An information theoretic sparse kernel algorithm for online learning

Kernel-based algorithms have been proven successful in many nonlinear modeling applications. However, the computational complexity of classical kernel-based methods grows superlinearly with the increasing number of training data, which is too expensive for online applications. In order to solve this problem, the paper presents an information theoretic method to train a sparse version of kernel learning algorithm. A concept named instantaneous mutual information is investigated to measure the system reliability of the estimated output. This measure is used as a criterion to determine the novelty of the training sample and informative ones are selected to form a compact dictionary to represent the whole data. Furthermore, we propose a robust learning scheme for the training of the kernel learning algorithm with an adaptive learning rate. This ensures the convergence of the learning algorithm and makes it converge to the steady state faster. We illustrate the performance of our proposed algorithm and compare it with some recent kernel algorithms by several experiments.     

An improved kernel-based incremental extreme learning machine with fixed budget for nonstationary time series prediction

In order to curb the model expansion of the kernel learning methods and adapt the nonlinear dynamics in the process of the nonstationary time series online prediction, a new online sequential learning algorithm with sparse update and adaptive regularization scheme is proposed based on kernel-based incremental extreme learning machine (KB-IELM). For online sparsification, a new method is presented to select sparse dictionary based on the instantaneous information measure. This method utilizes a pruning strategy, which can prune the least “significant” centers, and preserves the important ones by online minimizing the redundancy of dictionary. For adaptive regularization scheme, a new objective function is constructed based on basic ELM model. New model has different structural risks in different nonlinear regions. At each training step, new added sample could be assigned optimal regularization factor by optimization procedure. Performance comparisons of the proposed method with other existing online sequential learning methods are presented using artificial and real-word nonstationary time series data. The results indicate that the proposed method can achieve higher prediction accuracy, better generalization performance and stability.

     

基于核映射极限学习机的入口氮氧化物预测

针对在线贯序极限学习机(OS-ELM)算法隐含层输出不稳定、易产生奇异矩阵和在线贯序更新时没有考虑训练样本时效性的问题,提出一种基于核函数映射的正则化自适应遗忘因子(FFOS-RKELM)算法.该算法利用核函数代替隐含层,能够产生稳定的输出结果.在初始阶段加入正则化方法,通过构造非奇异矩阵提高模型的泛化能力;在贯序更新阶段,通过新到的数据自动更新遗忘因子.将FFOS-RKELM算法应用到混沌时间序列预测和入口氮氧化物时间序列预测中,相比于OS-ELM、FFOS-RELM、OS-RKELM算法,可有效地提高预测精度和泛化能力.     

基于改进极限学习机算法的行为识别

重点研究了极限学习机ELM对行为识别检测的效果。针对在线学习和行为分类上存在计算复杂性和时间消耗大的问题,提出了一种新的行为识别学习算法(ELM-Cholesky)。该算法首先引入了基于Cholesky分解求ELM的方法,接着依据在线学习期间核函数矩阵的更新特点,将分块矩阵Cholesky分解算法用于ELM的在线求解,使三角因子矩阵实现在线更新,从而得出一种新的ELM-Cholesky在线学习算法。新算法充分利用了历史训练数据,降低了计算的复杂性,提高了行为识别的准确率。最后,在基准数据库上采用该算法进行了大量实验,实验结果表明了这种在线学习算法的有效性。     

桥梁结构的未标记模态特征稀疏编码深度学习监测*

由于建筑物结构健康问题大部分是累积性损害,很难被检测到,实际结构和环境噪声的复杂性使得结构健康监测更加困难,并且现有方法在训练模型时需要大量的数据,但是实际中对于数据的标记是很复杂的。为克服该问题,通过配备无线传感器网络,并采用稀疏编码实现桥梁结构健康监测,然后通过大量未标记实例在实现特征提取基础上进行稀疏编码算法训练,实现数据维度压缩和无标记数据预处理。其次,利用深度学习算法实现桥梁结构健康监测类别预测,同时基于线性共轭梯度对Hessian优化进行改进,利用半正定高斯-牛顿曲率矩阵替换不确定Hessian矩阵,进行二次目标组合,以实现深度学习算法效率提升;实验结果表明,所提深度学习桥梁结构安全检测算法实现了环境噪声稀疏编码水平下的高精度结构健康监测。     

Online chaotic time series prediction using unbiased composite kernel machine via Cholesky factorization

The kernel method has proved to be an effective machine learning tool in many fields. Support vector machines with various kernel functions may have different performances, as the kernels belong to two different types, the local kernels and the global kernels. So the composite kernel, which can bring more stable results and good precision in classification and regression, is an inevitable choice. To reduce the computational complexity of the kernel machine’s online modeling, an unbiased least squares support vector regression model with composite kernel is proposed. The bias item of LSSVR is eliminated by improving the form of structure risk in this model, and then the calculating method of the regression coefficients is greatly simplified. Simultaneously, through introducing the composite kernel to the LSSVM, the model can easily adapt to the irregular variation of the chaotic time series. Considering the real-time performance, an online learning algorithm based on Cholesky factorization is designed according to the characteristic of extended kernel function matrix. Experimental results indicate that the unbiased composite kernel LSSVR is effective and suitable for online time series with both the steep variations and the smooth variations, as it can well track the dynamic character of the series with good prediction precisions, better generalization and stability. The algorithm can also save much computation time comparing to those methods using matrix inversion, although there is a little more loss in time than that with the usage of single kernels.     

基于图拉普拉斯变换和极限学习机的时间序列预测算法

由于时间效率的约束,多元时间序列预测算法往往存在预测准确率不足的问题。对此,提出基于图拉普拉斯变换和极限学习机的时间序列预测算法。基于图拉普拉斯变换对时间序列进行半监督的特征提取,通过散布矩阵将监督特征和无监督特征进行融合。设计在线的极限学习机学习算法,仅需要在线更新网络的输出权重矩阵即可完成神经网络的学习。利用提取的特征在线训练极限学习机,实现对多元时间序列的实时预测。基于多个数据集进行仿真实验,结果表明该算法有效地提高了预测准确率。     

Hessian matrix distribution for Bayesian policy gradient reinforcement learning

Bayesian policy gradient algorithms have been recently proposed for modeling the policy gradient of the performance measure in reinforcement learning as a Gaussian process. These methods were known to reduce the variance and the number of samples needed to obtain accurate gradient estimates in comparison to the conventional Monte-Carlo policy gradient algorithms. In this paper, we propose an improvement over previous Bayesian frameworks for the policy gradient. We use the Hessian matrix distribution as a learning rate schedule to improve the performance of the Bayesian policy gradient algorithm in terms of the variance and the number of samples. As in computing the policy gradient distributions, the Bayesian quadrature method is used to estimate the Hessian matrix distributions. We prove that the posterior mean of the Hessian distribution estimate is symmetric, one of the important properties of the Hessian matrix. Moreover, we prove that with an appropriate choice of kernel, the computational complexity of Hessian distribution estimate is equal to that of the policy gradient distribution estimates. Using simulations, we show encouraging experimental results comparing the proposed algorithm to the Bayesian policy gradient and the Bayesian policy natural gradient algorithms described in Ghavamzadeh and Engel [10].     

选矿过程精矿品位自适应在线支持向量预测方法

本文提出了一种基于支持向量回归的选矿过程精矿品位自适应在线预测方法,通过使用新的混合核函数和参数在线更新机制提高了精矿品位的预测精度.在分析经典核函数特性后,构造了一种混合核函数以兼顾模型的学习能力与泛化能力,同时为了提高预测方法对选矿生产动态过程的适应性,模型依据新工况样本对现有样本集统计特性的影响,引入了模型参数自适应调整机制,并采用在线迭代学习机制更新模型,提高了模型的计算速度.使用某选矿厂生产实际数据进行实验分析,结果表明本文方法比现有方法在计算时间和预测精度上都有明显优势,适合应用于动态变化的选矿生产过程.     

Hessian optimal design for image retrieval

Recently there has been a considerable interest in active learning from the perspective of optimal experimental design (OED). OED selects the most informative samples to minimize the covariance matrix of the parameters, so that the expected prediction error of the parameters, as well as the model output, can be minimized. Most of the existing OED methods are based on either linear regression or Laplacian regularized least squares (LapRLS) models. Although LapRLS has shown a better performance than linear regression, it suffers from the fact that the solution is biased towards a constant and the lack of extrapolating power. In this paper, we propose a novel active learning algorithm called Hessian optimal design (HOD). HOD is based on the second-order Hessian energy for semi-supervised regression which overcomes the drawbacks of Laplacian based methods. Specifically, HOD selects those samples which minimize the parameter covariance matrix of the Hessian regularized regression model. The experimental results on content-based image retrieval have demonstrated the effectiveness of our proposed approach.     

融合深度特征与多核学习的LSTWSVM及其工业应用

为了提高多核学习(MKL)的表示能力同时降低其计算成本,提出一种融合深度特征与多核学习的最小二乘孪生支持向量机(LSTWSVM)算法.针对支持向量机等核分类器在多核学习中高计算复杂度的问题,提出一种基于边缘错误最小化原则的多核LSTWSVM框架,利用分类器优势提高多核学习的性能.针对高斯多核浅层结构的问题,采用MKL法设计一种基于深度神经网络多层信息的高鲁棒性深度映射核,将此深度核与多尺度高斯基核以核矩阵哈达玛积方式相融合,构造一组新的具有高度表达能力的改进核.最后,将基于LSTWSVM的多核训练算法与改进的多核结构进行高度集成,通过大量基准数据集与工业数据实验表明,其能有效结合深度学习与多核学习的优势,且以较低的计算成本提高分类精度与泛化能力.     

Non‐negative sparse‐based SemiBoost for software defect prediction

Software defect prediction is an important decision support activity in software quality assurance. The limitation of the labelled modules usually makes the prediction difficult, and the class‐imbalance characteristic of software defect data leads to negative influence on decision of classifiers. Semi‐supervised learning can build high‐performance classifiers by using large amount of unlabelled modules together with the labelled modules. Ensemble learning achieves a better prediction capability for class‐imbalance data by using a series of weak classifiers to reduce the bias generated by the majority class. In this paper, we propose a new semi‐supervised software defect prediction approach, non‐negative sparse‐based SemiBoost learning. The approach is capable of exploiting both labelled and unlabelled data and is formulated in a boosting framework. In order to enhance the prediction ability, we design a flexible non‐negative sparse similarity matrix, which can fully exploit the similarity of historical data by incorporating the non‐negativity constraint into sparse learning for better learning the latent clustering relationship among software modules. The widely used datasets from NASA projects are employed as test data to evaluate the performance of all compared methods. Experimental results show that non‐negative sparse‐based SemiBoost learning outperforms several representative state‐of‐the‐art semi‐supervised software defect prediction methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Semi-supervised kernel density estimation for video annotation

Insufficiency of labeled training data is a major obstacle for automatic video annotation. Semi-supervised learning is an effective approach to this problem by leveraging a large amount of unlabeled data. However, existing semi-supervised learning algorithms have not demonstrated promising results in large-scale video annotation due to several difficulties, such as large variation of video content and intractable computational cost. In this paper, we propose a novel semi-supervised learning algorithm named semi-supervised kernel density estimation (SSKDE) which is developed based on kernel density estimation (KDE) approach. While only labeled data are utilized in classical KDE, in SSKDE both labeled and unlabeled data are leveraged to estimate class conditional probability densities based on an extended form of KDE. It is a non-parametric method, and it thus naturally avoids the model assumption problem that exists in many parametric semi-supervised methods. Meanwhile, it can be implemented with an efficient iterative solution process. So, this method is appropriate for video annotation. Furthermore, motivated by existing adaptive KDE approach, we propose an improved algorithm named semi-supervised adaptive kernel density estimation (SSAKDE). It employs local adaptive kernels rather than a fixed kernel, such that broader kernels can be applied in the regions with low density. In this way, more accurate density estimates can be obtained. Extensive experiments have demonstrated the effectiveness of the proposed methods.     

The Bayesian evidence scheme for regularizing probability-density estimating neural networks

Training probability-density estimating neural networks with the expectation-maximization (EM) algorithm aims to maximize the likelihood of the training set and therefore leads to overfitting for sparse data. In this article, a regularization method for mixture models with generalized linear kernel centers is proposed, which adopts the Bayesian evidence approach and optimizes the hyperparameters of the prior by type II maximum likelihood. This includes a marginalization over the parameters, which is done by Laplace approximation and requires the derivation of the Hessian of the log-likelihood function. The incorporation of this approach into the standard training scheme leads to a modified form of the EM algorithm, which includes a regularization term and adapts the hyperparameters on-line after each EM cycle. The article presents applications of this scheme to classification problems, the prediction of stochastic time series, and latent space models.     

Unsupervised feature selection based on kernel fisher discriminant analysis and regression learning

In this paper, we propose a new feature selection method called kernel fisher discriminant analysis and regression learning based algorithm for unsupervised feature selection. The existing feature selection methods are based on either manifold learning or discriminative techniques, each of which has some shortcomings. Although some studies show the advantages of two-steps method benefiting from both manifold learning and discriminative techniques, a joint formulation has been shown to be more efficient. To do so, we construct a global discriminant objective term of a clustering framework based on the kernel method. We add another term of regression learning into the objective function, which can impose the optimization to select a low-dimensional representation of the original dataset. We use L_2,1-norm of the features to impose a sparse structure upon features, which can result in more discriminative features. We propose an algorithm to solve the optimization problem introduced in this paper. We further discuss convergence, parameter sensitivity, computational complexity, as well as the clustering and classification accuracy of the proposed algorithm. In order to demonstrate the effectiveness of the proposed algorithm, we perform a set of experiments with different available datasets. The results obtained by the proposed algorithm are compared against the state-of-the-art algorithms. These results show that our method outperforms the existing state-of-the-art methods in many cases on different datasets, but the improved performance comes with the cost of increased time complexity.

     

基于局部保持的核稀疏表示字典学习

为了利用核技巧提高分类性能, 在局部保持的稀疏表示 字典学习的基础上, 提出了两种核化的稀疏表示字典学习方法. 首先, 原始训练数据被投影到高维核空间, 进行基于局部保持的核稀疏表示字典学习; 其次, 在稀疏系数上强加核局部保持约束, 进行基于核局部保持的核稀疏表示字典学习. 实验结果表明, 该方法的分类识别结果优于其他方法.     

Multiple kernel ensemble learning for software defect prediction

Software defect prediction aims to predict the defect proneness of new software modules with the historical defect data so as to improve the quality of a software system. Software historical defect data has a complicated structure and a marked characteristic of class-imbalance; how to fully analyze and utilize the existing historical defect data and build more precise and effective classifiers has attracted considerable researchers’ interest from both academia and industry. Multiple kernel learning and ensemble learning are effective techniques in the field of machine learning. Multiple kernel learning can map the historical defect data to a higher-dimensional feature space and make them express better, and ensemble learning can use a series of weak classifiers to reduce the bias generated by the majority class and obtain better predictive performance. In this paper, we propose to use the multiple kernel learning to predict software defect. By using the characteristics of the metrics mined from the open source software, we get a multiple kernel classifier through ensemble learning method, which has the advantages of both multiple kernel learning and ensemble learning. We thus propose a multiple kernel ensemble learning (MKEL) approach for software defect classification and prediction. Considering the cost of risk in software defect prediction, we design a new sample weight vector updating strategy to reduce the cost of risk caused by misclassifying defective modules as non-defective ones. We employ the widely used NASA MDP datasets as test data to evaluate the performance of all compared methods; experimental results show that MKEL outperforms several representative state-of-the-art defect prediction methods.     

A non-biased form of least squares support vector classifier and its fast online learning

As an effective learning technique based on structural risk minimization, SVM has been confirmed an useful tool in many machine learning fields. With the increase in application requirement for some real-time cases, such as fast prediction and pattern recognition, the online learning based on SVM gradually becomes a focus. But the common SVM has disadvantages in classifier’s bias and the computational complexity of online modeling, resulting in the reduction in classifier’s generality and the low learning speed. Therefore, an non-biased least square support vector classifier(LSSVC) model is proposed in this paper by improving the form of structure risk. Also, a fast online learning algorithm using Cholesky factorization is designed based on this model according to the characteristic of the non-biased kernel extended matrix in the model’s dynamic change process. In this way, the calculation of Lagrange multipliers is simplified, and the time of online learning is greatly reduced. Simulation results testify that the non-biased LSSVC has good universal applicability and better generalization capability, at the same time, the algorithm has a great improvement on learning speed.     

Iterative weighted least squares algorithms for neural networks classifiers

This paper discusses learning algorithms of layered neural networks from the standpoint of maximum likelihood estimation. At first we discuss learning algorithms for the most simple network with only one neuron. It is shown that Fisher information of the network, namely minus expected values of Hessian matrix, is given by a weighted covariance matrix of input vectors. A learning algorithm is presented on the basis of Fisher's scoring method which makes use of Fisher information instead of Hessian matrix in Newton's method. The algorithm can be interpreted as iterations of weighted least squares method. Then these results are extended to the layered network with one hidden layer. Fisher information for the layered network is given by a weighted covariance matrix of inputs of the network and outputs of hidden units. Since Newton's method for maximization problems has the difficulty when minus Hessian matrix is not positive definite, we propose a learning algorithm which makes use of Fisher information matrix, which is non-negative, instead of Hessian matrix. Moreover, to reduce the computation of full Fisher information matrix, we propose another algorithm which uses only block diagonal elements of Fisher information. The algorithm is reduced to an iterative weighted least squares algorithm in which each unit estimates its own weights by a weighted least squares method. It is experimentally shown that the proposed algorithms converge with fewer iterations than error back-propagation (BP) algorithm.     

An online AUC formulation for binary classification

The area under the ROC curve (AUC) provides a good scalar measure of ranking performance without requiring a specific threshold for performance comparison among classifiers. AUC is useful for imprecise environments since it operates independently with respect to class distributions and misclassification costs. A direct optimization of this AUC criterion thus becomes a natural choice for binary classifier design. However, a direct formulation based on the AUC criterion would require a high computational cost due to the drastically increasing input pair features. In this paper, we propose an online learning algorithm to circumvent this computational problem for binary classification. Different from those conventional recursive formulations, the proposed formulation involves a pairwise cost function which pairs up a newly arrived data point with those of opposite class in stored data. Moreover, with incorporation of a sparse learning into the online formulation, the computational effort can be significantly reduced. Our empirical results on three different scales of public databases show promising potential in terms of classification AUC, accuracy, and computational efficiency.