superiority of the proposed method, two excavation datasets including Beijing and Zhengzhou from the actual project under different geological conditions are utilized for comparison. The results show that the ERT outperforms the other models and the corresponding prediction accuracies are up to 0.93 and 0.99 for the cutterhead torque and thrust, respectively. Therefore, the ERT combined with HMM can be used as a valuable prediction tool for predicting the cutterhead torque and thrust, which is of positive significance to alert the operator to judge whether the excavation is normal and assist the intelligent tunneling. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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19 pages, 7208 KiB

Open AccessArticle

Boundary Controller Design for a Class of Horizontal Belt Transmission System with Boundary Vibration Constraint

by Runhuan Sun, Li Tang and Yanjun Liu

Mathematics 2022, 10(9), 1391; https://doi.org/10.3390/math10091391 - 21 Apr 2022

Cited by 1 | Viewed by 1520

Abstract

In this paper, the problem of transverse vibration suppression of a belt system moving in the horizontal direction is investigated. This system is characterized by the boundary vibration constraint and is affected by external disturbances. For it, we introduced a logarithmic function in [...] Read more.

In this paper, the problem of transverse vibration suppression of a belt system moving in the horizontal direction is investigated. This system is characterized by the boundary vibration constraint and is affected by external disturbances. For it, we introduced a logarithmic function in the candidate term of the Lyapunov function and used a symbolic function in the controller to compensate for the effects of boundary vibration constraints and boundary disturbances, respectively. In order to better achieve the control objective, we designed a boundary control scheme. The state feedback boundary controller was designed using the boundary signals of the system when they can be available directly. Considering the presence of noise in the practical system, some system signals cannot be measured accurately. Therefore, a high-gain observer was introduced to estimate these signals, and an output feedback boundary controller was designed. Finally, the simulation example showed that both controllers guarantee effective suppression of the transverse vibration of the system without violating the boundary vibration constraints. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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17 pages, 3315 KiB

Open AccessEditor’s ChoiceArticle

PFVAE: A Planar Flow-Based Variational Auto-Encoder Prediction Model for Time Series Data

by Xue-Bo Jin, Wen-Tao Gong, Jian-Lei Kong, Yu-Ting Bai and Ting-Li Su

Mathematics 2022, 10(4), 610; https://doi.org/10.3390/math10040610 - 16 Feb 2022

Cited by 100 | Viewed by 12118

Abstract

Prediction based on time series has a wide range of applications. Due to the complex nonlinear and random distribution of time series data, the performance of learning prediction models can be reduced by the modeling bias or overfitting. This paper proposes a novel [...] Read more.

Prediction based on time series has a wide range of applications. Due to the complex nonlinear and random distribution of time series data, the performance of learning prediction models can be reduced by the modeling bias or overfitting. This paper proposes a novel planar flow-based variational auto-encoder prediction model (PFVAE), which uses the long- and short-term memory network (LSTM) as the auto-encoder and designs the variational auto-encoder (VAE) as a time series data predictor to overcome the noise effects. In addition, the internal structure of VAE is transformed using planar flow, which enables it to learn and fit the nonlinearity of time series data and improve the dynamic adaptability of the network. The prediction experiments verify that the proposed model is superior to other models regarding prediction accuracy and proves it is effective for predicting time series data. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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16 pages, 412 KiB

Open AccessArticle

Analysis of Performance Measure in Q Learning with UCB Exploration

by Weicheng Ye and Dangxing Chen

Mathematics 2022, 10(4), 575; https://doi.org/10.3390/math10040575 - 12 Feb 2022

Cited by 5 | Viewed by 2004

Abstract

Compared to model-based Reinforcement Learning (RL) approaches, model-free RL algorithms, such as Q-learning, require less space and are more expressive, since specifying value functions or policies is more flexible than specifying the model for the environment. This makes model-free algorithms more prevalent [...] Read more.

Compared to model-based Reinforcement Learning (RL) approaches, model-free RL algorithms, such as Q-learning, require less space and are more expressive, since specifying value functions or policies is more flexible than specifying the model for the environment. This makes model-free algorithms more prevalent in modern deep RL. However, model-based methods can more efficiently extract the information from available data. The Upper Confidence Bound (UCB) bandit can improve the exploration bonuses, and hence increase the data efficiency in the Q-learning framework. The cumulative regret of the Q-learning algorithm with an UCB exploration policy in the episodic Markov Decision Process has recently been explored in the underlying environment of finite state-action space. In this paper, we study the regret bound of the Q-learning algorithm with UCB exploration in the scenario of compact state-action metric space. We present an algorithm that adaptively discretizes the continuous state-action space and iteratively updates Q-values. The algorithm is able to efficiently optimize rewards and minimize cumulative regret. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

24 pages, 8747 KiB

Open AccessArticle

Effect of a Novel Tooth Pitting Model on Mesh Stiffness and Vibration Response of Spur Gears

by Jingyu Hou, Shaopu Yang, Qiang Li and Yongqiang Liu

Mathematics 2022, 10(3), 471; https://doi.org/10.3390/math10030471 - 31 Jan 2022

Cited by 9 | Viewed by 2636

Abstract

The existence of pitting failure has a direct influence on the time-varying mesh stiffness (TVMS) and thus changes the vibration properties of the gears. The shape of pitting on the tooth surface is characterized by randomness and geometric complexity. The overlapping pitting shape [...] Read more.

The existence of pitting failure has a direct influence on the time-varying mesh stiffness (TVMS) and thus changes the vibration properties of the gears. The shape of pitting on the tooth surface is characterized by randomness and geometric complexity. The overlapping pitting shape has rarely been investigated, especially when the misalignment of gear base circle and root circle was considered. In this paper, the pitting shape is considered as approximately the union of several ellipse cylinders, in which the gear tooth is treated as a cantilever beam starting from the root circle. Then, the TVMS of perfect gear and that of gear with different pitting severity levels are solved by the potential energy method. The effect of pitting size on TVMS is discussed in detail. In addition, the vibration response in the frequency domain for the gear system is analyzed, and the effectiveness is qualitatively verified by comparing with the vibration signals of the experimental gearbox. The results indicate that the new pitting model overcomes the problem of ignoring the overlap between different pits and is more consistent with the actual situation. The presence of tooth pitting reduces the TVMS, and the complex sidebands appear around the gear mesh frequency and its harmonics. The proposed model can be used to predict the fluctuation of gear mesh stiffness when tooth pitting occurs, and the corresponding dynamic characteristics can provide the theoretical basis for gear condition monitoring and fault diagnosis. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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18 pages, 971 KiB

Open AccessArticle

Adaptive Sliding Mode Attitude-Tracking Control of Spacecraft with Prescribed Time Performance

by Runze Chen, Zhenling Wang and Weiwei Che

Mathematics 2022, 10(3), 401; https://doi.org/10.3390/math10030401 - 27 Jan 2022

Cited by 8 | Viewed by 2595

Abstract

In this article, a novel finite-time attitude-tracking control scheme is proposed by using the prescribed performance control (PPC) method for the spacecraft system under the external disturbance and an uncertain inertia matrix. First, a novel polynomial finite-time performance function (FTPF) was used to [...] Read more.

In this article, a novel finite-time attitude-tracking control scheme is proposed by using the prescribed performance control (PPC) method for the spacecraft system under the external disturbance and an uncertain inertia matrix. First, a novel polynomial finite-time performance function (FTPF) was used to avoid the complex calculation of exponential function from conventional FTPF. Then, a simpler error transformation was introduced to guarantee that the attitude-tracking error converges to a preselected region in prescribed time. Subsequently, a robust adaptive controller was proposed by using the backstepping method and the sliding mode control (SMC) technique. Unlike the existing attitude-tracking control results, the proposed PPC scheme guarantees the performance of spacecraft system under the static and transient conditions. Meanwhile, the state trajectory of system can be completely drawn into the designed sliding surface. The stability of the control scheme is proven rigorously by the Lyapunov’s theory of stability. Finally, the simulations show that the convergence rate and the convergence accuracy are better for the tracking errors of spacecraft system under the proposed control scheme. Full article

(This article belongs to the Special Issue Mathematical Method and Application of Machine Learning)

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