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OPTIMAL APPROXIMATION IN HILBERT SPACES WITH REPRODUCING kernel functions

MATHEMATICS OF COMPUTATION 1970年第112期24卷 911-&页

作者： LARKIN, FM Computing Centre Queens University Kingston Ontario Canada

Abstract: Characterisations of optimal linear estimation rules are given in terms of the reproducing kernel function of a suitable Hilbert space. The results are illustrated by means of three different, useful function spaces, showing, among other things, how Gaussian quadrature rules, and the Whittaker Cardinal Function, relate to optimal linear estimation rules in particular spaces.

关键词： Approximation Hilbert spaces kernel functions Mathematical functions Gaussian quadratures Inner products Numerical quadratures Mathematical independent variables Mathematical vectors

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Machine Learning for Predictive Maintenance: Support Vector Machines and Different kernel functions

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JOURNAL OF MACHINERY MANUFACTURE AND RELIABILITY 2022年第5期51卷 447-456页

作者： Efeoglu, Ebru Tuna, Gurkan Kutahya Dumlupinar Univ Dept Software Engn Kutahya Turkey Trakya Univ Dept Comp Programming Edirne Turkey

Predictive maintenance relies on machine learning techniques to learn from historical data and also uses live data to analyse failure patterns. Different from conservative maintenance procedures that generally lead to resource wastage, predictive maintenance can offer optimum resource utilisation and allow predict failures before they occur. Machine learning techniques are essential for automated predictive maintenance;therefore, in this paper the use and effectiveness of support vector machines for predictive maintenance is analysed. As the results show, support vector machines achieve the best performance when linear kernel function is used.

关键词： predictive maintenance support vector machines kernel functions confusion matrix accuracy

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Parameter investigation of support vector machine classifier with kernel functions

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KNOWLEDGE AND INFORMATION SYSTEMS 2019年第3期61卷 1269-1302页

作者： Tharwat, Alaa Frankfurt Univ Appl Sci Fac Comp Sci & Engn Frankfurt Germany

Support vector machine (SVM) is one of the well-known learning algorithms for classification and regression problems. SVM parameters such as kernel parameters and penalty parameter have a great influence on the complexity and performance of predicting models. Hence, the model selection in SVM involves the penalty parameter and kernel parameters. However, these parameters are usually selected and used as a black box, without understanding the internal details. In this paper, the behavior of the SVM classifier is analyzed when these parameters take different values. This analysis consists of illustrative examples, visualization, and mathematical and geometrical interpretations with the aim of providing the basics of kernel functions with SVM and to show how it works to serve as a comprehensive source for researchers who are interested in this field. This paper starts by highlighting the definition and underlying principles of SVM in details. Moreover, different kernel functions are introduced and the impact of each parameter in these kernel functions is explained from different perspectives.

关键词： Support vector machine (SVM) kernel functions Radial basis function Polynomial kernel Gaussian kernel Parameter optimization Linear kernel

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A Novel Combination of Whale Optimization Algorithm and Support Vector Machine with Different kernel functions for Prediction of Blasting-Induced Fly-Rock in Quarry Mines

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NATURAL RESOURCES RESEARCH 2021年第1期30卷 191-207页

作者： Nguyen, Hoang Bui, Xuan-Nam Choi, Yosoon Lee, Chang Woo Armaghani, Danial Jahed Duy Tan Univ Inst Res & Dev Da Nang 550000 Vietnam Hanoi Univ Min & Geol Min Fac Dept Surface Min Duc Thang Ward 18 Vien St Hanoi Vietnam Hanoi Univ Min & Geol Electromech Res Ctr Min Duc Thang Ward 18 Vien St Hanoi Vietnam Pukyong Natl Univ Dept Energy Resources Engn Busan 48513 South Korea Dong A Univ Dept Energy & Mineral Resources Coll Engn Busan 49315 South Korea Univ Malaya Dept Civil Engn Fac Engn Kuala Lumpur 50603 Malaysia

This study proposed a novel data-driven model for estimating distance of fly-rock in bench blasting in open-pit mines using a robust combination of the whale optimization algorithm (WOA), support vector machine (SVM) and kernel functions. Four kernel functions were investigated for embedding in the SVM model, including linear (L), radius basis function (RBF), polynomial (P), and hyperbolic tangent (HT) functions. Then, the WOA was applied to optimize the kernel-based SVM models, namely WOA-SVM-L, WOA-SVM-P, WOA-SVM-RBF, and WOA-SVM-HT. A variety of conventional data-driven models were also developed for predicting fly-rock distance, including adaptive neuro-fuzzy inference system (ANFIS), gradient boosting machine (GBM), random forest (RF), classification and regression tree (CART), and artificial neural network (ANN). The blasting parameters and maximum fly-rock distance, as well as their relationship, were carefully investigated for this aim. The predictive results of the models were evaluated through two performance indices: root-mean-squared error (RMSE) and correlation coefficient (R-2). These indices indicated that the linear function-based WOA-SVM model (i.e., WOA-SVM-L) seems to be not fit for predicting fly-rock with the largest error (i.e., RMSE = 9.080 andR(2) = 0.937). In contrast, the WOA-SVM-RBF model yielded the highest accuracy in predicting the distance of fly-rock (i.e., RMSE = 5.241,R-2 = 0.977). Meanwhile, the WOA-SVM-P and WOA-SVM-HT models provided lower performances than those of the WOA-SVM-RBF model, but they are acceptable. The conventional models (i.e., ANFIS, GBM, RF, CART, and ANN) are pretty well (i.e., RMSE in the range of 5.804 to 6.567;R(2)in the range of 0.965 to 0.973);however, their performance is lower than those of the WOA-SVM-RBF model as well. Based on these results, the WOA-SVM model was proposed as a useful data-driven model for predicting fly-rock with high reliability in practical engineering.

关键词： Bench blasting Fly-rock Hybrid intelligent model Whale optimization algorithm Support vector machine kernel functions

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A Comparison Study of Different kernel functions for SVM-based Classification of Multi-temporal Polarimetry SAR Data 1

A Comparison Study of Different Kernel Functions for SVM-bas...

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1st ISPRS International Conference on Geospatial Information Research

作者： Yekkehkhany, B. Safari, A. Homayouni, S. Hasanlou, M. Univ Tehran Coll Engn Dept Geomat Engn Tehran 14174 Iran Univ Ottawa Dept Geog Ottawa ON K1N 6N5 Canada

ISBN: (纸本)9781629935201

In this paper, a framework is developed based on Support Vector Machines (SVM) for crop classification using polarimetric features extracted from multi-temporal Synthetic Aperture Radar (SAR) imageries. The multi-temporal integration of data not only improves the overall retrieval accuracy but also provides more reliable estimates with respect to single-date data. Several kernel functions are employed and compared in this study for mapping the input space to higher Hilbert dimension space. These kernel functions include linear, polynomials and Radial Based Function (RBF). The method is applied to several UAVSAR L-band SAR images acquired over an agricultural area near Winnipeg, Manitoba, Canada. In this research, the temporal alpha features of H/A/alpha decomposition method are used in classification. The experimental tests show an SVM classifier with RBF kernel for three dates of data increases the Overall Accuracy (OA) to up to 3% in comparison to using linear kernel function, and up to 1% in comparison to a 3rd degree polynomial kernel function.

关键词： Full-polarimetric SAR data multi-temporal data SVM kernel functions cop classification

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A COMPARISON OF kernel functions FOR INTIMATE MIXTURE MODELS

A COMPARISON OF KERNEL FUNCTIONS FOR INTIMATE MIXTURE MODELS

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1st Workshop on Hyperspectral Image and Signal Processing - Evolution in Remote Sensing

作者： Broadwater, Joshua Banerjee, Amit Johns Hopkins Univ Appl Phys Lab Laurel MD 20723 USA

ISBN: (纸本)9781424446865

In previous work, kernel methods were introduced as a way to generalize the linear mixing model. This work led to a new set of algorithms that performed the unmixing of hyperspectral imagery in a reproducing kernel Hilbert space. By processing the imagery in this space different types of unmixing could be introduced including an approximation of intimate mixtures. Whereas previous research focused on developing the mathematical foundation for kernel unmixing, this paper focuses on the selection of the kernel function. Experiments are conducted on real-world hyperspectral data using a linear, a radial-basis function, a polynomial, and a proposed physics-based kernel. Results show which kernels provide the best ability to perform intimate unmixing.

关键词： kernel functions intimate mixtures abundance estimation

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Comparative Study of Anomaly Detection in Wireless Sensor Networks Using Different kernel functions

Comparative Study of Anomaly Detection in Wireless Sensor Ne...

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International Conference on VLSI, Communications, and Signal Processing (VCAS)

作者： Gavel, Shashank Raghuvanshi, Ajay Singh Tiwari, Sudarshan Natl Inst Technol Dept Elect & Telecommun Raipur Madhya Pradesh India Motilal Nehru Natl Inst Technol Dept Elect & Commun Allahabad Uttar Pradesh India

ISBN: (纸本)9789813297753;9789813297746

Wireless sensor network (WSN) is defined as an autonomous network composed of low power sensor nodes having limited computational, communication, and energy resources. Being short at resources they require efficient use of each resource to prolong network lifetime. Sensor networks are exposed to noise, compromised nodes, low battery levels, and damaged sensors, all these results in anomalous readings or anomaly. Presence of anomaly in system deteriorates the performance of WSN in terms of efficiency, accuracy, and reliability. Hence anomaly detection becomes a major challenge to decide the performance of network. Support vector machine (SVM) is a light weight, learning-based binary classifier that can classify the raw data into normal and anomalous. SVM suffers from computational complexity while handling large datasets, so sequential minimal optimization SVM (SMO-SVM) is used to reduce the complexity. In this paper, a comparative study is made on anomaly detection using SMO-SVM classifier utilizing different kernel functions.

关键词： Wireless sensor network Anomaly detection Support vector machine Sequential minimal optimization kernel functions

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A comparative approach of support vector machine kernel functions for GIS-based landslide susceptibility mapping

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APPLIED GEOMATICS 2021年第4期13卷 837-851页

作者： Kamran, Khalil Valizadeh Feizizadeh, Bakhtiar Khorrami, Behnam Ebadi, Yousef Univ Tabriz Dept Remote Sensing & GIS Tabriz Iran Humboldt Univ Dept Geog GISci Lab Berlin Germany Dokus Eylul Univ Grad Sch Nat & Appl Sci Dept GIS Izmir Turkey

Landslides are among the most destructive natural hazards with severe socio-economic ramifications all around the world. Understanding the critical combination of geoenvironmental factors involved in the occurrence of landslides can mitigate the adverse impacts ascribed to them. Among the several scenarios for studying and investigating this phenomenon, landslide susceptibility mapping (LSM) is the most prominent method. Applying the machine learning (ML) algorithms integrated with the geographic information systems (GIS) has become a trending means for accurate and rapid landslide mapping practices in the scientific community. Support vector machine (SVM) has been the most commonly applied ML algorithm for LSM in recent years. The current study aims to implement different SVM kernel functions including polynomial kernel function (PKF) (degree 1 to 5), radial basis function (RBF), sigmoid, and linear kernels, for a GIS-based LSM over the Tabriz Basin (TB). To this end, a total number of 9 conditioning parameters being involved in the occurrence of the landslide events were determined and utilized. The LSM maps of the TB were generated based on the different SVM kernels and were statistically validated according to the landslide inventory. The findings revealed that the polynomial-degree-2 (PKF-2) model (AUC = 0.9688) outperforms the rest of the utilized kernels. According to the SLM map generated through PKF-2, the northernmost parts of the TB are extremely susceptible to slope failures than the rest;therefore, the developmental policies over these parts have to be taken into account with privileged priority to hinder any humanitarian as well as environmental catastrophes.

关键词： Landslide susceptibility mapping Support vector machine kernel functions GIS Tabriz Basin

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The Equivalence Relationship between kernel functions Based on SVM and Four-Layer Functional Networks

The Equivalence Relationship between Kernel Functions Based ...

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10th International Conference on Intelligent Computing (ICIC)

作者： Zhou, Yongquan Luo, Qifang Ma, Mingzhi Li, Liangliang Guangxi Univ Nationalities Coll Informat Sci & Engn Nanning 530006 Guangxi Peoples R China

ISBN: (纸本)9783319093390;9783319093383

This paper based on the concept of function interpolation, a functional network interpolation mechanism was analyzed, the equivalent between functional network and kernel functions based SVM, and the equivalent relationship between functional networks with SVM is demonstrated. This result provides us a very useful guideline when we perform theoretical research and applications on design SVM, functional network systems.

关键词： Functional network interpolation representation kernel functions SVM

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GPES: An algorithm for evolving hybrid kernel functions of Support Vector Machines

GPES: An algorithm for evolving hybrid kernel functions of S...

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IEEE Congress on Evolutionary Computation

作者： Phienthrakul, Tanasanee Kijsirikul, Boonserm Chulalongkorn Univ Dept Comp Engn Bangkok 10330 Thailand Chulalongkorn Univ Fac Engn Dept Comp Sci Bangkok 10330 Thailand

ISBN: (纸本)9781424413393

The Support Vector Machine (SVM) is a popular approach to the classification of data. One problem of SVM is how to choose a kernel and the parameters for the kernel. This paper proposes 4 classification technique, called GPES, that combines Genetic Programming (GP) and Evolutionary Strategies (ES) to evolve a hybrid kernel for an SVM classifier. The hybrid kernels are represented as trees that have some adjustable parameters. These hybrid kernels are also the Mercer's kernels. The experimental results are compared with a standard SVM classifier using the polynomial and radial basis function kernels with various parameter settings.

关键词： parameter setting Hybrid electric vehicles kernel functions Polynomial Classifiers

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