Hybrid model based on wavelet support vector machine and modified genetic algorithm penalizing Gaussian noises for power load forecasts

In view of the dissatisfactory capability of the ε-insensitive loss function in field of white (Gaussian) noise of multi-dimensional load series, a new wavelet v-support vector machine with Gaussian loss function which is called Wg-SVM is put forward to penalize the Gaussian noises. To seek the optimal parameters of Wg-SVM, modified genetic algorithm (GA) is proposed to optimize parameters of Wg-SVM. The results of application in load forecasts show that the forecasting approach based on the Wg-SVM model is effective and feasible, the comparison between the method proposed in this paper and other ones is also given, which proves this method is better than other SVM methods.     

The forecasting model based on wavelet ν-support vector machine

Aiming at the series with small samples, seasonal character, nonlinearity, randomicity and fuzziness, the existing support vector kernel does not approach the random curve of the sales time series in the L²(Rⁿ) space (quadratic continuous integral space). A new wavelet support vector machine (WN ν-SVM) is proposed based on wavelet theory and modified support vector machine. A particle swarm optimization (PSO) algorithm is designed to select the best parameters of WN ν-SVM model in the scope of constraint permission. The results of application in car sale series forecasting show that the forecasting approach based on the PSOWN ν-SVM model is effective and feasible, the comparison between the method proposed in this paper and other ones is also given which proves this method is better than PSOW ν-SVM and other traditional methods.     

Hybrid model based on SVM with Gaussian loss function and adaptive Gaussian PSO

In view of the bad capability of the standard support vector machine (SVM) in field of white noise of input series, a new v-SVM with Gaussian loss function which is call g-SVM is put forward to handle white noises. To seek the unknown parameters of g-SVM, an adaptive normal Gaussian particle swarm optimization (ANPSO) is also proposed. The results of applications show that the hybrid forecasting model based on the g-SVM and ANPSO is feasible and effective, the comparison between the method proposed in this paper and other ones is also given which proves this method is better than v-SVM and other traditional methods.     

基于鲁棒小波ν-支持向量机的产品销售预测模型

针对产品销售时序具有正态高斯分布、幅值较大、奇异点等混合噪音, 设计一种鲁棒损失函数, 并采用小波核函数, 由此得到一种新的小波ν-支持向量机, 即鲁棒小波ν-支持向量机(Robust wavelet ν-support vector machine, RWν-SVM). 它可以有效地压制销售时序的多种噪音和奇异点, 具有很强的鲁棒性, 而且它比标准小波ν-支持向量机(Wν-SVM)具有更简洁的对偶优化问题. 最后进行了汽车销售预测的实例分析, 结果表明基于RWν-SVM的预测模型是有效可行的.     

The complex fuzzy system forecasting model based on fuzzy SVM with triangular fuzzy number input and output

This paper presents a new version of fuzzy support vector machine to forecast the nonlinear fuzzy system with multi-dimensional input variables. The input and output variables of the proposed model are described as triangular fuzzy numbers. Then by integrating the triangular fuzzy theory and v-support vector regression machine, the triangular fuzzy v-support vector machine (TFv-SVM) is proposed. To seek the optimal parameters of TFv-SVM, particle swarm optimization is also applied to optimize parameters of TFv-SVM. A forecasting method based on TFv-SVRM and PSO are put forward. The results of the application in sale system forecasts confirm the feasibility and the validity of the forecasting method. Compared with the traditional model, TFv-SVM method requires fewer samples and has better forecasting precision.     

An intelligent forecasting model based on robust wavelet ν-support vector machine

Aiming at the problem of small samples, season character, nonlinearity, randomicity and fuzziness in product demand series, the existing support vector kernel does not approach the random curve of the demands time series in the L²(Rⁿ) space (quadratic continuous integral space). The robust loss function is also proposed to solve the shortcoming of ε-insensitive loss function during handling hybrid noises. A novel robust wavelet support vector machine (RW ν-SVM) is proposed based on wavelet theory and the modified support vector machine. Particle swarm optimization algorithm is designed to select the optimal parameters of RW ν-SVM model in the scope of constraint permission. The results of application in car demand forecasts show that the forecasting approach based on the RW ν-SVM model is effective and feasible, the comparison between the method proposed in this paper and other ones is also given which proves this method is better than RW ν-SVM and other traditional methods.     

Hybrid wavelet ν-support vector machine and chaotic particle swarm optimization for regression estimation

In view of the bad approximate results of the existing support vector (SV) kernel for series influenced by multi-factors in quadratic continuous integral space, combining wavelet theory with kernel technique, a wavelet kernel function is put forward in quadratic continuous integral space. And then, wavelet ν-support vector machine (W ν-SVM) with wavelet kernel is proposed. To seek the optimal parameters of W ν-SVM, embedded chaotic particle swarm optimization (ECPSO) is also proposed to optimize parameters of W ν-SVM. The results of application in car sale estimation show that the estimation approach based on the W ν-SVM and ECPSO is effective and feasible. Compared with the traditional model, W ν-SVM method requires fewer samples and has better estimating precision.     

The complex fuzzy system forecasting model based on triangular fuzzy robust wavelet ν-support vector machine

This paper presents a new version of fuzzy wavelet support vector regression machine to forecast the nonlinear fuzzy system with multi-dimensional input variables. The input and output variables of the proposed model are described as triangular fuzzy numbers. Then by integrating the triangular fuzzy theory, wavelet analysis theory and ν-support vector regression machine, a polynomial slack variable is also designed, the triangular fuzzy robust wavelet ν-support vector regression machine (TFRWν-SVM) is proposed. To seek the optimal parameters of TFRWν-SVM, particle swarm optimization is also applied to optimize parameters of TFRWν-SVM. A forecasting method based on TFRWν-SVRM and PSO are put forward. The results of the application in sale system forecasts confirm the feasibility and the validity of the forecasting method. Compared with the traditional model, TFRWν-SVM method requires fewer samples and has better forecasting precision.     

A self-adaptive embedded chaotic particle swarm optimization for parameters selection of Wv-SVM

Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Based on the chaotic system theory, this paper proposes new PSO method that uses chaotic mappings for parameter adaptation of Wavelet v-support vector machine (Wv-SVM). Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed PSO introduces chaos mapping using logistic mapping sequences which increases its convergence rate and resulting precision. The simulation results show the parameter selection of Wv-SVM model can be solved with high search efficiency and solution accuracy under the proposed PSO method.     

基于具有自适应分段损失函数支持向量机的产品销售预测模型

针对产品销售时序包含噪声的数据特征, 提出一种基于自适应分段损失函数的支持向量机模型(AS??-SVM). AS??-SVM 为每个样本点赋一个单独的不敏感损失值, 以此降低模型对包含较大噪声的样本点的依赖性, 并从理论上证明了该方法可增强模型部分的泛化性能. 将AS??-SVM 与??-SVM 共同应用于处理一个数值算例和一个汽车销售预测实例中, 仿真实验结果表明, AS??-SVM 是有效可行的, 可获得比??-SVM 更精确的预测结果.

     

Gaussian小波SVM及其混沌时间序列预测

为了提高混沌时间序列的预测精度,针对小波有利于信号细微特征提取的优点,结合小波技术和SVM的核函数方法,提出基于Gaussian小波SVM的混沌时间序列预测模型.证明了偶数阶Ganssian小波函数满足SVM平移不变核条件,并构建相应的Gaussian小波SVM.时混沌时间序列进行相空间重构,将重构相空间中的向量作为SVM的输入参量.用Ganssian小波SVM与常用的径向基SVM及Morlet小渡SVM进行对比实验,通过对Chen's混沌时间序列和负荷混沌时间序列的预测,结果表明,Ganssian小波SVM的效果比其他两种SVM更好.     

Fuzzy fault diagnosis based on fuzzy robust v-support vector classifier and modified genetic algorithm

This paper presents a new version of fuzzy support vector classifier machine (SVM) which can penalize those hybrid noises to forecast fuzzy nonlinear system. Since there exist some problems of uncertain data in many actual forecasting problem, the input variables are described as fuzzy numbers by fuzzy comprehensive evaluation. To solve the shortage of ε-insensitive loss function for hybrid noises such as singularity points, biggish magnitude noises and Gaussian noises, a novel robust loss function is proposed in this paper. Then by the integration of the triangular fuzzy theory, v-SVC and robust loss function theory, fuzzy robust v-SVC (FRv-SVM) which can penalize those hybrid noises is proposed. To seek the optimal parameters of FRv-SVC, genetic algorithm is also proposed to optimize the unknown parameters of FRv-SVC. The results of the application in fuzzy car assembly line system diagnosis confirm the feasibility and the validity of the FRv-SVC model. Compared with other SVC methods, FRv-SVC method has better classifier precison for small sample with hybrid noises.     

基于自适应边界向量提取的多尺度v-支持向量机建模

针对v-支持向量机(v-SVM)用于大规模、多峰样本建模时易出现训练速度慢和回归精度低的问题,提出基于边界向量提取的多尺度v-SVM建模方法.该方法采用一种自适应边界向量提取算法,从训练样本中预提取出包含全部支持向量的边界向量集,以缩减训练样本规模,并通过求解多尺度v-SVM二次规划问题获取全局最优回归模型,从多个尺度上对复杂分布样本进行逼近.仿真结果表明,基于边界向量提取的多尺度v-SVM比v-SVM具有更好的回归结果.     

Fuzzy robust ν-support vector machine with penalizing hybrid noises on symmetric triangular fuzzy number space

In view of the shortage of ε-insensitive loss function for hybrid noises such as singularity points, biggish magnitude noises and Gaussian noises, this paper presents a new version of fuzzy support vector machine (SVM) which can penalize those hybrid noises to forecast fuzzy nonlinear system. Since there exist some problems of hybrid noises and uncertain data in many actual forecasting problem, the input variables are described as fuzzy numbers by fuzzy comprehensive evaluation. Then by the integration of the triangular fuzzy theory, ν-SVM and loss function theory, the fuzzy robust ν-SVM with robust loss function (FRν-SVM) which can penalize those hybrid noises is proposed. To seek the optimal parameters of FRν-SVM, particle swarm optimization is also proposed to optimize the unknown parameters of FRν-SVM. The results of the application in fuzzy sale system forecasts confirm the feasibility and the validity of the FRν-SVM model. Compared with the traditional model and other SVM methods, FRν-SVM method requires fewer samples and has better generalization capability for Gaussian noise.     

The forecasting model based on fuzzy novel ν-support vector machine

This paper presents a new version of fuzzy support vector machine to forecast multi-dimension fuzzy sample. By combining the triangular fuzzy theory with the modified ν-support vector machine, the fuzzy novel ν-support vector machine (FNν-SVM) is proposed, whose constraint conditions are less than those of the standard Fν-SVM by one, is proved to satisfy the structure risk minimum rule under the condition of probability. Moreover, there is no parameter b in the regression function of the FNν-SVM. To seek the optimal parameters of the FNν-SVM, particle swarm optimization is also proposed to optimize the unknown parameters of the FNν-SVM. The results of the application in sale forecasts confirm the feasibility and the validity of the FNν-SVM model. Compared with the traditional model, the FNν-SVM method requires fewer samples and has better forecasting precision.     

ε-支持向量回归机算法及其应用

针对现有传统的一些图像去噪方法难以获得清晰图像边缘的问题,提出了利用ε-SVR技术构建图像去噪滤波器的新方法。ε-支持向量回归机通过引入ε不敏感损失函数,可以实现具有较强鲁棒性的回归,而且回归估计是稀疏的,保留了SVM的所有优点。分析了ε-支持向量回归机理论算法及其在图像去噪中的应用,使用ε-支持向量回归机对图像进行滤波并且与最小值滤波、均值滤波和维纳滤波等常用的滤波方法相比较,还比较了SVM各种核函数对不同噪声的滤波效果和分析了不同阶数的Multinomial核的滤波效果。实验结果表明了ε-支持向量回归机能够有效地去除噪声,不但信噪比较高而且比较清晰,同时具有良好的稀疏性。     

A clustering-based short-term load forecasting using independent component analysis and multi-scale decomposition transform

The Journal of Supercomputing - A short-term electrical load forecasting model is proposed in this work. The proposed model is based on independent component analysis (ICA), discrete wavelet...     

A novel method of short-term load forecasting based on multiwavelet transform and multiple neural networks

This paper aims to develop a load forecasting method for short-term load forecasting based on multiwavelet transform and multiple neural networks. Firstly, a variable weight combination load forecasting model for power load is proposed and discussed. Secondly, the training data are extracted from power load data through multiwavelet transform. Lastly, the obtained data are trained through a variable weight combination model. BP network, RBF network and wavelet neural network are adopted as the training network, and the trained data from three neural networks are input to a three-layer feedforward neural network for the load forecasting. Simulation results show that accuracy of the combination load forecasting model proposed in the paper is higher than any one single network model and the combination forecast model of three neural networks without preprocessing method of multiwavelet transform.     

GARCH prediction using spline wavelet support vector machine

Volatility forecasting is vital important in finance to reduce risk and take better decisions. This paper proposes a spline wavelet support vector machine (SWSVM) to forecast the volatility of financial time series based on generalized autoregressive conditional heteroscedasticity model. An admissible spline wavelet kernel is constructed by incorporating the wavelet technique and spline theory into support vector machine (SVM). Since spline wavelet function can yield features that describe the stock time series both at various locations and at varying time granularities, the SWSVM gains the cluster feature of volatility well. Compared with Gaussian kernel in the standard SVM, the applicability and validity of spline wavelet kernel in SWSVM are confirmed through computer simulations and experiments on real-world stock data.     

Harmonic Wavelet Transform and Image Approximation

In 2006, Saito and Remy proposed a new transform called the Laplace Local Sine Transform (LLST) in image processing as follows. Let f be a twice continuously differentiable function on a domain Ω. First we approximate f by a harmonic function u such that the residual component v=f−u vanishes on the boundary of Ω. Next, we do the odd extension for v, and then do the periodic extension, i.e. we obtain a periodic odd function v ^*. Finally, we expand v ^* into Fourier sine series. In this paper, we propose to expand v ^* into a periodic wavelet series with respect to biorthonormal periodic wavelet bases with the symmetric filter banks. We call this the Harmonic Wavelet Transform (HWT). HWT has an advantage over both the LLST and the conventional wavelet transforms. On the one hand, it removes the boundary mismatches as LLST does. On the other hand, the HWT coefficients reflect the local smoothness of f in the interior of Ω. So the HWT algorithm approximates data more efficiently than LLST, periodic wavelet transform, folded wavelet transform, and wavelets on interval. We demonstrate the superiority of HWT over the other transforms using several standard images.