基于稀疏表示剪枝集成建模的烧结终点位置智能预测

烧结终点位置(BTP)是烧结过程至关重要的参数,直接决定着最终烧结矿的质量.由于BTP难以直接在线检测,因此,通过智能学习建模来实现BTP的在线预测并在此基础上进行操作参数调节对提高烧结矿质量具有重要意义.针对这一实际工程问题,首先提出一种基于遗传优化的Wrapper特征选择方法,可选取使后续预测建模性能最优的特征组合;在此基础上,为了解决单一学习器容易过拟合的问题,提出了基于随机权神经网络(RVFLNs)的稀疏表示剪枝(SRP)集成建模算法,即SRP-ERVFLNs算法.所提算法采用建模速度快、泛化性能好的RVFLNs作为个体基学习器,采用对基学习器基函数与隐层节点数等参数进行扰动的方式来增加集成学习子模型间的差异性;同时,为了进一步提高集成模型的泛化性能与计算效率,引入稀疏表示剪枝算法,实现对集成模型的高效剪枝;最后,将所提算法用于烧结过程BTP的预测建模.工业数据实验表明,所提方法相比于其他方法具有更好的预测精度、泛化性能和计算效率.     

Accurate ensemble pruning with PL-bagging

Ensemble pruning deals with the selection of base learners prior to combination in order to improve prediction accuracy and efficiency. In the ensemble literature, it has been pointed out that in order for an ensemble classifier to achieve higher prediction accuracy, it is critical for the ensemble classifier to consist of accurate classifiers which at the same time diverse as much as possible. In this paper, a novel ensemble pruning method, called PL-bagging, is proposed. In order to attain the balance between diversity and accuracy of base learners, PL-bagging employs positive Lasso to assign weights to base learners in the combination step. Simulation studies and theoretical investigation showed that PL-bagging filters out redundant base learners while it assigns higher weights to more accurate base learners. Such improved weighting scheme of PL-bagging further results in higher classification accuracy and the improvement becomes even more significant as the ensemble size increases. The performance of PL-bagging was compared with state-of-the-art ensemble pruning methods for aggregation of bootstrapped base learners using 22 real and 4 synthetic datasets. The results indicate that PL-bagging significantly outperforms state-of-the-art ensemble pruning methods such as Boosting-based pruning and Trimmed bagging.     

A fast ensemble pruning algorithm based on pattern mining process

Ensemble pruning deals with the reduction of base classifiers prior to combination in order to improve generalization and prediction efficiency. Existing ensemble pruning algorithms require much pruning time. This paper presents a fast pruning approach: pattern mining based ensemble pruning (PMEP). In this algorithm, the prediction results of all base classifiers are organized as a transaction database, and FP-Tree structure is used to compact the prediction results. Then a greedy pattern mining method is explored to find the ensemble of size k. After obtaining the ensembles of all possible sizes, the one with the best accuracy is outputted. Compared with Bagging, GASEN, and Forward Selection, experimental results show that PMEP achieves the best prediction accuracy and keeps the size of the final ensemble small, more importantly, its pruning time is much less than other ensemble pruning algorithms.     

融入差异性的帕累托集成剪枝方法

相比于集成学习,集成剪枝方法是在多个分类器中搜索最优子集从而改善分类器的泛化性能,简化集成过程。帕累托集成剪枝方法同时考虑了分类器的精准度及集成规模两个方面,并将二者均作为优化的目标。然而帕累托集成剪枝算法只考虑了基分类器的精准度与集成规模,忽视了分类器之间的差异性,从而导致了分类器之间的相似度比较大。本文提出了融入差异性的帕累托集成剪枝算法,该算法将分类器的差异性与精准度综合为第1个优化目标,将集成规模作为第2个优化目标,从而实现多目标优化。实验表明,当该改进的集成剪枝算法与帕累托集成剪枝算法在集成规模相当的前提下,由于差异性的融入该改进算法能够获得较好的性能。     

A two-stage minimax concave penalty based method in pruned AdaBoost ensemble

AdaBoost is a highly effective ensemble learning method that combines several weak learners to produce a strong committee with higher accuracy. However, similar to other ensemble methods, AdaBoost uses a large number of base learners to produce the final outcome while addressing high-dimensional data. Thus, it poses a critical challenge in the form of high memory-space consumption. Feature selection methods can significantly reduce dimensionality in regression and have been established to be applicable in ensemble pruning. By pruning the ensemble, it is possible to generate a simpler ensemble with fewer base learners but a higher accuracy. In this article, we propose the minimax concave penalty (MCP) function to prune an AdaBoost ensemble to simplify the model and improve its accuracy simultaneously. The MCP penalty function is compared with LASSO and SCAD in terms of performance in pruning the ensemble. Experiments performed on real datasets demonstrate that MCP-pruning outperforms the other two methods. It can reduce the ensemble size effectively, and generate marginally more accurate predictions than the unpruned AdaBoost model.     

基于FP-Tree 的快速选择性集成算法

选择性集成通过选择部分基分类器参与集成,从而提高集成分类器的泛化能力,降低预测开销.但已有的选择性集成算法普遍耗时较长,将数据挖掘的技术应用于选择性集成,提出一种基于FP-Tree(frequent pattern tree)的快速选择性集成算法:CPM-EP(coverage based pattern mining for ensemble pruning).该算法将基分类器对校验样本集的分类结果组织成一个事务数据库,从而使选择性集成问题可转化为对事务数据集的处理问题.针对所有可能的集成分类器大小,CPM-EP算法首先得到一个精简的事务数据库,并创建一棵FP-Tree树保存其内容;然后,基于该FP-Tree获得相应大小的集成分类器.在获得的所有集成分类器中,对校验样本集预测精度最高的集成分类器即为算法的输出.实验结果表明,CPM-EP算法以很低的计算开销获得优越的泛化能力,其分类器选择时间约为GASEN的1/19以及Forward-Selection的1/8,其泛化能力显著优于参与比较的其他方法,而且产生的集成分类器具有较少的基分类器.     

Backward elimination model construction for regression and classification using leave-one-out criteria

A fundamental principle in practical nonlinear data modeling is the parsimonious principle of constructing the minimal model that explains the training data well. Leave-one-out (LOO) cross validation is often used to estimate generalization errors by choosing amongst different network architectures (M. Stone, “Cross validatory choice and assessment of statistical predictions”, J. R. Stast. Soc., Ser. B, 36, pp. 117–147, 1974). Based upon the minimization of LOO criteria of either the mean squares of LOO errors or the LOO misclassification rate respectively, we present two backward elimination algorithms as model post-processing procedures for regression and classification problems. The proposed backward elimination procedures exploit an orthogonalization procedure to enable the orthogonality between the subspace as spanned by the pruned model and the deleted regressor. Subsequently, it is shown that the LOO criteria used in both algorithms can be calculated via some analytic recursive formula, as derived in this contribution, without actually splitting the estimation data set so as to reduce computational expense. Compared to most other model construction methods, the proposed algorithms are advantageous in several aspects; (i) There are no tuning parameters to be optimized through an extra validation data set; (ii) The procedure is fully automatic without an additional stopping criteria; and (iii) The model structure selection is directly based on model generalization performance. The illustrative examples on regression and classification are used to demonstrate that the proposed algorithms are viable post-processing methods to prune a model to gain extra sparsity and improved generalization.     

Model selection of extreme learning machine based on multi-objective optimization

As a novel learning algorithm for single-hidden-layer feedforward neural networks, extreme learning machines (ELMs) have been a promising tool for regression and classification applications. However, it is not trivial for ELMs to find the proper number of hidden neurons due to the nonoptimal input weights and hidden biases. In this paper, a new model selection method of ELM based on multi-objective optimization is proposed to obtain compact networks with good generalization ability. First, a new leave-one-out (LOO) error bound of ELM is derived, and it can be calculated with negligible computational cost once the ELM training is finished. Furthermore, the hidden nodes are added to the network one-by-one, and at each step, a multi-objective optimization algorithm is used to select optimal input weights by minimizing this LOO bound and the norm of output weight simultaneously in order to avoid over-fitting. Experiments on five UCI regression data sets are conducted, demonstrating that the proposed algorithm can generally obtain better generalization performance with more compact network than the conventional gradient-based back-propagation method, original ELM and evolutionary ELM.     

神经网络的两种结构优化算法研究

提出了一种基于权值拟熵的“剪枝算法”与权值敏感度相结合的新方法，在“剪枝算法”中将权值拟熵作为惩罚项加入目标函数中，使多层前向神经网络在学习过程中自动约束权值分布，并以权值敏感度作为简化标准，避免了单纯依赖权值大小剪枝的随机性．同时，又针对剪枝算法在优化多输入多输出网络过程中计算量大、效率不高的问题，提出了一种在级联—相关(cascade correlation, CC)算法的基础上从适当的网络结构开始对网络进行构建的快速“构造算法”．仿真结果表明这种快速构造算法在收敛速度、运行效率乃至泛化性能上都更胜一筹．     

基于动态权重的Adaboost算法研究 *

针对Adaboost算法只能静态分配基分类器权重,不能自适应地对每个测试样本动态调整权重的问题,提出了一种基于动态权重的Adaboost算法。算法通过对训练样本集合进行聚类,并分析每个基分类器和每个类簇的适应性,进而为每个基分类器在不同类簇上设置不同权重,最终根据测试样本与类簇之间的相似性来计算基分类器在测试样本上的权重。在UCI数据集上的实验结果表明本文提出算法有效利用了测试样本之间的差异性,得到了比Adaboost算法更好的效果。     

Empirical analysis and evaluation of approximate techniques for pruning regression bagging ensembles

Identifying the optimal subset of regressors in a regression bagging ensemble is a difficult task that has exponential cost in the size of the ensemble. In this article we analyze two approximate techniques especially devised to address this problem. The first strategy constructs a relaxed version of the problem that can be solved using semidefinite programming. The second one is based on modifying the order of aggregation of the regressors. Ordered aggregation is a simple forward selection algorithm that incorporates at each step the regressor that reduces the training error of the current subensemble the most. Both techniques can be used to identify subensembles that are close to the optimal ones, which can be obtained by exhaustive search at a larger computational cost. Experiments in a wide variety of synthetic and real-world regression problems show that pruned ensembles composed of only 20% of the initial regressors often have better generalization performance than the original bagging ensembles. These improvements are due to a reduction in the bias and the covariance components of the generalization error. Subensembles obtained using either SDP or ordered aggregation generally outperform subensembles obtained by other ensemble pruning methods and ensembles generated by the Adaboost.R2 algorithm, negative correlation learning or regularized linear stacked generalization. Ordered aggregation has a slightly better overall performance than SDP in the problems investigated. However, the difference is not statistically significant. Ordered aggregation has the further advantage that it produces a nested sequence of near-optimal subensembles of increasing size with no additional computational cost.     

Random subspace method with class separability weighting

The random subspace method (RSM) is one of the ensemble learning algorithms widely used in pattern classification applications. RSM has the advantages of small error rate and improved noise insensitivity due to ensemble construction of the base‐learners. However, randomness may cause a reduction of the final ensemble decision performance because of contributions of classifiers trained by subsets with low class separability. In this study, we present a new and improved version of the RSM by introducing a weighting factor into the combination phase. One of the class separability criteria, J3, is used as a weighting factor to improve the classification performance and eliminate the drawbacks of the standard RSM algorithm. The randomly selected subsets are quantified by computing their J3 measure to determine voting weights in the model combination phase, assigning lower voting weight to classifiers trained by subsets with poor class separability. Two models are presented including J3‐weighted RSM and optimized J3 weighted RSM. In J3 weighted RSM, computed weighting values are directly multiplied by class assignment posteriors, whereas in optimized J3 weighted RSM, computed weighting values are optimized by a pattern search algorithm before multiplying by posteriors. Both models are shown to provide better error rates at lower subset dimensionality.     

An Analysis of Ensemble Pruning Techniques Based on Ordered Aggregation

Several pruning strategies that can be used to reduce the size and increase the accuracy of bagging ensembles are analyzed. These heuristics select subsets of complementary classifiers that, when combined, can perform better than the whole ensemble. The pruning methods investigated are based on modifying the order of aggregation of classifiers in the ensemble. In the original bagging algorithm, the order of aggregation is left unspecified. When this order is random, the generalization error typically decreases as the number of classifiers in the ensemble increases. If an appropriate ordering for the aggregation process is devised, the generalization error reaches a minimum at intermediate numbers of classifiers. This minimum lies below the asymptotic error of bagging. Pruned ensembles are obtained by retaining a fraction of the classifiers in the ordered ensemble. The performance of these pruned ensembles is evaluated in several benchmark classification tasks under different training conditions. The results of this empirical investigation show that ordered aggregation can be used for the efficient generation of pruned ensembles that are competitive, in terms of performance and robustness of classification, with computationally more costly methods that directly select optimal or near-optimal subensembles.     

Leave-one-out cross-validation-based model selection for multi-input multi-output support vector machine

As an effective approach for multi-input multi-output regression estimation problems, a multi-dimensional support vector regression (SVR), named M-SVR, is generally capable of obtaining better predictions than applying a conventional support vector machine (SVM) independently for each output dimension. However, although there are many generalization error bounds for conventional SVMs, all of them cannot be directly applied to M-SVR. In this paper, a new leave-one-out (LOO) error estimate for M-SVR is derived firstly through a virtual LOO cross-validation procedure. This LOO error estimate can be straightway calculated once a training process ended with less computational complexity than traditional LOO method. Based on this LOO estimate, a new model selection methods for M-SVR based on multi-objective optimization strategy is further proposed in this paper. Experiments on toy noisy function regression and practical engineering data set, that is, dynamic load identification on cylinder vibration system, are both conducted, demonstrating comparable results of the proposed method in terms of generalization performance and computational cost.     

基于蚁群优化的极限学习机选择性集成学习算法

针对现有极限学习机集成学习算法分类精度低、泛化能力差等缺点,提出了一种基于蚁群优化思想的极限学习机选择性集成学习算法。该算法首先通过随机分配隐层输入权重和偏置的方法生成大量差异的极限学习机分类器,然后利用一个二叉蚁群优化搜索算法迭代地搜寻最优分类器组合,最终使用该组合分类测试样本。通过12个标准数据集对该算法进行了测试,该算法在9个数据集上获得了最优结果,在另3个数据集上获得了次优结果。采用该算法可显著提高分类精度与泛化性能。     

A novel weight pruning method for MLP classifiers based on the MAXCORE principle

We introduce a novel weight pruning methodology for MLP classifiers that can be used for model and/or feature selection purposes. The main concept underlying the proposed method is the MAXCORE principle, which is based on the observation that relevant synaptic weights tend to generate higher correlations between error signals associated with the neurons of a given layer and the error signals propagated back to the previous layer. Nonrelevant (i.e. prunable) weights tend to generate smaller correlations. Using the MAXCORE as a guiding principle, we perform a cross-correlation analysis of the error signals at successive layers. Weights for which the cross-correlations are smaller than a user-defined error tolerance are gradually discarded. Computer simulations using synthetic and real-world data sets show that the proposed method performs consistently better than standard pruning techniques, with much lower computational costs.     

A new reverse reduce-error ensemble pruning algorithm

Although greedy algorithms possess high efficiency, they often receive suboptimal solutions of the ensemble pruning problem, since their exploration areas are limited in large extent. And another marked defect of almost all the currently existing ensemble pruning algorithms, including greedy ones, consists in: they simply abandon all of the classifiers which fail in the competition of ensemble selection, causing a considerable waste of useful resources and information. Inspired by these observations, an interesting greedy Reverse Reduce-Error (RRE) pruning algorithm incorporated with the operation of subtraction is proposed in this work. The RRE algorithm makes the best of the defeated candidate networks in a way that, the Worst Single Model (WSM) is chosen, and then, its votes are subtracted from the votes made by those selected components within the pruned ensemble. The reason is because, for most cases, the WSM might make mistakes in its estimation for the test samples. And, different from the classical RE, the near-optimal solution is produced based on the pruned error of all the available sequential subensembles. Besides, the backfitting step of RE algorithm is replaced with the selection step of a WSM in RRE. Moreover, the problem of ties might be solved more naturally with RRE. Finally, soft voting approach is employed in the testing to RRE algorithm. The performances of RE and RRE algorithms, and two baseline methods, i.e., the method which selects the Best Single Model (BSM) in the initial ensemble, and the method which retains all member networks of the initial ensemble (ALL), are evaluated on seven benchmark classification tasks under different initial ensemble setups. The results of the empirical investigation show the superiority of RRE over the other three ensemble pruning algorithms.     

Recognition algorithms for the connection machine

This paper describes an object recognition algorithm both on a sequential machine and on a single instruction multiple data (SIMD) parallel processor such as the MIT connection machine. The problem, in the way it is presently formulated on a sequential machine, is essentially a propagation of constraints through a tree of possibilities in an attempt to prune the tree to a small number of leaves. The tree can become excessively large, however, and so implementations on massively parallel machines are sought in order to speed up the problem. Two fast parallel algorithms are described here, a static algorithm and a dynamic algorithm. The static algorithm reformulates the problem by assigning every leaf in the completely expanded unpruned tree to a separate processor in the connection machine. Then pruning is done in nearly constant time by broadcasting constraints to the entire SIMD array. This parallel version is shown to run three to four orders of magnitude faster than the sequential version. For large recognition problems which would exceed the capacity of the machine, a dynamic algorithm is described which performs a series of loading and pruning steps, dynamically allocating and deallocating processors through the use of the connection machine's global router communications mechanism.     

A new boosting design of Support Vector Machine classifiers

Boosting algorithms pay attention to the particular structure of the training data when learning, by means of iteratively emphasizing the importance of the training samples according to their difficulty for being correctly classified. If common kernel Support Vector Machines (SVMs) are used as basic learners to construct a Real AdaBoost ensemble, the resulting ensemble can be easily compacted into a monolithic architecture by simply combining the weights that correspond to the same kernels when they appear in different learners, avoiding to increase the operation computational effort for the above potential advantage. This way, the performance advantage that boosting provides can be obtained for monolithic SVMs, i.e., without paying in classification computational effort because many learners are needed. However, SVMs are both stable and strong, and their use for boosting requires to unstabilize and to weaken them. Yet previous attempts in this direction show a moderate success.In this paper, we propose a combination of a new and appropriately designed subsampling process and an SVM algorithm which permits sparsity control to solve the difficulties in boosting SVMs for obtaining improved performance designs. Experimental results support the effectiveness of the approach, not only in performance, but also in compactness of the resulting classifiers, as well as that combining both design ideas is needed to arrive to these advantageous designs.     

集成学习算法的研究与应用

集成学习算法的思想就是集成多个学习器,并组合它们的预测结果,以形成最终的结论。典型的学习模型组合方法有投票法,专家混合方法,堆叠泛化法与级联法,但这些方法的性能都有待进一步提高。提出了一种新颖的集成学习算法--增强的集成学习算法（ReinforcedEnsemble）。ReinforcedEnsemble集成算法由两大部分组成：ReinforcedEnsemble特征提取算法与ReinforcedEnsemble基分类器。通过实验,将ReinforcedEnsemble算法与其他集成学习算法进行了性能比较。实验结果表明,所提出的算法在多项指标上均达到最优。