NMC: nearest matrix classification – A new combination model for pruning One-vs-One ensembles by transforming the aggregation problem

The One-vs-One strategy is among the most used techniques to deal with multi-class problems in Machine Learning. This way, any binary classifier can be used to address the original problem, since one classifier is learned for each possible pair of classes. As in every ensemble method, classifier combination becomes a vital step in the classification process. Even though many combination models have been developed in the literature, none of them have dealt with the possibility of reducing the number of generated classifiers after the training phase, i.e., ensemble pruning, since every classifier is supposed to be necessary.On this account, our objective in this paper is two-fold: (1) We propose a transformation of the aggregation step, which lead us to a new combination strategy where instances are classified on the basis of the similarities among score-matrices. (2) This fact allows us to introduce the possibility of reducing the number of binary classifiers without affecting the final accuracy. We will show that around 50% of classifiers can be removed (depending on the base learner and the specific problem) and that the confidence degrees obtained by these base classifiers have a strong influence on the improvement in the final accuracy.A thorough experimental study is carried out in order to show the behavior of the proposed approach in comparison with the state-of-the-art combination models in the One-vs-One strategy. Different classifiers from various Machine Learning paradigms are considered as base classifiers and the results obtained are contrasted with the proper statistical analysis.     

Dynamic classifier selection for One-vs-One strategy: Avoiding non-competent classifiers

The One-vs-One strategy is one of the most commonly used decomposition technique to overcome multi-class classification problems; this way, multi-class problems are divided into easier-to-solve binary classification problems considering pairs of classes from the original problem, which are then learned by independent base classifiers.The way of performing the division produces the so-called non-competence. This problem occurs whenever an instance is classified, since it is submitted to all the base classifiers although the outputs of some of them are not meaningful (they were not trained using the instances from the class of the instance to be classified). This issue may lead to erroneous classifications, because in spite of their incompetence, all classifiers' decisions are usually considered in the aggregation phase.In this paper, we propose a dynamic classifier selection strategy for One-vs-One scheme that tries to avoid the non-competent classifiers when their output is probably not of interest. We consider the neighborhood of each instance to decide whether a classifier may be competent or not. In order to verify the validity of the proposed method, we will carry out a thorough experimental study considering different base classifiers and comparing our proposal with the best performer state-of-the-art aggregation within each base classifier from the five Machine Learning paradigms selected. The findings drawn from the empirical analysis are supported by the appropriate statistical analysis.     

Cost-Sensitive back-propagation neural networks with binarization techniques in addressing multi-class problems and non-competent classifiers

Multi-class classification problems can be addressed by using decomposition strategy. One of the most popular decomposition techniques is the One-vs-One (OVO) strategy, which consists of dividing multi-class classification problems into as many as possible pairs of easier-to-solve binary sub-problems. To discuss the presence of classes with different cost, in this paper, we examine the behavior of an ensemble of Cost-Sensitive Back-Propagation Neural Networks (CSBPNN) with OVO binarization techniques for multi-class problems. To implement this, the original multi-class cost-sensitive problem is decomposed into as many sub-problems as possible pairs of classes and each sub-problem is learnt in an independent manner using CSBPNN. Then a combination method is used to aggregate the binary cost-sensitive classifiers. To verify the synergy of the binarization technique and CSBPNN for multi-class cost-sensitive problems, we carry out a thorough experimental study. Specifically, we first develop the study to check the effectiveness of the OVO strategy for multi-class cost-sensitive learning problems. Then, we develop a comparison of several well-known aggregation strategies in our scenario. Finally, we explore whether further improvement can be achieved by using the management of non-competent classifiers. The experimental study is performed with three types of cost matrices and proper statistical analysis is employed to extract the meaningful findings.     

基于分解策略处理多分类不均衡问题的方法

针对多分类不均衡问题,提出了一种新的基于一对一（one-versus-one,OVO）分解策略的方法。首先基于OVO分解策略将多分类不均衡问题分解成多个二值分类问题;再利用处理不均衡二值分类问题的算法建立二值分类器;接着利用SMOTE过抽样技术处理原始数据集;然后采用基于距离相对竞争力加权方法处理冗余分类器;最后通过加权投票法获得输出结果。在KEEL不均衡数据集上的大量实验结果表明,所提算法比其他经典方法具有显著的优势。     

Analyzing the presence of noise in multi-class problems: alleviating its influence with the One-vs-One decomposition

The presence of noise in data is a common problem that produces several negative consequences in classification problems. In multi-class problems, these consequences are aggravated in terms of accuracy, building time, and complexity of the classifiers. In these cases, an interesting approach to reduce the effect of noise is to decompose the problem into several binary subproblems, reducing the complexity and, consequently, dividing the effects caused by noise into each of these subproblems. This paper analyzes the usage of decomposition strategies, and more specifically the One-vs-One scheme, to deal with noisy multi-class datasets. In order to investigate whether the decomposition is able to reduce the effect of noise or not, a large number of datasets are created introducing different levels and types of noise, as suggested in the literature. Several well-known classification algorithms, with or without decomposition, are trained on them in order to check when decomposition is advantageous. The results obtained show that methods using the One-vs-One strategy lead to better performances and more robust classifiers when dealing with noisy data, especially with the most disruptive noise schemes.     

Combining binary classifiers in different dichotomy spaces for text categorization

Several supervised machine learning applications are commonly represented as multi-class problems, but it is harder to distinguish several classes rather than just two classes. In contrast to the approaches one-against-all and all-pairs that transform a multi-class problem into a set of binary problems, Dichotomy Transformation (DT) converts a multi-class problem into a different problem where the goal is to verify if a pair of documents belongs to the same class or not. To perform this task, DT generates a dichotomy set obtained by combining a pair of documents, each belongs to either a positive class (documents in the pair that have the same class) or a negative class (documents in the pair that come from different classes). The definition of this dichotomy set plays an important role in the overall accuracy of the system. So, an alternative to avoid searching for the best dichotomy set is using multiple classifier systems because we can have many different sets where each one is used to train one binary classifier instead of having only one dichotomy set. Herein we propose Combined Dichotomy Transformations (CoDiT), a Text Categorization system that combines binary classifiers that are trained with different dichotomy sets using DT. By using DT, the number of training examples increases exponentially when compared with the original training set. This is a desirable property because each classifier can be trained with different data without reducing the number of examples or features. Therefore, it is possible to compose an ensemble with diverse and strong classifiers. Experiments using 14 databases show that CoDiT achieves statistically better results in comparison to SVM, Bagging, Random Subspace, BoosTexter, and Random Forest.     

Subclass problem-dependent design for error-correcting output codes

A common way to model multi-class classification problems is by means of Error-Correcting Output Codes (ECOC). Given a multi-class problem, the ECOC technique designs a code word for each class, where each position of the code identifies the membership of the class for a given binary problem. A classification decision is obtained by assigning the label of the class with the closest code. One of the main requirements of the ECOC design is that the base classifier is capable of splitting each sub-group of classes from each binary problem. However, we can not guarantee that a linear classifier model convex regions. Furthermore, non-linear classifiers also fail to manage some type of surfaces. In this paper, we present a novel strategy to model multi-class classification problems using sub-class information in the ECOC framework. Complex problems are solved by splitting the original set of classes into sub-classes, and embedding the binary problems in a problem-dependent ECOC design. Experimental results show that the proposed splitting procedure yields a better performance when the class overlap or the distribution of the training objects conceil the decision boundaries for the base classifier. The results are even more significant when one has a sufficiently large training size.     

A multi-class classification strategy for Fisher scores: Application to signer independent sign language recognition

Fisher kernels combine the powers of discriminative and generative classifiers by mapping the variable-length sequences to a new fixed length feature space, called the Fisher score space. The mapping is based on a single generative model and the classifier is intrinsically binary. We propose a multi-class classification strategy that applies a multi-class classification on each Fisher score space and combines the decisions of multi-class classifiers. We experimentally show that the Fisher scores of one class provide discriminative information for the other classes as well. We compare several multi-class classification strategies for Fisher scores generated from the hidden Markov models of sign sequences. The proposed multi-class classification strategy increases the classification accuracy in comparison with the state of the art strategies based on combining binary classifiers. To reduce the computational complexity of the Fisher score extraction and the training phases, we also propose a score space selection method and show that, similar or even higher accuracies can be obtained by using only a subset of the score spaces. Based on the proposed score space selection method, a signer adaptation technique is also presented that does not require any re-training.     

多分类问题代价敏感AdaBoost算法

针对目前多分类代价敏感分类问题在转换成二分类代价敏感分类问题存在的代价合并问题, 研究并构造出了可直接应用于多分类问题的代价敏感AdaBoost算法.算法具有与连续AdaBoost算法 类似的流程和误差估计. 当代价完全相等时, 该算法就变成了一种新的多分类的连续AdaBoost算法, 算法能够确保训练错误率随着训练的分类器的个数增加而降低, 但不直接要求各个分类器相互独立条件, 或者说独立性条件可以通过算法规则来保证, 但现有多分类连续AdaBoost算法的推导必须要求各个分类器相互独立. 实验数据表明, 算法可以真正实现分类结果偏向错分代价较小的类, 特别当每一类被错分成其他类的代价不平衡但平均代价相等时, 目前已有的多分类代价敏感学习算法会失效, 但新方法仍然能 实现最小的错分代价. 研究方法为进一步研究集成学习算法提供了一种新的思路, 得到了一种易操作并近似满足分类错误率最小的多标签分类问题的AdaBoost算法.     

一种新的多类支持向量机决策方法及其应用

讨论和比较了现有的几种多类SVM方法．在此基础上,提出了一种组合多个两类分类器结果的多类SVM决策方法．在该方法中,定义了新的决策函数,其值是在传统投票决策值的基础上乘以不同分类器的权重．新的多类SVM在一定程度上解决了传统投票决策方法的不可分区域问题,因此具有更好的分类性能．最后,将新方法作为关键技术应用于故障诊断实例,实际诊断结果证明了所提多类SVM决策方法的优越性．     

A simple and fast multi-class piecewise linear pattern classifier

A simple and fast multi-class piecewise linear classifier is proposed and implemented. For a pair of classes, the piecewise linear boundary is a collection of segments of hyperplanes created as perpendicular bisectors of line segments linking centroids of the classes or parts of classes. For a multi-class problem, a binary partition tree is initially created which represents a hierarchical division of given pattern classes into groups, with each non-leaf node corresponding to some group. After that, a piecewise linear boundary is constructed for each non-leaf node of the partition tree as for a two-class problem. The resulting piecewise linear boundary is a set of boundaries corresponding to all non-leaf nodes of the tree. The basic data structures of algorithms of synthesis of a piecewise linear classifier and classification of unknown patterns are described. The proposed classifier is compared with a number of known pattern classifiers by benchmarking with the use of real-world data sets.     

Tight risk bounds for multi-class margin classifiers

We consider a problem of risk estimation for large-margin multi-class classifiers. We propose a novel risk bound for the multi-class classification problem. The bound involves the marginal distribution of the classifier and the Rademacher complexity of the hypothesis class. We prove that our bound is tight in the number of classes. Finally, we compare our bound with the related ones and provide a simplified version of the bound for the multi-class classification with kernel based hypotheses.     

Hierarchical classification method based on selective learning of slacked hierarchy for activity recognition systems

Physical activity recognition using wearable sensors has gained significant interest from researchers working in the field of ambient intelligence and human behavior analysis. The problem of multi-class classification is an important issue in the applications which naturally has more than two classes. A well-known strategy to convert a multi-class classification problem into binary sub-problems is the error-correcting output coding (ECOC) method. Since existing methods use a single classifier with ECOC without considering the dependency among multiple classifiers, it often fails to generalize the performance and parameters in a real-life application, where different numbers of devices, sensors and sampling rates are used. To address this problem, we propose a unique hierarchical classification model based on the combination of two base binary classifiers using selective learning of slacked hierarchy and integrating the training of binary classifiers into a unified objective function. Our method maps the multi-class classification problem to multi-level classification. A multi-tier voting scheme has been introduced to provide a final classification label at each level of the solicited model. The proposed method is evaluated on two publicly available datasets and compared with independent base classifiers. Furthermore, it has also been tested on real-life sensor readings for 3 different subjects to recognize four activities i.e. Walking, Standing, Jogging and Sitting. The presented method uses same hierarchical levels and parameters to achieve better performance on all three datasets having different number of devices, sensors and sampling rates. The average accuracies on publicly available dataset and real-life sensor readings were recorded to be 95% and 85%, respectively. The experimental results validate the effectiveness and generality of the proposed method in terms of performance and parameters.     

Binary tree versus single level tree classification of white blood cells

For the problem of white blood cell recognition, the use of various binary tree classification schemes is compared with the application of single tree classifiers.

In principle, in a multi-class problem, binary tree classifiers have the advantage that only a restricted number of features per branch point is needed, enabling an economical design of the classification process, taking into account prior probabilities for all classes.

While these reasons remain valid, the results presented here show that binary tree classifiers do not necessarily improve the correct recognition rate.     

多子域隔离学习组合决策用于不均衡样本

为进一步弱化数据不均衡对分类算法的束缚,从数据集区域分布特性着手,提出了不均衡数据集上基于子域学习的复合分类模型。子域划分阶段,扩展支持向量数据描述（SVDD）算法给出类的最小界定域,划分出域内密集区与域外稀疏区。借鉴不同类存在相似样本的类重叠概念,对边界样本进行搜索,组合构成重叠域。子域清理阶段,基于邻近算法（KNN）的邻近性假设,结合不同域的密疏程度,设置样本有效性参数,对域内样本逐个检测以清理噪声。各子域隔离参与分类建模,按序组合产生出用于不均衡数据集的复合分类器CCRD。在相似算法对比以及代价敏感MetaCost对比中,CCRD对正类的正确分类改善明显,且未加重负类误判;在SMOTE抽样比较中,CCRD改善了负类的误判情形,且未影响正类的正确分类;在五类数据集的逐个比较中,CCRD分类性能均有提升,在Haberman_sur的正类分类性能提升上尤为明显。结果表明,基于子域学习的复合分类模型的分类性能较好,是一种研究不均衡数据集的较有效的方法。     

面向文本分类的混淆类判别技术

分析了文本分类过程中存在的混淆类现象,主要研究混淆类的判别技术,进而改善文本分类的性能.首先,提出了一种基于分类错误分布的混淆类识别技术,识别预定义类别中的混淆类集合.为了有效判别混淆类,提出了一种基于判别能力的特征选取技术,通过评价某一特征对类别之间的判别能力实现特征选取.最后,通过基于两阶段的分类器设计框架,将初始分类器和混淆类分类器进行集成,组合了两个阶段的分类结果作为最后输出.混淆类分类器的激活条件是:当测试文本被初始分类器标注为混淆类类别时,即采用混淆类分类器进行重新判别.在比较实验中采用了Newsgroup和863中文评测语料,针对单标签、多类分类器.实验结果显示,该技术有效地改善了分类性能.     

一种LDA与SVM混合的多类分类方法

针对决策有向无环图支持向量机（ＤＤＡＧＳＶＭ）需训练大量支持向量机（ＳＶＭ）和误差积累的问题,提出一种线性判别分析（ＬＤＡ）与ＳＶＭ 混合的多类分类算法．首先根据高维样本在低维空间中投影的特点,给出一种优化ＬＤＡ 分类阈值;然后以优化ＬＤＡ 对每个二类问题的分类误差作为类间线性可分度,对线性可分度较低的问题采用非线性ＳＶＭ 加以解决,并以分类误差作为对应二类问题的可分度;最后将可分度作为混合ＤＤＡＧ 分类器的决策依据．实验表明,与ＤＤＡＧＳＶＭ 相比,所提出算法在确保泛化精度的条件下具有更高的训练和分类速度．     

Multidimensional hierarchical classification

Hierarchical classification can be seen as a multidimensional classification problem where the objective is to predict a class, or set of classes, according to a taxonomy. There have been different proposals for hierarchical classification, including local and global approaches. Local approaches can suffer from the inconsistency problem, that is, if a local classifier has a wrong prediction, the error propagates down the hierarchy. Global approaches tend to produce more complex models. In this paper, we propose an alternative approach inspired in multidimensional classification. It starts by building a multi-class classifier per each parent node in the hierarchy. In the classification phase, all the local classifiers are applied simultaneously to each instance, providing a probability for each class in the taxonomy. Then the probability of the subset of classes, for each path in the hierarchy, is obtained by combining the local classifiers results. The path with highest probability is returned as the result for all the levels in the hierarchy. As an extension of the proposal method, we also developed a new technique, based on information gain, to classifies at different levels in the hierarchy. The proposed method was tested on different hierarchical classification data sets and was compared against state-of-the-art methods, resulting in superior predictive performance and/or efficiency to the other approaches in all the datasets.     

Learning Bayesian network classifiers from label proportions

This paper deals with a classification problem known as learning from label proportions. The provided dataset is composed of unlabeled instances and is divided into disjoint groups. General class information is given within the groups: the proportion of instances of the group that belong to each class.We have developed a method based on the Structural EM strategy that learns Bayesian network classifiers to deal with the exposed problem. Four versions of our proposal are evaluated on synthetic data, and compared with state-of-the-art approaches on real datasets from public repositories. The results obtained show a competitive behavior for the proposed algorithm.     

One versus one multi-class classification fusion using optimizing decision directed acyclic graph for predicting listing status of companies

Most existing research has demonstrated the success of different decomposition and ensemble strategies for solving multi-class classification problems. This study proposes a new ensemble strategy for One-vs-One (OVO) scheme that uses optimizing decision directed acyclic graph (ODDAG) whose structure is determined by maximizing the fitness on the training set instead of by predefined rules. It makes an attempt to reduce the effect of non-competent classifiers in OVO scheme like decision directed acyclic graph (DDAG) but in another way. We test the proposed method on some public data sets and compare it to some other widely used methods to select the proper candidates and related settings for a problem with practical concern from financial industry in China, i.e. the prediction of listing status of companies. The experimental result shows that our model can outperform the benchmarked methods on this real problem. In addition, the ODDAG combined with decision tree is a white box model whose internal rules can be viewed and checked by decision makers.