Polynomial Kernel Function Research Articles

Performance of Support Vector Machine Kernels (SVM-K) on Breast Cancer (BC) Dataset

Breast cancer (BC) most diagnosed invasive disorder and important cause of casualty for women worldwide. Indian contest BC most commonly spread disease among females. This problem is more alarming to economically developing country like India. Government of India made a lot of effort to make aware the women of the country, but despite of availability of diagnostic tool, prediction of disease in real situation is still a puzzle for researchers. Timely detection and categorization of BC using the evolving techniques like Machine Learning (ML) can show a significant role in BC identification and this could be a preventive policy which effectively reduces the risk of BC patients. Although there are four Kernels in ML, are widely in use but their performance varies with the kind of data available. In this study we, apply four different Kernels such as Linear Kernel (LK), Polynomial Kernel (PK), Sigmoid Kernel (SK) and Radial Basis Function Kernel (RBFK) on BC dataset. We estimated the performance of Support Vector Machine Kernels (SVM-K) on BC dataset .The basic idea is to check the exactness of SVM-K to classify WBCD in terms of effectiveness with respect to accuracy, runtime, specificity and precision. The investigations outcome displays that RBFK provides greater accuracy with minimal errors

A Face Recognition System Based on Principal Component Analysis-Wavelet and Support Vector Machines

Face recognition can represent a key requirement in various types of applications such as human-computer interface, monitoring systems, as well as personal identification. In this paper, design and implement of face recognition system are introduced. In this system, a combination of principal component analysis (PCA) and wavelet feature extraction algorithms with support vector machine (SVM) and K-nearest neighborhood classifier is used. PCA and wavelet transform methods are used to extract features from face image using and identify the image of the face using SVMs classifier as well as the neural network are used as a classifier to compare its results with the proposed system. For a more comprehensive comparison, two face image databases (Yale and ORL) are used to test the performance of the system. Finally, the experimental results show the efficiency and reliability of face recognition system, and the results demonstrate accuracy on two databases indicated that the results enhancement 5% using the SVM classifier with polynomial Kernel function compared to use feedforward neural network classifier.

Generalized Legendre Polynomials for Support Vector Machines (SVMS) Classification

In this paper, we introduce a set of new kernel functions derived from the generalized Legendre polynomials to obtain more robust and higher support vector machine (SVM) classification accuracy. The generalized Legendre kernel functions are suggested to provide a value of how two given vectors are like each other by changing the inner product of these two vectors into a greater dimensional space. The proposed kernel functions satisfy the Mercer’s condition and orthogonality properties for reaching the optimal result with low number support vector (SV). For that, the new set of Legendre kernel functions could be utilized in classification applications as effective substitutes to those generally used like Gaussian, Polynomial and Wavelet kernel functions. The suggested kernel functions are calculated in compared to the current kernels such as Gaussian, Polynomial, Wavelets and Chebyshev kernels by application to various non-separable data sets with some attributes. It is seen that the suggested kernel functions could give competitive classification outcomes in comparison with other kernel functions. Thus, on the basis test outcomes, we show that the suggested kernel functions are more robust about the kernel parameter change and reach the minimal SV number for classification generally.

A new surrogate modeling method combining polynomial chaos expansion and Gaussian kernel in a sparse Bayesian learning framework

SummarySurrogate modeling techniques have been increasingly developed for optimization and uncertainty quantification problems in many engineering fields. The development of surrogates requires modeling high‐dimensional and nonsmooth functions with limited information. To this end, the hybrid surrogate modeling method, where different surrogate models are combined, offers an effective solution. In this paper, a new hybrid modeling technique is proposed by combining polynomial chaos expansion and kernel function in a sparse Bayesian learning framework. The proposed hybrid model possesses both the global characteristic advantage of polynomial chaos expansion and the local characteristic advantage of the Gaussian kernel. The parameterized priors are utilized to encourage the sparsity of the model. Moreover, an optimization algorithm aiming at maximizing Bayesian evidence is proposed for parameter optimization. To assess the performance of the proposed method, a detailed comparison is made with the well‐established PC‐Kriging technique. The results show that the proposed method is superior in terms of accuracy and robustness.

Spatial prediction of landslide susceptibility in Taleghan basin, Iran

Identifying landslide-susceptible zones is warranted to prevent and mitigate associated hazards in mountainous regions, where a landslide is a destructive type of erosion. A landslide susceptibility map was developed for the Taleghan basin based on frequency ratio (FR), logistic regression (LR), maximum entropy (MaxEnt), and support vector machine (SVM) with radial base (RBF), sigmoid (SIG), linear (LN), and polynomial (PL) kernel functions. To this end, an inventory map with 166 landslide locations was prepared and partitioned into 70% and 30% to train and validate the models, respectively. Subsequently, the models were designed based on 13 factors including elevation, slope degree, slope aspect, distance to stream, Stream Power Index, Topographic Wetness Index, Stream Transport Index, distance to fault, lithology, soil texture, land use, distance to road and precipitation. The performance of the methods was assessed using the area under the receiver operating characteristic curve, the Seed Cell Area Index (SCAI), the precision index (P). Moreover, statistical measures including sensitivity, specificity, and accuracy were calculated. Friedman test was also applied to confirm significant statistical differences among the seven models employed in this research. The validation results showed that MaxEnt had the maximum area under the curve (0.812). The results obtained using the models LR, FR, PL-SVM, SIG-SVM, LN-SVM, and RBF-SVM were 0.807, 0.732, 0.679, 0.663, 0.643 and 0.660, respectively. The obtained P index showed the better performance of MaxEnt and LR models. Moreover, the trend of changes in the SCAI values, from low- to high-susceptibility, indicated that the MaxEnt and LR models had the best performance. Decision makers can effectively use the findings of the present study to mitigate the financial and human costs resulting from the landslides.

Estimation of wind energy power using different artificial intelligence techniques and empirical equations

ABSTRACT The understanding of the behavior of a wind turbine is difficult due to changes in weather conditions. To obtain the response of a wind turbine influenced by changes in both wind speed and its direction, using the meteorological station data is often preferred to using the real turbine data. Furthermore, simulated data can be easily extrapolated to varied turbine hub heights. In order to estimate the most effective power output in this study, a wind turbine simulation was developed. The simulation depends on the real meteorological data. For the purpose, three modeling techniques, namely Multi-Nonlinear Regression (MNLR), Adaptive Neuro-Fuzzy Inference System (ANFIS), and support vector machines (SVM) were used. In SVM learning process, polynomial and radial basis kernel functions were used. Models were compared to wind turbine measurement values in the same region for similar data. MNLR was used to determine quantify the strength of the relationship between parameters and to eliminate the ineffective parameters. Efficient parameters preferred for training and testing phases of the SVM and ANFIS. The Subtractive Clustering and Grid Partitioning methods were used to identify the inference parameters of ANFIS. According to performance evaluations, MNLR-ANFIS modeling based on Subtractive Clustering gave better results than Grid Partitioning. The results showed that proposed collaborative model could be applied to wind power estimation problems.

Prediction of water quality index (WQI) using support vector machine (SVM) and least square-support vector machine (LS-SVM)

ABSTRACT The current calculations of water quality index (WQI) were sometimes can be very complex and time-consuming which involves sub-index calculation like BOD and COD, however with the support vector machine (SVM) and least squares support vector machine (LS-SVM) models, the WQI can be predicted immediately using directly measured physical data by using the same predictors used in the numerical approach without any sub-index calculation. There were three main parameters that control the performance of the SVM model however only the type of kernel function was investigated, they were linear, radial basis function (RBF) and polynomial kernel functions. The results of the model were then analysed by using sum squares error (SSE), mean of sum squares error (MSSE) and coefficient of determination (R 2). It was found that the best kernel function for the SVM model was polynomial kernel function with R 2 of 0.8796. Furthermore, the LS-SVM model that trained with correct predictors had higher accuracy with R 2 of 0.9227 as compared with SVM model that trained with all the predictors with R 2 of 0.9184. The SSE and MSSE are 74.78 and 1.5594, 1.6454 for LS-SVM and SVM respectively.

Comparation Between Linear and Polynomial Kernel Function For Ovarium Cancer Classification

Ovarium cancer is a kind of cancer disease which often attacks a woman. Ovarium cancer consists of benign and malignant type. Based on the data set obtained, this research try to classify the data set with support vector machine algorithm. The principle of SVM is how to identify a hyperplanes with maximal margin. Hyperplanes is a border line between the data. Here, we will used two kernel function in SVM, linear and polynomial kernel function. Next We will compare both of them algorithm to reach the hyperplanes with maximal margin. The hyperplanes then used to predict the class of data testing given. Finally, comparation result will be obtained from confussion matrix and accuration calculation for each kernel function while used to classify the ovarium cancer data set. Accuration result with Linear kernel function is 68.98% for first schema and 66.67% for second schema. Then accuration result with Polynomial Kernel Function is 83.79% for both of schema.

Smooth Support Vector Machine (SSVM) for classification of Human Development Index

Human Development Index (HDI) is measuring achievements of human development based on basic components of quality of life. Human development index is low score if HDI is less than 60, moderate HDI between 60 to less than 70, high HDI between 70 to less than 80, and equal to 80 and more than 80 belong to high HDI. Smooth Support Vector Machine (SSVM) is a classification technique that is new. The algorithm used is Newton Armijo with linear kernel, polynomial kernel, and Radial Basis Function (RBF) kernel. The result of classification of human development index with SSVM method with linear kernel shows the prediction accuracy 84.77%, polynomial kernel 61.65%, and RBF kernel 100%. Radial Base Function Kernel (RBF) is the most accurate kernel in predicting human development index.

SpliceCombo: A Hybrid Technique Efficiently Use for Principal Component Analysis of Splice Site Prediction

The primary step in search of the gene prediction is an identification of the coding region from genomic DNA sequence. Gene structure in the case of a eukaryotic organism is composed of promoter, intron, start codon, exons, stop codon, etc. Splice site prediction, which separates the junction between exon and intron, though the sequence beside. The splice sites have huge preservation, however, the precision of the tool exhibits less than 90%. The main objective of this work to exhibits a hybrid technique that efficiently improves the existing gene recognition technique. Therefore to enhance the identification of splice sites, the respective algorithm needs to be improved. Over the last decade, the researcher paid more attention to improve the accuracy of a predicted model in this domain. Our proposed method, SpliceCombo involves three stages. At initial stage, which considers the principal Component Analysis, based on the feature extracted. In the intermediate stage, i.e.,, the second stage Case- Based Reasoning is done, i.e., feature selection. The third stage uses support vector machine based along with polynomial kernel function for final classification. In comparison with other methods, the proposed SpliceCombo model outperforms other prediction models with respect to prediction accuracies. Particularly for donor splice site the methodology exhibits sensitivity is 97.25% accurate and specificity is 97.46% accurate. For acceptor Splice Site the sensitivity is 96.51% and Specificity is 94.48% correct.

Automated discrimination of deveined shrimps based on grayscale image parameters

AbstractThe “Vein” in a shrimp is its digestive tract filled with grit, sand, and sediments stretching along the back of the abdomen. In most shrimp market forms, presence of vein is highly restricted and limited according to the U.S. standard for imports. This research aims to develop an image‐based approach for detection of improperly deveined shrimps. Two hundred shrimp images were subjected to a sequence of image processing techniques before extracting significant parameters from grayscale images. These parameters include shape measurements and pixel value measurements drawn from an image histogram. In this research, disqualified shrimps were identified by two classification techniques: linear discriminant analysis and support vector machine (SVM). Better than 98% classification accuracy was obtained with the SVM using a polynomial kernel function. The success of this research has filled a void left by past studies to facilitate fully automated shrimp quality inspection.Practical applicationsRising wages and labor scarcity are among critical problems to seafood industries, along with low productivity due to ergonomics limitations. Such problems will be even worse in the near future and automated machines are becoming a popular alternative to tackle them. These machines must be driven by an intelligent processing unit capable of handling unavoidable variability naturally found in agricultural products. In most shrimp market forms, presence of veins is highly restricted and limited by the U.S. standards for imports. Deveining always leaves remnants of uncertain length. Employing statistical learning techniques, the approach developed in this study can accurately and automatically discriminate shrimps by acceptability based on the vein. Findings of this research contribute to the development of a fully automated shrimp processing machine, supporting sustainability of the industry by reducing reliance on labor policies and workforce availability.

Empirical approach for bearing capacity prediction of geogrid-reinforced sand over vertically encased stone columns floating in soft clay using support vector regression

Due to the complex, elaborate and expensive estimation of bearing capacity (qrs) of geogrid-reinforced sand bed resting over a group of vertically encased stone columns floating in soft clay, it is required to develop a precise empirical model, which is supposed to be nonlinear. To date, there is no established bearing capacity equation available on this topic. The aim of this work is to develop a precise qrs prediction model using support vector regression (SVR) technique. A total of 245 experimental datasets were collected and used to train and test the SVM models estimating the qrs. Three SVR models were developed based on three different kernel functions, namely exponential radial basis kernel function (ERBF), radial basis kernel function (RBF) and polynomial kernel function (POLY), and their performances were examined. Out of the three SVR models, one with ERBF was found to be the best one, having the lowest statistical error and maximum generalization ability of the training and testing data. The performance of SVR-ERBF model was compared with adaptive neuro-fuzzy inference system (ANFIS) model, and it was observed that SVR-ERBF model outperforms ANFIS model to predict qrs. A sensitivity analysis was also conducted to identify the relative importance and contribution of each input variable on output (qrs) prediction. Finally, using the SVR-ERBF model, an empirical equation is proposed to predict qrs for practical application purposes. Obtained results approve that the SVR-ERBF model can be used as a powerful and reliable alternative to solve highly nonlinear problems such as indirect estimation of qrs.

The Mixed Kernel Function SVM-Based Point Cloud Classification

Measurement and detection of ground information by airborne Lidar are one of the hot topics in the field of intelligent sensing in recent years. This study proposes a new point cloud classification algorithm of Mixed Kernel Function SVM to distinguish different types of ground objects. Firstly, the combined features including the coordinate values, the RGB value, normalized elevation, standard deviation of elevation, and elevation difference of point cloud data were extracted. A mixed kernel function of Gauss and Polynomial was designed. Then, one-versus-rest SVM multiple classifiers was constructed. Finally, the feature of 3D point cloud data was employed to train the SVM classifiers. The overall classification accuracies of test data were 97.69% and 99.13% for two data sets, I and II respectively. In addition, the experimental results have showed that the performance of the proposed method with mixed kernel function SVM was better than standard SVM method with Gaussian kernel function and polynomial kernel function only, which demonstrates the effectiveness of the proposed method.

Using direct transformation approach as an alternative technique to fuse global digital elevation models with GPS/levelling measurements in Egypt

Abstract Open global digital elevation models (GDEMs) represent a free and important source of information that is available to any country. Fusion processing between global and national digital elevation models is neither easy nor inexpensive. Hence, an alternative solution to fuse a GDEM (GTOPO30 or SRTM 1) with national GPS/levelling measurements is adopted. Herein, a transformation process between the GDEMs and national GPS/levelling measurements is applied using parametric and non-parametric equations. Two solutions are implemented before and after the filtration of raw data from outliers to assess the ability of the generated corrector surface model to absorb the effect of the outliers’ existence. In addition, a reliability analysis is conducted to select the most suitable transformation technique. We found that when both the fitting and prediction properties have equal priority, least-squares collocation integrated with a least-squares support vector machine inherited with a linear or polynomial kernel function exhibits the most accurate behavior. For the GTOPO30 model, before filtration of the raw data, there is an improvement in the mean and root mean square of errors by 39.31 % and 68.67 %, respectively. For the SRTM 1 model, the improvement in mean and root mean square values reached 86.88 % and 75.55 %, respectively. Subsequently, after the filtration process, these values became 3.48 % and 36.53 % for GTOPO30 and 85.18 % and 47.90 % for SRTM 1. Furthermore, it is found that using a suitable mathematical transformation technique can help increase the precision of classic GDEMs, such as GTOPO30, making them to be equal or more accurate than newer models, such as SRTM 1, which are supported by more advanced technologies. This can help overcome the limitation of shortage of technology or restricted data, particularly in developed countries. Henceforth, the proposed direct transformation technique represents an alternative faster and more economical way to utilize unfiltered measurements of GDEMs to estimate national digital elevations in areas with limited data.

Knots timber detection and classification with C-Support Vector Machine

Timber knots recognition is of prime importance to further determine the timber grade. The recognition is normally based on the human expert’s eyes in which can lead to some flaws based on human limitations and weaknesses. The use of X-ray can cause emits radiation and can be dangerous to the workers. This paper addresses the employment of computational methods for knot detection. A pre-processing and feature extraction methods include contrast stretching, median blur and thresholding, gray scale and local binary pattern were used. More than 400 datasets of knot images of the tropical timbers, namely Acacia and Hevea Brasiliensis have been tested using C-support vector machine as a knot classifier. The findings demonstrate different performances for three types of kernel. Linear kernel function outperformed both radial basis function and polynomial kernel functions for Acacia and Hevea Brasiliensis species. Both species classifications using linear kernel have managed to achieve a promising accuracy. Knots classification with the used of support vector machine has shown a promising result to improve the classifier and test with different types of tropical timbers.

Method for detecting avian influenza disease of chickens based on sound analysis

A new audio analysis-based detection method is put forward in this paper to detect avian influenza as early as possible. Because a distinctive difference exists in the short-time auto-correlation functions of recorded chicken sound and ambient noise, the former can be extracted from the record and the latter discarded. The mel-frequency cepstral coefficients (MFCC) are determined by analysing and processing the frequency domain of the extracted chicken sound signal. The coefficients serve as distinction criteria for healthy and infected chickens. The extracted chicken sound is trained and identified with a binary-classification support vector machine (SVM). The penalty parameter and kernel function parameter of the optimal SVM are determined through 4-fold cross validation. The maximum recognition rates for the verification set are 87.25% (for polynomial kernel function), 88.1250% (for radial basis function), and 87.1250% (for S-kernel function), respectively. According to the experimental results for the testing set, the accuracy rate of the avian-influenza detection method ranged between 84% and 90%. This work shows preliminary potential for fast and efficient detection of avian-influenza in large-scale poultry farming and poultry trading markets.

MCK-ELM: multiple composite kernel extreme learning machine for hyperspectral images

Multiple kernel (MK) learning (MKL) methods have a significant impact on improving the classification performance. Besides that, composite kernel (CK) methods have high capability on the analysis of hyperspectral images due to making use of the contextual information. In this work, it is aimed to aggregate both CKs and MKs autonomously without the need of kernel coefficient adjustment manually. Convex combination of predefined kernel functions is implemented by using multiple kernel extreme learning machine. Thus, complex optimization processes of standard MKL are disposed of and the facility of multi-class classification is profited. Different types of kernel functions are placed into MKs in order to realize hybrid kernel scenario. The proposed methodology is performed over Pavia University, Indian Pines, and Salinas hyperspectral scenes that have ground-truth information. Multiple composite kernels are constructed using Gaussian, polynomial, and logarithmic kernel functions with various parameters, and then the obtained results are presented comparatively along with the state-of-the-art standard machine learning, MKL, and CK methods.

Estimation of forest development stage and crown closure using different classification methods and satellite images: A case study from Turkey

The objective of this study is to estimate stand development stages (SDS) and stand crown closures (SCC) of forest using different classification methods (maximum likelihood, support vector machine: linear, polynomial, radial and sigmoid kernel functions and artificial neural network) based on satellite imagery of different resolution (Landsat 7 ETM+ and IKONOS). The results showed that SDS and SCC were estimated with Landsat 7 ETM+ image using the artificial neural network with a 0.83 and 0.78 kappa statistic value, and 92.57 and 89.77% overall accuracy assessments, respectively. On the other hand, SDS and SCC were predicted with IKONOS image using support vector machine (polynomial) method with a 0.94 and 0.88 kappa statistic value, and 95.95 and 91.17% overall accuracy assessments, respectively. Our results demonstrated that IKONOS satellite image and support vector machine (polynomial) method produced a better estimation of SDS and SCC as compared to Landsat 7 ETM+ and other supervised classification methods used in this study.

Scenario simulation of urban energy-related CO2 emissions by coupling the socioeconomic factors and spatial structures

As cities constitute the main sources of CO2 emissions, accurate simulation and prediction of urban CO2 emissions are becoming increasingly necessary for understanding environmental impacts and supporting the policy-making toward a low-carbon development. However, most previous studies on estimating CO2 emissions have only considered the effects of socioeconomic driving factors while disregarding the contributions of urban spatial structures (with the exception of those of urban expansion) to carbon abatement. Therefore, this study presented a model that integrates system dynamics, cellular automata and support vector regression to evaluate the impacts of different socioeconomic developments and urban spatial structures on the CO2 emissions of Guangzhou city. In the integrated model, system dynamics was used to model the developments of socioeconomic variables including urban land-use demand. An artificial neural network cellular automata model based on patch simulation strategy was then built to simulate the urban spatial structures, which were further quantified by landscape metrics. Using both socioeconomic variables and landscape metrics, a support vector regression with polynomial kernel function was finally employed to predict CO2 emissions. Through comparisons drawn between the simulated results and actual data, the integrated model coupling socioeconomic factors and urban spatial structures was demonstrated to be an effective tool for accurately simulating CO2 emissions. Furthermore, scenario simulations derived from the integrated model showed that the scenario of executing moderate population and economic growth, more technological investment, and the compact development of urban spatial pattern constitutes the best development mode for Guangzhou to balance economic growth and CO2 emissions reduction. From these findings, it is suggested that the government should not only develop a series of socioeconomic policies on carbon mitigation but also construct an ideal urban structure of compact and multiple-nuclei development through urban planning and spatial optimization for building a low-carbon city.

Fault diagnosis of a centrifugal pump using MLP-GABP and SVM with CWT

This paper presents a comparative study of Multilayer Feedforward Perceptron Neural Network which is trained with Back Propagation (MLP-BP) and also using hybrid training using Genetic Algorithm (GA) (MLP-GABP), and Support Vector Machine (SVM) classifiers to classify the fault conditions of a centrifugal pump. Continuous Wavelet Transform (CWT) with three different wavelet functions (Morlet, db8 and rbio1.5) is used to extract the features. GA is also used to optimize the number of hidden layers and neurons of MLP. From the results obtained, MLP-BP has shown better performance than MLP-GABP and SVM using a lower number of features. SVM has performed better using polynomial kernel function using a smaller number of features and parameters. A centrifugal pump test rig has been specifically designed and built for this work in order to create the desired faults.