Optimal approximation in Hilbert spaces can be found if the space has a reproducing kernel function and if this kernel can be obtained in closed form. This paper contains the reproducing kernel function for the genera...
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Optimal approximation in Hilbert spaces can be found if the space has a reproducing kernel function and if this kernel can be obtained in closed form. This paper contains the reproducing kernel function for the general Sard spaces of the type B. A numerical illustration of optimal approximation for a “nonstandard” Hilbert space is given.
The fluctuation of wind cause threat to power grid, this paper proposed a wind power prediction method to improving this situation. The proposed method is based on time series and regime of switching kernel functions....
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The fluctuation of wind cause threat to power grid, this paper proposed a wind power prediction method to improving this situation. The proposed method is based on time series and regime of switching kernel functions. First, the mutual information method and the false nearest neighbor method were used to calculate parameters to reconstruct the original data. The recurrence figure and the Lyapunov exponent were applied to verify that the time series data was from a chaotic system. Then, this paper proposed a prediction method based on the kernel function and also a switching regime based on the support vectors machine. The new prediction method combining these two parts was proposed to predict wind power. The comparison of wind power prediction by the proposed method and traditional methods were present, the results validated that the proposed method is feasible to predict wind power, and that the precision of prediction is improved, which will be useful for the future analysis of wind power. (C) 2016 Elsevier Ltd. All rights reserved.
In this paper, we generalize polynomial-time primal-dual interior-point methods for symmetric optimization based on a class of kernel functions, which is not coercive. The corresponding barrier functions have a finite...
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In this paper, we generalize polynomial-time primal-dual interior-point methods for symmetric optimization based on a class of kernel functions, which is not coercive. The corresponding barrier functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like many usual barrier functions. Moreover, we analyse the accuracy of the algorithm for this class of functions and we obtain an upper bound for the accuracy which depends on a parameter of the class.
A nonlinear feature extraction method is presented which can reduce the data dimension down to the number of classes, providing dramatic savings in computational costs. The dimension reducing nonlinear transformation ...
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A nonlinear feature extraction method is presented which can reduce the data dimension down to the number of classes, providing dramatic savings in computational costs. The dimension reducing nonlinear transformation is obtained by implicitly mapping the input data into a feature space using a kernel function, and then finding a linear mapping based on an orthonormal basis of centroids in the feature space that maximally separates the between-class relationship. The experimental results demonstrate that our method is capable of extracting nonlinear features effectively so that competitive performance of classification can be obtained with linear classifiers in the dimension reduced space. (C) 2003 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.
We present a generalization to symmetric optimization of interior-point methods for linear optimization based on kernel functions. Symmetric optimization covers the three most common conic optimization problems: linea...
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We present a generalization to symmetric optimization of interior-point methods for linear optimization based on kernel functions. Symmetric optimization covers the three most common conic optimization problems: linear, second-order cone and semi-definite optimization problems. Namely, we adapt the interior-point algorithm described in Peng et al. [Self-regularity: A New Paradigm for Primal-Dual Interior-point Algorithms. Princeton University Press, Princeton, NJ, 2002.] for linear optimization to symmetric optimization. The analysis is performed through Euclidean Jordan algebraic tools and a complexity bound is derived.
This paper proposes an infeasible interior-point algorithm with full Nesterov-Todd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. First w...
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This paper proposes an infeasible interior-point algorithm with full Nesterov-Todd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. First we present a full NT step infeasible interior-point algorithm based on the classic logarithmical barrier function. After that a specific kernel function is introduced. The feasibility step is induced by this kernel function instead of the classic logarithmical barrier function. This kernel function has a finite value on the boundary. The result of polynomial complexity, O(n log n/epsilon), coincides with the best known one for infeasible interior-point methods. (c) 2010 Elsevier Inc. All rights reserved.
kernel functions have revolutionized theory and practice in the field of pattern recognition, especially to perform image classification. Besides giving rise to nonlinear variants of the well-known support vector mach...
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kernel functions have revolutionized theory and practice in the field of pattern recognition, especially to perform image classification. Besides giving rise to nonlinear variants of the well-known support vector machine (SVM), these functions have also been successfully used to classify nonvectorial data (e.g., graphs and collection of sets), in which customized metrics are created to precisely measure the similarity among such contextual data entities. This letter introduces two cantext-inspired kernel functions as new SVM-driven methods for remote sensing image classification. In contrast to the existing SVM-based approaches that assume only multiattribute vectors as representative features in a high-dimensional space, the proposed models formally establish comparisons between the entire sets of context-given data, thus employing these contextual measurements to drive the classification. More precisely, stochastic distances as well as hypothesis tests are conveniently handled and "kernelized" to build our models. A complete battery of experiments involving both remote sensing and real-world images is conducted to validate the performance of the proposed kernels against various well-established SVM-based methods.
This study attempted to map land subsidence susceptibility using a support vector machine (SVM) model and their different kernel functions in Kerman province, Iran. Initially, land subsidence locations were recognized...
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This study attempted to map land subsidence susceptibility using a support vector machine (SVM) model and their different kernel functions in Kerman province, Iran. Initially, land subsidence locations were recognized using extensive field surveys and Google Earth images and, subsequently, a land subsidence distribution map was created in a GIS environment. Then, different effective factors in the occurrence of land subsidence in the study area including percentage slope, slope aspect, altitude, profile curvature, plan curvature, topographic wetness index (TWI), distance from river, lithological units, piezometric changes, land use and normalized difference vegetation index (NDVI) were selected as independent variables for the modeling process. Land subsidence susceptibility maps in the study area were produced using an SVM model and different kernel functions related to it such as linear, polynomial, sigmoid and radial basis functions. The results of model validation using 30% of the unused locations in the modeling process and receiver operating characteristic (ROC) showed that the maps of land subsidence susceptibility obtained from the SVM technique and kernel functions had the highest accuracy with AUC values of 0.894 to 0.857. According to the results of prioritization of effective factors, piezometric data (utilization of groundwater), NDVI and altitude were the most significant factors affecting the occurrence of land subsidence in Kerman province. Therefore, the results of spatial modeling of land subsidence and their susceptibility maps have a key role in the planning of land allocation and water resource management in the study area.
In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance using kernel functions are proposed. kernel functions which map the data from the original space into higher dimensional feat...
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In this paper, two new clustering algorithms based on fuzzy c-means for data with tolerance using kernel functions are proposed. kernel functions which map the data from the original space into higher dimensional feature space are introduced into the proposed algorithms. Nonlinear boundary of clusters can be easily found by using the kernel functions. First, two clustering algorithms for data with tolerance are introduced. One is based on standard method and the other is on entropy-based one. Second, the tolerance in feature space is discussed taking account into soft margin algorithm in Support Vector Machine. Third, two objective functions in feature space are shown corresponding to two methods, respectively. Fourth, Karush-Kuhn-Tucker conditions of two objective functions are considered, respectively, and these conditions are re-expressed with kernel functions as the representation of an inner product for mapping from the original pattern space into a higher dimensional feature space. Fifth, two iterative algorithms are proposed for the objective functions, respectively. Through some numerical experiments,the proposed algorithms are discussed.
Objective: In many medical areas, there exist different regression formulas to predict/evaluate a medical outcome on the same problem, each of them being efficient only in a particular sub-space of the problem space. ...
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Objective: In many medical areas, there exist different regression formulas to predict/evaluate a medical outcome on the same problem, each of them being efficient only in a particular sub-space of the problem space. The paper aims at the development of a generic, incremental Learning model that includes all available regression formulas for a particular prediction problem to define local areas of the problem space with their best performing formula along with useful explanation rules. Another objective of the paper is to develop a specific model for renal function evaluation using nine existing formulas. Methods and materials: We have used a connectionist neuro-fuzzy approach and have developed a knowledge-based neural network model (KBNN) which incorporates and adapts incrementally several existing regression formulas and kernel functions. The model incorporates different non-linear regression functions as neurons in its hidden layer and adapts these functions through incremental learning from data in particular local areas of the space. More specifically, each hidden neural node has a pair of functions associated with it-one regression formula, that represents existing knowledge and one Gaussian kernel function, that defines the sub-space of the whole problem space, in which the formula is Locally adapted to new data. All these functions are aggregated and changed through incremental learning. The proposed KBNN model is illustrated using a medical dataset of observed patient glomerular filtration rate (GFR) measurements for renal function evaluation. In this case study, the regression function for each cluster is selected by the model from nine formulas commonly used by medical practitioners to predict GFR. 441 GFR data vectors from 141 patients taken from 12 sites in Australia and New Zealand have been used as a case study experimental data set. Results: The proposed GFR prediction model, based on the proposed generic KBNN model, outperforms at least by 10% accu
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