Ensemble feature selection with the simple Bayesian classification

A popular method for creating an accurate classifier from a set of training data is to build several classifiers, and then to combine their predictions. The ensembles of simple Bayesian classifiers have traditionally not been a focus of research. One way to generate an ensemble of accurate and diverse simple Bayesian classifiers is to use different feature subsets generated with the random subspace method. In this case, the ensemble consists of multiple classifiers constructed by randomly selecting feature subsets, that is, classifiers constructed in randomly chosen subspaces. In this paper, we present an algorithm for building ensembles of simple Bayesian classifiers in random subspaces. The EFS_SBC algorithm includes a hill-climbing-based refinement cycle, which tries to improve the accuracy and diversity of the base classifiers built on random feature subsets. We conduct a number of experiments on a collection of 21 real-world and synthetic data sets, comparing the EFS_SBC ensembles with the single simple Bayes, and with the boosted simple Bayes. In many cases the EFS_SBC ensembles have higher accuracy than the single simple Bayesian classifier, and than the boosted Bayesian ensemble. We find that the ensembles produced focusing on diversity have lower generalization error, and that the degree of importance of diversity in building the ensembles is different for different data sets. We propose several methods for the integration of simple Bayesian classifiers in the ensembles. In a number of cases the techniques for dynamic integration of classifiers have significantly better classification accuracy than their simple static analogues. We suggest that a reason for that is that the dynamic integration better utilizes the ensemble coverage than the static integration.     

Diversity-based combination of non-parametric classifiers for EMG signal decomposition

Non-parametric classification procedures based on a certainty measure and nearest neighbour rule for motor unit potential classification (MUP) during electromyographic (EMG) signal decomposition were explored. A diversity-based classifier fusion approach is developed and evaluated to achieve improved classification performance. The developed system allows the construction of a set of non-parametric base classifiers and then automatically chooses, from the pool of base classifiers, subsets of classifiers to form candidate classifier ensembles. The system selects the classifier ensemble members by exploiting a diversity measure for selecting classifier teams. The kappa statistic is used as the diversity measure to estimate the level of agreement between base classifier outputs, i.e., to measure the degree of decision similarity between base classifiers. The pool of base classifiers consists of two kinds of classifiers: adaptive certainty-based classifiers (ACCs) and adaptive fuzzy k-NN classifiers (AFNNCs) and both utilize different types of features. Once the patterns are assigned to their classes, by the classifier fusion system, firing pattern consistency statistics for each class are calculated to detect classification errors in an adaptive fashion. Performance of the developed system was evaluated using real and simulated EMG signals and was compared with the performance of the constituent base classifiers and the performance of the fixed ensemble containing the full set of base classifiers. Across the EMG signal data sets used, the diversity-based classifier fusion approach had better average classification performance overall, especially in terms of reducing classification errors.     

Ensemble component selection for improving ICA based microarray data prediction models

Independent component analysis (ICA) has been widely used to tackle the microarray dataset classification problem, but there still exists an unsolved problem that the independent component (IC) sets may not be reproducible after different ICA transformations. Inspired by the idea of ensemble feature selection, we design an ICA based ensemble learning system to fully utilize the difference among different IC sets. In this system, some IC sets are generated by different ICA transformations firstly. A multi-objective genetic algorithm (MOGA) is designed to select different biologically significant IC subsets from these IC sets, which are then applied to build base classifiers. Three schemes are used to fuse these base classifiers. The first fusion scheme is to combine all individuals in the final generation of the MOGA. In addition, in the evolution, we design a global-recording technique to record the best IC subsets of each IC set in a global-recording list. Then the IC subsets in the list are deployed to build base classifier so as to implement the second fusion scheme. Furthermore, by pruning about half of less accurate base classifiers obtained by the second scheme, a compact and more accurate ensemble system is built, which is regarded as the third fusion scheme. Three microarray datasets are used to test the ensemble systems, and the corresponding results demonstrate that these ensemble schemes can further improve the performance of the ICA based classification model, and the third fusion scheme leads to the most accurate ensemble system with the smallest ensemble size.     

基于特征选择的集成分类器抗噪性能分析

特征选择有助于增强集成分类器成员间的随机差异性,从而提高泛化精度。研究了随机子空间法（RandomSub-space）和旋转森林法（RotationForest）两种基于特征选择的集成分类器构造算法,分析讨论了两算法特征选择的方式与随机差异程度之间的关系。通过对UCI数据集引入噪声,比较两者在噪声环境下的分类精度。实验结果表明：当噪声增加及特征关联度下降时,基本学习算法及噪声程度对集成效果均有影响,当噪声增强到一定程度后。集成效果和单分类器的性能趋于一致。     

Diversity in search strategies for ensemble feature selection

Ensembles of learnt models constitute one of the main current directions in machine learning and data mining. Ensembles allow us to achieve higher accuracy, which is often not achievable with single models. It was shown theoretically and experimentally that in order for an ensemble to be effective, it should consist of base classifiers that have diversity in their predictions. One technique, which proved to be effective for constructing an ensemble of diverse base classifiers, is the use of different feature subsets, or so-called ensemble feature selection. Many ensemble feature selection strategies incorporate diversity as an objective in the search for the best collection of feature subsets. A number of ways are known to quantify diversity in ensembles of classifiers, and little research has been done about their appropriateness to ensemble feature selection. In this paper, we compare five measures of diversity with regard to their possible use in ensemble feature selection. We conduct experiments on 21 data sets from the UCI machine learning repository, comparing the ensemble accuracy and other characteristics for the ensembles built with ensemble feature selection based on the considered measures of diversity. We consider four search strategies for ensemble feature selection together with the simple random subspacing: genetic search, hill-climbing, and ensemble forward and backward sequential selection. In the experiments, we show that, in some cases, the ensemble feature selection process can be sensitive to the choice of the diversity measure, and that the question of the superiority of a particular measure depends on the context of the use of diversity and on the data being processed. In many cases and on average, the plain disagreement measure is the best. Genetic search, kappa, and dynamic voting with selection form the best combination of a search strategy, diversity measure and integration method.     

Rotation forest: A new classifier ensemble method

We propose a method for generating classifier ensembles based on feature extraction. To create the training data for a base classifier, the feature set is randomly split into K subsets (K is a parameter of the algorithm) and Principal Component Analysis (PCA) is applied to each subset. All principal components are retained in order to preserve the variability information in the data. Thus, K axis rotations take place to form the new features for a base classifier. The idea of the rotation approach is to encourage simultaneously individual accuracy and diversity within the ensemble. Diversity is promoted through the feature extraction for each base classifier. Decision trees were chosen here because they are sensitive to rotation of the feature axes, hence the name "forest.” Accuracy is sought by keeping all principal components and also using the whole data set to train each base classifier. Using WEKA, we examined the Rotation Forest ensemble on a random selection of 33 benchmark data sets from the UCI repository and compared it with Bagging, AdaBoost, and Random Forest. The results were favorable to Rotation Forest and prompted an investigation into diversity-accuracy landscape of the ensemble models. Diversity-error diagrams revealed that Rotation Forest ensembles construct individual classifiers which are more accurate than these in AdaBoost and Random Forest, and more diverse than these in Bagging, sometimes more accurate as well.     

Financial distress prediction using support vector machines: Ensemble vs. individual

Financial distress prediction (FDP) is of great importance to both inner and outside parts of companies. Though lots of literatures have given comprehensive analysis on single classifier FDP method, ensemble method for FDP just emerged in recent years and needs to be further studied. Support vector machine (SVM) shows promising performance in FDP when compared with other single classifier methods. The contribution of this paper is to propose a new FDP method based on SVM ensemble, whose candidate single classifiers are trained by SVM algorithms with different kernel functions on different feature subsets of one initial dataset. SVM kernels such as linear, polynomial, RBF and sigmoid, and the filter feature selection/extraction methods of stepwise multi discriminant analysis (MDA), stepwise logistic regression (logit), and principal component analysis (PCA) are applied. The algorithm for selecting SVM ensemble's base classifiers from candidate ones is designed by considering both individual performance and diversity analysis. Weighted majority voting based on base classifiers’ cross validation accuracy on training dataset is used as the combination mechanism. Experimental results indicate that SVM ensemble is significantly superior to individual SVM classifier when the number of base classifiers in SVM ensemble is properly set. Besides, it also shows that RBF SVM based on features selected by stepwise MDA is a good choice for FDP when individual SVM classifier is applied.     

Input decimated ensembles

Using an ensemble of classifiers instead of a single classifier has been shown to improve generalization performance in many pattern recognition problems. However, the extent of such improvement depends greatly on the amount of correlation among the errors of the base classifiers. Therefore, reducing those correlations while keeping the classifiers’ performance levels high is an important area of research. In this article, we explore Input Decimation (ID), a method which selects feature subsets for their ability to discriminate among the classes and uses these subsets to decouple the base classifiers. We provide a summary of the theoretical benefits of correlation reduction, along with results of our method on two underwater sonar data sets, three benchmarks from the Probenl/UCI repositories, and two synthetic data sets. The results indicate that input decimated ensembles outperform ensembles whose base classifiers use all the input features; randomly selected subsets of features; and features created using principal components analysis, on a wide range of domains. ID="A1"Correspondance and offprint requests to: Kagan Tumer, NASA Ames Research Center, Moffett Field, CA, USA     

一种基于旋转森林的集成协同训练算法

集成协同训练算法（ensemble co-training）是将集成学习（ensemble learning）和协同训练算法（co-training）相结合的半监督学习方法,旋转森林（rotation forest）是利用特征提取来构造基分类器差异性的集成学习方法,在对现有的集成协同训练算法研究基础上,提出了基于旋转森林的协同训练算法——ROFCO,该方法重在利用未标记数据提高基分类器之间的差异性和特征提取效果,使基分类器的泛化误差保持不变或下降的同时,能保持甚至提高基分类器之间的差异性,提高集成效果。实验结果表明该方法能取得较好效果。     

The effects of combining classifiers with the same training statistics using Bayesian decision rules

Multiple classifier systems (MCS) are attracting increasing interest in the field of pattern recognition and machine learning. Recently, MCS are also being introduced in the remote sensing field where the importance of classifier diversity for image classification problems has not been examined. In this article, Satellite Pour l'Observation de la Terre (SPOT) IV panchromatic and multispectral satellite images are classified into six land cover classes using five base classifiers: contextual classifier, k-nearest neighbour classifier, Mahalanobis classifier, maximum likelihood classifier and minimum distance classifier. The five base classifiers are trained with the same feature sets throughout the experiments and a posteriori probability, derived from the confusion matrix of these base classifiers, is applied to five Bayesian decision rules (product rule, sum rule, maximum rule, minimum rule and median rule) for constructing different combinations of classifier ensembles. The performance of these classifier ensembles is evaluated for overall accuracy and kappa statistics. Three statistical tests, the McNemar's test, the Cochran's Q test and the Looney's F-test, are used to examine the diversity of the classification results of the base classifiers compared to the results of the classifier ensembles. The experimental comparison reveals that (a) significant diversity amongst the base classifiers cannot enhance the performance of classifier ensembles; (b) accuracy improvement of classifier ensembles can only be found by using base classifiers with similar and low accuracy; (c) increasing the number of base classifiers cannot improve the overall accuracy of the MCS and (d) none of the Bayesian decision rules outperforms the others.     

Ensemble classification based on supervised clustering for credit scoring

Credit scoring aims to assess the risk associated with lending to individual consumers. Recently, ensemble classification methodology has become popular in this field. However, most researches utilize random sampling to generate training subsets for constructing the base classifiers. Therefore, their diversity is not guaranteed, which may lead to a degradation of overall classification performance. In this paper, we propose an ensemble classification approach based on supervised clustering for credit scoring. In the proposed approach, supervised clustering is employed to partition the data samples of each class into a number of clusters. Clusters from different classes are then pairwise combined to form a number of training subsets. In each training subset, a specific base classifier is constructed. For a sample whose class label needs to be predicted, the outputs of these base classifiers are combined by weighted voting. The weight associated with a base classifier is determined by its classification performance in the neighborhood of the sample. In the experimental study, two benchmark credit data sets are adopted for performance evaluation, and an industrial case study is conducted. The results show that compared to other ensemble classification methods, the proposed approach is able to generate base classifiers with higher diversity and local accuracy, and improve the accuracy of credit scoring.     

EUSBoost: Enhancing ensembles for highly imbalanced data-sets by evolutionary undersampling

Classification with imbalanced data-sets has become one of the most challenging problems in Data Mining. Being one class much more represented than the other produces undesirable effects in both the learning and classification processes, mainly regarding the minority class. Such a problem needs accurate tools to be undertaken; lately, ensembles of classifiers have emerged as a possible solution. Among ensemble proposals, the combination of Bagging and Boosting with preprocessing techniques has proved its ability to enhance the classification of the minority class.In this paper, we develop a new ensemble construction algorithm (EUSBoost) based on RUSBoost, one of the simplest and most accurate ensemble, which combines random undersampling with Boosting algorithm. Our methodology aims to improve the existing proposals enhancing the performance of the base classifiers by the usage of the evolutionary undersampling approach. Besides, we promote diversity favoring the usage of different subsets of majority class instances to train each base classifier. Centered on two-class highly imbalanced problems, we will prove, supported by the proper statistical analysis, that EUSBoost is able to outperform the state-of-the-art methods based on ensembles. We will also analyze its advantages using kappa-error diagrams, which we adapt to the imbalanced scenario.     

Improvements in image categorization using codebook ensembles

The problem of object category classification by committees or ensembles of classifiers, each of which is based on one diverse codebook, is addressed in this paper. Two methods of constructing visual codebook ensembles are proposed in this study. The first technique introduces diverse individual visual codebooks using different clustering algorithms. The second uses various visual codebooks of different sizes for constructing an ensemble with high diversity. Codebook ensembles are trained to capture and convey image properties from different aspects. Based on these codebook ensembles, different types of image representations can be acquired. A classifier ensemble can be trained based on different expression datasets from the same training image set. The use of a classifier ensemble to categorize new images can lead to improved performance. Detailed experimental analysis on a Pascal VOC challenge dataset reveals that the present ensemble approach performs well, consistently improves the performance of visual object classifiers, and results in state-of-the-art performance in categorization.     

A hybrid classifier committee for analysing asymmetry features in breast thermograms

Breast cancer is the most commonly occurring form of cancer in women. While mammography is the standard modality for diagnosis, thermal imaging provides an interesting alternative as it can identify tumors of smaller size and hence lead to earlier detection. In this paper, we present an approach to analysing breast thermograms based on image features and a hybrid multiple classifier system. The employed image features provide indications of asymmetry between left and right breast regions that are encountered when a tumor is locally recruiting blood vessels on one side, leading to a change in the captured temperature distribution. The presented multiple classifier system is based on a hybridisation of three computational intelligence techniques: neural networks or support vector machines as base classifiers, a neural fuser to combine the individual classifiers, and a fuzzy measure for assessing the diversity of the ensemble and removal of individual classifiers from the ensemble. In addition, we address the problem of class imbalance that often occurs in medical data analysis, by training base classifiers on balanced object subspaces. Our experimental evaluation, on a large dataset of about 150 breast thermograms, convincingly shows our approach not only to provide excellent classification accuracy and sensitivity but also to outperform both canonical classification approaches as well as other classifier ensembles designed for imbalanced datasets.     

基于聚类与排序修剪的分类器集成方法*

为了提高分类器集成性能,提出了一种基于聚类算法与排序修剪结合的分类器集成方法。首先将混淆矩阵作为量化基分类器间差异度的工具,通过聚类将分类器划分为若干子集;然后提出一种排序修剪算法,以距离聚类中心最近的分类器为起点,根据分类器的距离对差异度矩阵动态加权,以加权差异度作为排序标准对子集中的分类器进行按比例修剪;最后使用投票法对选出的基分类器进行集成。同时与多种集成方法在UCI数据库中的10组数据集上进行对比与分析,实验结果表明基于聚类与排序修剪的分类器选择方法有效提升了集成系统的分类能力。     

A variant of Rotation Forest for constructing ensemble classifiers

Rotation Forest, an effective ensemble classifier generation technique, works by using principal component analysis (PCA) to rotate the original feature axes so that different training sets for learning base classifiers can be formed. This paper presents a variant of Rotation Forest, which can be viewed as a combination of Bagging and Rotation Forest. Bagging is used here to inject more randomness into Rotation Forest in order to increase the diversity among the ensemble membership. The experiments conducted with 33 benchmark classification data sets available from the UCI repository, among which a classification tree is adopted as the base learning algorithm, demonstrate that the proposed method generally produces ensemble classifiers with lower error than Bagging, AdaBoost and Rotation Forest. The bias–variance analysis of error performance shows that the proposed method improves the prediction error of a single classifier by reducing much more variance term than the other considered ensemble procedures. Furthermore, the results computed on the data sets with artificial classification noise indicate that the new method is more robust to noise and kappa-error diagrams are employed to investigate the diversity–accuracy patterns of the ensemble classifiers.     

Classifier ensemble construction with rotation forest to improve medical diagnosis performance of machine learning algorithms

Improving accuracies of machine learning algorithms is vital in designing high performance computer-aided diagnosis (CADx) systems. Researches have shown that a base classifier performance might be enhanced by ensemble classification strategies. In this study, we construct rotation forest (RF) ensemble classifiers of 30 machine learning algorithms to evaluate their classification performances using Parkinson's, diabetes and heart diseases from literature.While making experiments, first the feature dimension of three datasets is reduced using correlation based feature selection (CFS) algorithm. Second, classification performances of 30 machine learning algorithms are calculated for three datasets. Third, 30 classifier ensembles are constructed based on RF algorithm to assess performances of respective classifiers with the same disease data. All the experiments are carried out with leave-one-out validation strategy and the performances of the 60 algorithms are evaluated using three metrics; classification accuracy (ACC), kappa error (KE) and area under the receiver operating characteristic (ROC) curve (AUC).Base classifiers succeeded 72.15%, 77.52% and 84.43% average accuracies for diabetes, heart and Parkinson's datasets, respectively. As for RF classifier ensembles, they produced average accuracies of 74.47%, 80.49% and 87.13% for respective diseases.RF, a newly proposed classifier ensemble algorithm, might be used to improve accuracy of miscellaneous machine learning algorithms to design advanced CADx systems.     

Attribute bagging: improving accuracy of classifier ensembles by using random feature subsets

We present attribute bagging (AB), a technique for improving the accuracy and stability of classifier ensembles induced using random subsets of features. AB is a wrapper method that can be used with any learning algorithm. It establishes an appropriate attribute subset size and then randomly selects subsets of features, creating projections of the training set on which the ensemble classifiers are built. The induced classifiers are then used for voting. This article compares the performance of our AB method with bagging and other algorithms on a hand-pose recognition dataset. It is shown that AB gives consistently better results than bagging, both in accuracy and stability. The performance of ensemble voting in bagging and the AB method as a function of the attribute subset size and the number of voters for both weighted and unweighted voting is tested and discussed. We also demonstrate that ranking the attribute subsets by their classification accuracy and voting using only the best subsets further improves the resulting performance of the ensemble.     

Structural diversity for decision tree ensemble learning

Decision trees are a kind of off-the-shelf predictive models, and they have been successfully used as the base learners in ensemble learning. To construct a strong classifier ensemble, the individual classifiers should be accurate and diverse. However, diversity measure remains a mystery although there were many attempts. We conjecture that a deficiency of previous diversity measures lies in the fact that they consider only behavioral diversity, i.e., how the classifiers behave when making predictions, neglecting the fact that classifiers may be potentially different even when they make the same predictions. Based on this recognition, in this paper, we advocate to consider structural diversity in addition to behavioral diversity, and propose the TMD (tree matching diversity) measure for decision trees. To investigate the usefulness of TMD, we empirically evaluate performances of selective ensemble approaches with decision forests by incorporating different diversity measures. Our results validate that by considering structural and behavioral diversities together, stronger ensembles can be constructed. This may raise a new direction to design better diversity measures and ensemble methods.     

使用PCA建立基于规则的组合分类器

提出了一种使用基于规则的基分类器建立组合分类器的新方法PCARules。尽管新方法也采用基分类器预测的加权投票来决定待分类样本的类,但是为基分类器创建训练数据集的方法与bagging和boosting完全不同。该方法不是通过抽样为基分类器创建数据集,而是随机地将特征划分成K个子集,使用PCA得到每个子集的主成分,形成新的特征空间,并将所有训练数据映射到新的特征空间作为基分类器的训练集。在UCI机器学习库的30个随机选取的数据集上的实验表明:算法不仅能够显著提高基于规则的分类方法的分类性能,而且与bagging和boosting等传统组合方法相比,在大部分数据集上都具有更高的分类准确率。