Search results for: Kernel regression

Authors: Wei Zhang, Su-Yan Tang, Yi-Fan Zhu, Wei-Ping Wang

Abstract:

Support vector regression (SVR) has been regarded as a state-of-the-art method for approximation and regression. The importance of kernel function, which is so-called admissible support vector kernel (SV kernel) in SVR, has motivated many studies on its composition. The Gaussian kernel (RBF) is regarded as a “best" choice of SV kernel used by non-expert in SVR, whereas there is no evidence, except for its superior performance on some practical applications, to prove the statement. Its well-known that reproducing kernel (R.K) is also a SV kernel which possesses many important properties, e.g. positive definiteness, reproducing property and composing complex R.K by simpler ones. However, there are a limited number of R.Ks with explicit forms and consequently few quantitative comparison studies in practice. In this paper, two R.Ks, i.e. SV kernels, composed by the sum and product of a translation invariant kernel in a Sobolev space are proposed. An exploratory study on the performance of SVR based general R.K is presented through a systematic comparison to that of RBF using multiple criteria and synthetic problems. The results show that the R.K is an equivalent or even better SV kernel than RBF for the problems with more input variables (more than 5, especially more than 10) and higher nonlinearity.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, support vector regression.

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Authors: Dursun Aydin

Abstract:

This paper study about using of nonparametric models for Gross National Product data in Turkey and Stanford heart transplant data. It is discussed two nonparametric techniques called smoothing spline and kernel regression. The main goal is to compare the techniques used for prediction of the nonparametric regression models. According to the results of numerical studies, it is concluded that smoothing spline regression estimators are better than those of the kernel regression.

Keywords: Kernel regression, Nonparametric models, Prediction, Smoothing spline.

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Authors: Wei Zhang, Xin Zhao, Yi-Fan Zhu, Xin-Jian Zhang

Abstract:

Kernel function, which allows the formulation of nonlinear variants of any algorithm that can be cast in terms of dot products, makes the Support Vector Machines (SVM) have been successfully applied in many fields, e.g. classification and regression. The importance of kernel has motivated many studies on its composition. It-s well-known that reproducing kernel (R.K) is a useful kernel function which possesses many properties, e.g. positive definiteness, reproducing property and composing complex R.K by simple operation. There are two popular ways to compute the R.K with explicit form. One is to construct and solve a specific differential equation with boundary value whose handicap is incapable of obtaining a unified form of R.K. The other is using a piecewise integral of the Green function associated with a differential operator L. The latter benefits the computation of a R.K with a unified explicit form and theoretical analysis, whereas there are relatively later studies and fewer practical computations. In this paper, a new algorithm for computing a R.K is presented. It can obtain the unified explicit form of R.K in general reproducing kernel Hilbert space. It avoids constructing and solving the complex differential equations manually and benefits an automatic, flexible and rigorous computation for more general RKHS. In order to validate that the R.K computed by the algorithm can be used in SVM well, some illustrative examples and a comparison between R.K and Gaussian kernel (RBF) in support vector regression are presented. The result shows that the performance of R.K is close or slightly superior to that of RBF.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, Green function, support vectorregression

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Authors: S. Deswal, M. Pal

Abstract:

Presently various computational techniques are used in modeling and analyzing environmental engineering data. In the present study, an intra-comparison of polynomial and radial basis kernel functions based on Support Vector Regression and, in turn, an inter-comparison with Multi Linear Regression has been attempted in modeling mass transfer capacity of vertical (θ = 90O) and inclined (θ multiple plunging jets (varying from 1 to 16 numbers). The data set used in this study consists of four input parameters with a total of eighty eight cases, forty four each for vertical and inclined multiple plunging jets. For testing, tenfold cross validation was used. Correlation coefficient values of 0.971 and 0.981 along with corresponding root mean square error values of 0.0025 and 0.0020 were achieved by using polynomial and radial basis kernel functions based Support Vector Regression respectively. An intra-comparison suggests improved performance by radial basis function in comparison to polynomial kernel based Support Vector Regression. Further, an inter-comparison with Multi Linear Regression (correlation coefficient = 0.973 and root mean square error = 0.0024) reveals that radial basis kernel functions based Support Vector Regression performs better in modeling and estimating mass transfer by multiple plunging jets.

Keywords: Mass transfer, multiple plunging jets, polynomial and radial basis kernel functions, Support Vector Regression.

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Authors: Shahin Mirshekari, Mohammadreza Moradi, Hossein Jafari, Mehdi Jafari, Mohammad Ensaf

Abstract:

This research employs Gaussian Process Regression (GPR) with an ensemble kernel, integrating Exponential Squared, Revised Matérn, and Rational Quadratic kernels to analyze pharmaceutical sales data. Bayesian optimization was used to identify optimal kernel weights: 0.76 for Exponential Squared, 0.21 for Revised Matérn, and 0.13 for Rational Quadratic. The ensemble kernel demonstrated superior performance in predictive accuracy, achieving an R² score near 1.0, and significantly lower values in MSE, MAE, and RMSE. These findings highlight the efficacy of ensemble kernels in GPR for predictive analytics in complex pharmaceutical sales datasets.

Keywords: Gaussian Process Regression, Ensemble Kernels, Bayesian Optimization, Pharmaceutical Sales Analysis, Time Series Forecasting, Data Analysis.

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Authors: Wei Zhang, Yao-Yu Li, Yi-Fan Zhu, Qun Li, Wei-Ping Wang

Abstract:

It-s known that incorporating prior knowledge into support vector regression (SVR) can help to improve the approximation performance. Most of researches are concerned with the incorporation of knowledge in the form of numerical relationships. Little work, however, has been done to incorporate the prior knowledge on the structural relationships among the variables (referred as to Structural Prior Knowledge, SPK). This paper explores the incorporation of SPK in SVR by constructing appropriate admissible support vector kernel (SV kernel) based on the properties of reproducing kernel (R.K). Three-levels specifications of SPK are studied with the corresponding sub-levels of prior knowledge that can be considered for the method. These include Hierarchical SPK (HSPK), Interactional SPK (ISPK) consisting of independence, global and local interaction, Functional SPK (FSPK) composed of exterior-FSPK and interior-FSPK. A convenient tool for describing the SPK, namely Description Matrix of SPK is introduced. Subsequently, a new SVR, namely Motivated Support Vector Regression (MSVR) whose structure is motivated in part by SPK, is proposed. Synthetic examples show that it is possible to incorporate a wide variety of SPK and helpful to improve the approximation performance in complex cases. The benefits of MSVR are finally shown on a real-life military application, Air-toground battle simulation, which shows great potential for MSVR to the complex military applications.

Keywords: admissible support vector kernel, reproducing kernel, structural prior knowledge, motivated support vector regression

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Authors: Wei Zhang, Yao-Yu Li, Yi-Fan Zhu, Qun Li, Wei-Ping Wang

Abstract:

It-s known that incorporating prior knowledge into support vector regression (SVR) can help to improve the approximation performance. Most of researches are concerned with the incorporation of knowledge in form of numerical relationships. Little work, however, has been done to incorporate the prior knowledge on the structural relationships among the variables (referred as to Structural Prior Knowledge, SPK). This paper explores the incorporation of SPK in SVR by constructing appropriate admissible support vector kernel (SV kernel) based on the properties of reproducing kernel (R.K). Three-levels specifications of SPK are studies with the corresponding sub-levels of prior knowledge that can be considered for the method. These include Hierarchical SPK (HSPK), Interactional SPK (ISPK) consisting of independence, global and local interaction, Functional SPK (FSPK) composed of exterior-FSPK and interior-FSPK. A convenient tool for describing the SPK, namely Description Matrix of SPK is introduced. Subsequently, a new SVR, namely Motivated Support Vector Regression (MSVR) whose structure is motivated in part by SPK, is proposed. Synthetic examples show that it is possible to incorporate a wide variety of SPK and helpful to improve the approximation performance in complex cases. The benefits of MSVR are finally shown on a real-life military application, Air-toground battle simulation, which shows great potential for MSVR to the complex military applications.

Keywords: admissible support vector kernel, reproducing kernel, structural prior knowledge, motivated support vector regression

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Authors: Rasmus Engholm, Eva B. Vedel Jensen, Henrik Karstoft

Abstract:

In this paper we present a noise reduction filter for video processing. It is based on the recently proposed two dimensional steering kernel, extended to three dimensions and further augmented to suit the spatial-temporal domain of video processing. Two alternative filters are proposed - the time symmetric kernel and the time asymmetric kernel. The first reduces the noise on single sequences, but to handle the problems at scene shift the asymmetric kernel is introduced. The performance of both are tested on simulated data and on a real video sequence together with the existing steering kernel. The proposed kernels improves the Rooted Mean Squared Error (RMSE) compared to the original steering kernel method on video material.

Keywords: Adaptive image filtering, noise reduction, kernel methods, video processing.

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Authors: József Valyon, Gábor Horváth

Abstract:

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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Authors: Kei Kawamorita, Ryouta Kasahara, Yuuki Mochizuki, Kenichiro Noguchi

Abstract:

A separation-kernel-based operating system (OS) has been designed for use in secure embedded systems by applying formal methods to the design of the separation-kernel part. The separation kernel is a small OS kernel that provides an abstract distributed environment on a single CPU. The design of the separation kernel was verified using two formal methods, the B method and the Spin model checker. A newly designed semi-formal method, the extended state transition method, was also applied. An OS comprising the separation-kernel part and additional OS services on top of the separation kernel was prototyped on the Intel IA-32 architecture. Developing and testing of a prototype embedded application, a point-of-sale application, on the prototype OS demonstrated that the proposed architecture and the use of formal methods to design its kernel part are effective for achieving a secure embedded system having a high-assurance separation kernel.

Keywords: B method, embedded systems, extended state transition, formal methods, separation kernel, Spin.

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Authors: Hamza Nejib, Okba Taouali

Abstract:

This paper presents two of the most knowing kernel adaptive filtering (KAF) approaches, the kernel least mean squares and the kernel recursive least squares, in order to predict a new output of nonlinear signal processing. Both of these methods implement a nonlinear transfer function using kernel methods in a particular space named reproducing kernel Hilbert space (RKHS) where the model is a linear combination of kernel functions applied to transform the observed data from the input space to a high dimensional feature space of vectors, this idea known as the kernel trick. Then KAF is the developing filters in RKHS. We use two nonlinear signal processing problems, Mackey Glass chaotic time series prediction and nonlinear channel equalization to figure the performance of the approaches presented and finally to result which of them is the adapted one.

Keywords: KLMS, online prediction, KAF, signal processing, RKHS, Kernel methods, KRLS, KLMS.

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Authors: Hany Alashwal, Safaai Deris, Razib M. Othman

Abstract:

Understanding proteins functions is a major goal in the post-genomic era. Proteins usually work in context of other proteins and rarely function alone. Therefore, it is highly relevant to study the interaction partners of a protein in order to understand its function. Machine learning techniques have been widely applied to predict protein-protein interactions. Kernel functions play an important role for a successful machine learning technique. Choosing the appropriate kernel function can lead to a better accuracy in a binary classifier such as the support vector machines. In this paper, we describe a Bayesian kernel for the support vector machine to predict protein-protein interactions. The use of Bayesian kernel can improve the classifier performance by incorporating the probability characteristic of the available experimental protein-protein interactions data that were compiled from different sources. In addition, the probabilistic output from the Bayesian kernel can assist biologists to conduct more research on the highly predicted interactions. The results show that the accuracy of the classifier has been improved using the Bayesian kernel compared to the standard SVM kernels. These results imply that protein-protein interaction can be predicted using Bayesian kernel with better accuracy compared to the standard SVM kernels.

Keywords: Bioinformatics, Protein-protein interactions, Bayesian Kernel, Support Vector Machines.

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Authors: Elena Kotevska

Abstract:

This paper presents a generalization kernel for gravitational potential determination by harmonic splines. It was shown in [10] that the gravitational potential can be approximated using a kernel represented as a Newton integral over the real Earth body. On the other side, the theory of geopotential approximation by harmonic splines uses spherically oriented kernels. The purpose of this paper is to show that in the spherical case both kernels have the same type of representation, which leads us to conclusion that it is possible to consider the kernel represented as a Newton integral over the real Earth body as a kind of generalization of spherically harmonic kernels to real geometries.

Keywords: Geopotential, Reproducing Kernel, Approximation, Regular Surface

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Authors: Mohamed EL Boujnouni, Mohamed Jedra, Noureddine Zahid

Abstract:

Support Vector Domain Description (SVDD) is one of the best-known one-class support vector learning methods, in which one tries the strategy of using balls defined on the feature space in order to distinguish a set of normal data from all other possible abnormal objects. As all kernel-based learning algorithms its performance depends heavily on the proper choice of the kernel parameter. This paper proposes a new approach to select kernel's parameter based on maximizing the distance between both gravity centers of normal and abnormal classes, and at the same time minimizing the variance within each class. The performance of the proposed algorithm is evaluated on several benchmarks. The experimental results demonstrate the feasibility and the effectiveness of the presented method.

Keywords: Gravity centers, Kernel’s parameter, Support Vector Domain Description, Variance.

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Authors: Willem Waegeman, Luc Boullart

Abstract:

Instead of traditional (nominal) classification we investigate the subject of ordinal classification or ranking. An enhanced method based on an ensemble of Support Vector Machines (SVM-s) is proposed. Each binary classifier is trained with specific weights for each object in the training data set. Experiments on benchmark datasets and synthetic data indicate that the performance of our approach is comparable to state of the art kernel methods for ordinal regression. The ensemble method, which is straightforward to implement, provides a very good sensitivity-specificity trade-off for the highest and lowest rank.

Keywords: Ordinal regression, support vector machines, ensemblelearning.

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Authors: Sepehr Damavandinejadmonfared, Ali Khalili Mobarakeh, Mohsen Pashna, , Jiangping Gou Sayedmehran Mirsafaie Rizi, Saba Nazari, Shadi Mahmoodi Khaniabadi, Mohamad Ali Bagheri

Abstract:

In this paper a novel algorithm is proposed to merit the accuracy of finger vein recognition. The performances of Principal Component Analysis (PCA), Kernel Principal Component Analysis (KPCA), and Kernel Entropy Component Analysis (KECA) in this algorithm are validated and compared with each other in order to determine which one is the most appropriate one in terms of finger vein recognition.

Keywords: Biometrics, finger vein recognition, PrincipalComponent Analysis (PCA), Kernel Principal Component Analysis(KPCA), Kernel Entropy Component Analysis (KPCA).

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Authors: Essam Al Daoud

Abstract:

To improve the classification rate of the face recognition, features combination and a novel non-linear kernel are proposed. The feature vector concatenates three different radius of local binary patterns and Gabor wavelet features. Gabor features are the mean, standard deviation and the skew of each scaling and orientation parameter. The aim of the new kernel is to incorporate the power of the kernel methods with the optimal balance between the features. To verify the effectiveness of the proposed method, numerous methods are tested by using four datasets, which are consisting of various emotions, orientations, configuration, expressions and lighting conditions. Empirical results show the superiority of the proposed technique when compared to other methods.

Keywords: Face recognition, Gabor wavelet, LBP, Non-linearkerner

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Authors: Habibeh Nalbandi, Sadegh Seiiedlou, Hamid R. Ghasemzadeh, Naser Hamdami

Abstract:

The purpose of present work was to study the drying kinetics of whole acorn and its kernel at different drying air temperatures and their effective moisture diffusivity. The results indicated that the drying time of whole acorn was 442, 206 and 188 min at the air temperature of 65, 75 and 85ºC, respectively. At the same temperatures, the drying time of kernel was 131, 56 and 76min. The results showed that the effect of drying air temperature increasing on the drying time reduction could not be significant on acorn drying at all conditions. The effective moisture diffusivity of whole acorn and kernel increased with increasing air temperature from 65 to 75ºC. However more air temperature increasing, led to decreasing this property of acorn kernel. The critical temperature of acorn drying was about 75°C in which acorn kernel had the highest effective moisture diffusivity.

Keywords: Critical temperature, Drying kinetics, Moisture diffusivity, Oak acorn.

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Authors: Nabil M. Abdel-Jabbar, Essam A.H. Al Zubaidy, Mehrab Mehrvar

Abstract:

Waste lubricating oil re-refining adsorption process by different adsorbent materials was investigated. Adsorbent materials such as oil adsorbent, egg shale powder, date palm kernel powder, and acid activated date palm kernel powder were used. The adsorption process over fixed amount of adsorbent at ambient conditions was investigated. The adsorption/extraction process was able to deposit the asphaltenic and metallic contaminants from the waste oil to lower values. It was found that the date palm kernel powder with contact time of 4 h was able to give the best conditions for treating the waste oil. The recovered solvent could be also reused. It was also found that the activated bentonite gave the best physical properties followed by the date palm kernel powder.

Keywords: activated bentonite, egg shale powder, datepalm kernel powder, used oil treatment, used oilcharacteristics.

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Authors: Mingtao Ding, Zheng Tian, Haixia Xu

Abstract:

The batch nature limits the standard kernel principal component analysis (KPCA) methods in numerous applications, especially for dynamic or large-scale data. In this paper, an efficient adaptive approach is presented for online extraction of the kernel principal components (KPC). The contribution of this paper may be divided into two parts. First, kernel covariance matrix is correctly updated to adapt to the changing characteristics of data. Second, KPC are recursively formulated to overcome the batch nature of standard KPCA.This formulation is derived from the recursive eigen-decomposition of kernel covariance matrix and indicates the KPC variation caused by the new data. The proposed method not only alleviates sub-optimality of the KPCA method for non-stationary data, but also maintains constant update speed and memory usage as the data-size increases. Experiments for simulation data and real applications demonstrate that our approach yields improvements in terms of both computational speed and approximation accuracy.

Keywords: adaptive method, kernel principal component analysis, online extraction, recursive algorithm

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Authors: D.N. Zheng, J.X. Wang, Y.N. Zhao, Z.H. Yang

Abstract:

The Linear discriminant analysis (LDA) can be generalized into a nonlinear form - kernel LDA (KLDA) expediently by using the kernel functions. But KLDA is often referred to a general eigenvalue problem in singular case. To avoid this complication, this paper proposes an iterative algorithm for the two-class KLDA. The proposed KLDA is used as a nonlinear discriminant classifier, and the experiments show that it has a comparable performance with SVM.

Keywords: Linear discriminant analysis (LDA), kernel LDA (KLDA), conjugate gradient algorithm, nonlinear discriminant classifier.

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Authors: Amir Hajian, Sepehr Damavandinejadmonfared

Abstract:

In this paper the issue of dimensionality reduction is investigated in finger vein recognition systems using kernel Principal Component Analysis (KPCA). One aspect of KPCA is to find the most appropriate kernel function on finger vein recognition as there are several kernel functions which can be used within PCA-based algorithms. In this paper, however, another side of PCA-based algorithms -particularly KPCA- is investigated. The aspect of dimension of feature vector in PCA-based algorithms is of importance especially when it comes to the real-world applications and usage of such algorithms. It means that a fixed dimension of feature vector has to be set to reduce the dimension of the input and output data and extract the features from them. Then a classifier is performed to classify the data and make the final decision. We analyze KPCA (Polynomial, Gaussian, and Laplacian) in details in this paper and investigate the optimal feature extraction dimension in finger vein recognition using KPCA.

Keywords: Biometrics, finger vein recognition, Principal Component Analysis (PCA), Kernel Principal Component Analysis (KPCA).

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Authors: Dursun Aydın, Bilgin Senel

Abstract:

In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

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Authors: A. Schirru, A. Irimescu, S. Merola, A. d’Adamo, S. Fontanesi

Abstract:

One of the aspects that are usually neglected during the design phase of an engine is the effect of the spark plug on the flow field inside the combustion chamber. Because of the difficulties in the experimental investigation of the mutual interaction between flow alteration and early flame kernel convection effect inside the engine combustion chamber, CFD-3D simulation is usually exploited in such cases. Experimentally speaking, a particular type of engine has to be used in order to directly observe the flame propagation process. In this study, a double electrode spark plug was fitted into an optically accessible engine and a high-speed camera was used to capture the initial stages of the combustion process. Both the arc and the kernel phases were observed. Then, a morphologic analysis was carried out and the position of the center of mass of the flame, relative to the spark plug position, was calculated. The crossflow orientation was chosen for the spark plug and the kernel growth process was observed for different air-fuel ratios. It was observed that during a normal cycle the flow field between the electrodes tends to transport the arc deforming it. Because of that, the kernel growth phase takes place away from the electrodes and the flame propagates with a preferential direction dictated by the flow field.

Keywords: Combustion, Kernel growth, optically accessible engine, spark-ignition engine, spark plug orientation.

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Authors: O. Abiodun Adeyinka, B. Adeyemo Adesesan

Abstract:

The forensic use of handwriting depends on the analysis, comparison, and evaluation decisions made by forensic document examiners. When using biometric technology in forensic applications, it is necessary to compute Likelihood Ratio (LR) for quantifying strength of evidence under two competing hypotheses, namely the prosecution and the defense hypotheses wherein a set of assumptions and methods for a given data set will be made. It is therefore important to know how repeatable and reproducible our estimated LR is. This paper evaluated the accuracy and reproducibility of examiners' decisions. Confidence interval for the estimated LR were presented so as not get an incorrect estimate that will be used to deliver wrong judgment in the court of Law. The estimate of LR is fundamentally a Bayesian concept and we used two LR estimators, namely Logistic Regression (LoR) and Kernel Density Estimator (KDE) for this paper. The repeatability evaluation was carried out by retesting the initial experiment after an interval of six months to observe whether examiners would repeat their decisions for the estimated LR. The experimental results, which are based on handwriting dataset, show that LR has different confidence intervals which therefore implies that LR cannot be estimated with the same certainty everywhere. Though the LoR performed better than the KDE when tested using the same dataset, the two LR estimators investigated showed a consistent region in which LR value can be estimated confidently. These two findings advance our understanding of LR when used in computing the strength of evidence in handwriting using forensics.

Keywords: Logistic Regression LoR, Kernel Density Estimator KDE, Handwriting, Confidence Interval, Repeatability, Reproducibility.

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Authors: A. Perolini

Abstract:

Feature and model selection are in the center of attention of many researches because of their impact on classifiers- performance. Both selections are usually performed separately but recent developments suggest using a combined GA-SVM approach to perform them simultaneously. This approach improves the performance of the classifier identifying the best subset of variables and the optimal parameters- values. Although GA-SVM is an effective method it is computationally expensive, thus a rough method can be considered. The paper investigates a joined approach of Genetic Algorithm and kernel matrix criteria to perform simultaneously feature and model selection for SVM classification problem. The purpose of this research is to improve the classification performance of SVM through an efficient approach, the Kernel Matrix Genetic Algorithm method (KMGA).

Keywords: Feature and model selection, Genetic Algorithms, Support Vector Machines, kernel matrix.

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Authors: Chien-Hung Chen, Yan-Chun Hsing, Yung-Chun Chang

Abstract:

The Internet has grown into a powerful medium for information dispersion and social interaction that leads to a rapid growth of social media which allows users to easily post their emotions and perspectives regarding certain topics online. Our research aims at using natural language processing and text mining techniques to explore the public emotions expressed on Twitter by analyzing the sentiment behind tweets. In this paper, we propose a composite kernel method that integrates tree kernel with the linear kernel to simultaneously exploit both the tree representation and the distributed emotion keyword representation to analyze the syntactic and content information in tweets. The experiment results demonstrate that our method can effectively detect public emotion of tweets while outperforming the other compared methods.

Keywords: Public emotion recognition, natural language processing, composite kernel, sentiment analysis, text mining.

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Authors: R. Fatehi, M.A. Fayazbakhsh, M.T. Manzari

Abstract:

Discretization of spatial derivatives is an important issue in meshfree methods especially when the derivative terms contain non-linear coefficients. In this paper, various methods used for discretization of second-order spatial derivatives are investigated in the context of Smoothed Particle Hydrodynamics. Three popular forms (i.e. "double summation", "second-order kernel derivation", and "difference scheme") are studied using one-dimensional unsteady heat conduction equation. To assess these schemes, transient response to a step function initial condition is considered. Due to parabolic nature of the heat equation, one can expect smooth and monotone solutions. It is shown, however in this paper, that regardless of the type of kernel function used and the size of smoothing radius, the double summation discretization form leads to non-physical oscillations which persist in the solution. Also, results show that when a second-order kernel derivative is used, a high-order kernel function shall be employed in such a way that the distance of inflection point from origin in the kernel function be less than the nearest particle distance. Otherwise, solutions may exhibit oscillations near discontinuities unlike the "difference scheme" which unconditionally produces monotone results.

Keywords: Heat conduction, Meshfree methods, Smoothed ParticleHydrodynamics (SPH), Second-order derivatives.

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Authors: Kozak K, M. Kozak, K. Stapor

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The k-nearest neighbors (knn) is a simple but effective method of classification. In this paper we present an extended version of this technique for chemical compounds used in High Throughput Screening, where the distances of the nearest neighbors can be taken into account. Our algorithm uses kernel weight functions as guidance for the process of defining activity in screening data. Proposed kernel weight function aims to combine properties of graphical structure and molecule descriptors of screening compounds. We apply the modified knn method on several experimental data from biological screens. The experimental results confirm the effectiveness of the proposed method.

Keywords: biological screening, kernel methods, KNN, QSAR

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Authors: Wen Liu

Abstract:

With the rapid progress of modern cities, the railway construction must be developing quickly in China.As a typical high-density country, shopping center on the subway should be one important factor during the process of urban development. The paper discusses the influence of the layout of shopping center on the subway, and put it in the time and space’s axis of Shanghai urban development. We usethe digital technology to establish the database of relevant information. And then get the change role about shopping center on subway in Shanghaiby the Kernel density estimate.The result shows the development of shopping center on subway has a relationship with local economic strength, population size, policysupport, and city construction. And the suburbanization trend of shopping center would be increasingly significant.By this case research, we could see the Kernel density estimate is an efficient analysis method on the spatial layout. It could reveal the characters of layout form of shopping center on subway in essence. And it can also be applied to the other research of space form.

Keywords: Shanghai, Shopping center on the subway, Layout form, The Kernel density estimate.

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