Comparing Combination Rules of Pairwise Neural Networks Classifiers

A decomposition approach to multiclass classification problems consists in decomposing a multiclass problem into a set of binary ones. Decomposition splits the complete multiclass problem into a set of smaller classification problems involving only two classes (binary classification: dichotomies). With a decomposition, one has to define a recombination which recomposes the outputs of the dichotomizers in order to solve the original multiclass problem. There are several approaches to the decomposition, the most famous ones being one-against-all and one-against-one also called pairwise. In this paper, we focus on pairwise decomposition approach to multiclass classification with neural networks as the base learner for the dichotomies. We are primarily interested in the different possible ways to perform the so-called recombination (or decoding). We review standard methods used to decode the decomposition generated by a one-against-one approach. New decoding methods are proposed and compared to standard methods. A stacking decoding is also proposed which consists in replacing the whole decoding or a part of it by a trainable classifier to arbiter among the conflicting predictions of the pairwise classifiers. Proposed methods try to cope with the main problem while using pairwise decomposition: the use of irrelevant classifiers. Substantial gain is obtained on all datasets used in the experiments. Based on the above, we provide future research directions which consider the recombination problem as an ensemble method.     

A decision based one-against-one method for multi-class support vector machine

The support vector machine (SVM) has a high generalisation ability to solve binary classification problems, but its extension to multi-class problems is still an ongoing research issue. Among the existing multi-class SVM methods, the one-against-one method is one of the most suitable methods for practical use. This paper presents a new multi-class SVM method that can reduce the number of hyperplanes of the one-against-one method and thus it returns fewer support vectors. The proposed algorithm works as follows. While producing the boundary of a class, no more hyperplanes are constructed if the discriminating hyperplanes of neighbouring classes happen to separate the rest of the classes. We present a large number of experiments that show that the training time of the proposed method is the least among the existing multi-class SVM methods. The experimental results also show that the testing time of the proposed method is less than that of the one-against-one method because of the reduction of hyperplanes and support vectors. The proposed method can resolve unclassifiable regions and alleviate the over-fitting problem in a much better way than the one-against-one method by reducing the number of hyperplanes. We also present a direct acyclic graph SVM (DAGSVM) based testing methodology that improves the testing time of the DAGSVM method.     

A new fast algorithm for multiclass hyperspectral image classification with SVM

The support vector machine (SVM) has been a dominant machine-learning technique in the last decade and has demonstrated its efficiency in many applications. Research on classification of hyperspectral images have shown the efficiency of this method to overcome the Hughes phenomenon for classification of such images. A major drawback of classification by SVM is that this classifier was originally developed to solve binary problems, and the algorithms for multiclass problems usually have a high-computational load. In this article, a new and fast method for multiclass problems is proposed. This method has two stages. In the first stage, samples are classified by a maximum likelihood (ML) classifier, and in the second stage, SVM selects the final label of a sample among high-probability classes for that sample by a tree structure. So, for each sample, only some classes must be searched by SVM to find its label. The uncertainty of ML classification for a sample is obtained by the entropy of probabilities, and the number of classes that must be searched by SVM for a sample is obtained based on the uncertainty of that sample in the primary ML classification. This approach is compared with two widely used multiclass algorithms: one-against-one (OAO) and directed acyclic graph (DAGSVM). The obtained results on real data from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) revealed less computational time and better accuracy compared to these multiclass algorithms.     

A Novel and Principled Multiclass Support Vector Machine

Support vector machines (SVMs) have been demonstrated very efficient for binary classification problems; however, computationally efficient and effective multiclass SVMs are still missing. Most existing multiclass SVM classifiers are constructed either by combining multiple binary SVM classifiers, which often perform moderately for some problems, or by converting multiclass problems into one single optimization problem, which is unfortunately computationally expensive. To address these issues, a novel and principled multiclass SVM based on geometric properties of hyperspheres, termed SVMGH, is proposed in this paper. Different from existing SVM‐based methods that seek a cutting hyperplane between two classes, SVMGH draws the discriminative information of each class by constructing a minimum hypersphere containing all class members, and then defines a label function based on the geometric properties of the minimum hyperspheres. We prove theoretically the geometric properties of the minimum hyperspheres to guarantee the validation of SVMGH. The computational efficiency is enhanced by a data reduction strategy as well as a fast training method. Experimental results demonstrate that the proposed SVMGH shows better performance and higher computational efficiency than the state of the art on multiclassification problems while maintaining comparable performance and efficiency on binary classification problems.     

一种新的支持向量机多类分类方法

分析了目前的支持向量机多类分类方法存在的问题以及缺点．针对以上问题及缺点，提出了基于二叉树的支持向量机的多类分类方法，并在UCI数据库上进行了验证，取得了良好效果．     

快速的支持向量机多类分类研究

研究了支持向量机多类算法DAGSVM（Direct Acyclic Graph SVM）的速度优势,提出了结合DAGSVM和简化支持向量技术的一种快速支持向量机多类分类方法。该方法一方面减少了一次分类所需的两类支持向量机的数量,另一方面减少了支持向量的数量。实验采用UCI和Statlog数据库的多类数据,并和四种多类方法进行比较,结果表明该方法能有效地加快分类速度。     

后验概率在多分类支持向量机上的应用

支持向量机是基于统计学习理论的一种新的分类规则挖掘方法。在已有多分类支持向量机基础上,首次提出了几何距离多分类支持向量分类器;随后,将二值支持向量机的后验概率输出也推广到多分类问题,避免了使用迭代算法,在快速预测的前提下提高了预测准确率。数值实验的结果表明,这两种方法都具有很好的推广性能,能明显提高分类器对未知样本的分类准确率。     

一种新的基于二叉树的SVM多类分类方法

介绍了几种常用的支持向量机多类分类方法,分析其存在的问题及缺点。提出了一种基于二叉树的支持向量机多类分类方法（BT SVM）,并将基于核的自组织映射引入进行聚类。结果表明,采用该方法进行多类分类比1 v r SVMs和1 v 1 SVMs具有更高的分类精度。     

基于混合粒子群算法的运动估计研究

针对块匹配运动估计算法中传统搜索方法的不足,提出了一种新的基于混合粒子群的块匹配运动估计算法。在保留系统随机搜索性能的同时根据运动矢量特性合理地设计初始搜索种群,并通过混沌差分进化搜索协同粒子群算法迭代寻优,混沌序列用于优化差分变异算子,以提高算法的精细搜索能力。通过相同点检测技术和恰当的终止计划有效地降低了系统的运算复杂度。经实验测试与验证,该算法在搜索质量和运算复杂度中达到了一种动态平衡的状态,其整体性能高于传统的快速运动估计算法,效果更逼近于穷举搜索法。     

Fast Multiclass SVM Classification Using Decision Tree Based One-Against-All Method

We present an improved version of One-Against-All (OAA) method for multiclass SVM classification based on a decision tree approach. The proposed decision tree based OAA (DT-OAA) is aimed at increasing the classification speed of OAA by using posterior probability estimates of binary SVM outputs. DT-OAA decreases the average number of binary SVM tests required in testing phase to a greater extent when compared to OAA and other multiclass SVM methods. For a balanced multiclass dataset with K classes, under best situation, DT-OAA requires only (K + 1)/2 binary tests on an average as opposed to K binary tests in OAA; however, on imbalanced multiclass datasets we observed DT-OAA to be much faster with proper selection of order in which the binary SVMs are arranged in the decision tree. Computational comparisons on publicly available datasets indicate that the proposed method can achieve almost the same classification accuracy as that of OAA, but is much faster in decision making.     

一种新的基于ART的支持向量机多类分类方法

基于支持向量机的二值分类原理，提出了一种由自适应共振理论方法与支持向量机相结合的改进型多类分类方法,此方法改进了传统支持向量机的一对一多类分类方法；对于每个二值分类器的结果进行决策时没有采用投票原则，而是采用自适应共振理论网络融合二值分类器的输出信息，从而克服了当分类器输出结果接近于O时投票法容易出现决策错误和票数相同时无法决策的不足．此算法已应用于玻璃的分类．仿真实验证明，此方法具有较好的分类效果．     

Adaptive binary tree for fast SVM multiclass classification

This paper presents an adaptive binary tree (ABT) to reduce the test computational complexity of multiclass support vector machine (SVM). It achieves a fast classification by: (1) reducing the number of binary SVMs for one classification by using separating planes of some binary SVMs to discriminate other binary problems; (2) selecting the binary SVMs with the fewest average number of support vectors (SVs). The average number of SVs is proposed to denote the computational complexity to exclude one class. Compared with five well-known methods, experiments on many benchmark data sets demonstrate our method can speed up the test phase while remain the high accuracy of SVMs.     

DESIGN OF DECISION TREE VIA KERNELIZED HIERARCHICAL CLUSTERING FOR MULTICLASS SUPPORT VECTOR MACHINES

As a very effective method for universal purpose pattern recognition, support vector machine (SVM) was proposed for dichotomic classification problem, which exhibits a remarkable resistance to overfitting, a feature explained by the fact that it directly implements the principle of structural risk minimization. However, in real world, most of classification problems consist of multiple categories. In an attempt to extend the binary SVM classifier for multiclass classification, decision-tree-based multiclass SVM was proposed recently, in which the structure of decision tree plays an important role in minimizing the classification error. The present study aims at developing a systematic way for the design of decision tree for multiclass SVM. Kernel-induced distance function between datasets was discussed and then kernelized hierarchical clustering was developed and used in determining the structure of decision tree. Further, simulation results on satellite image interpretation show the superiority of the proposed classification strategy over the conventional multiclass SVM algorithms.     

支持向量机多类分类算法研究

提出一种新的基于二叉树结构的支持向量(SVM)多类分类算法.该算法解决了现有主要算法所存在的不可分区域问题.为了获得较高的推广能力,必须让样本分布广的类处于二叉树的上层节点,才能获得更大的划分空间.所以,该算法采用最小超立方体和最小超球体类包含作为二叉树的生成算法.实验结果表明,该算法具有一定的优越性.     

Binary tree of SVM: a new fast multiclass training and classification algorithm

We present a new architecture named Binary Tree of support vector machine (SVM), or BTS, in order to achieve high classification efficiency for multiclass problems. BTS and its enhanced version, c-BTS, decrease the number of binary classifiers to the greatest extent without increasing the complexity of the original problem. In the training phase, BTS has N-1 binary classifiers in the best situation (N is the number of classes), while it has log/sub 4/3/((N+3)/4) binary tests on average when making a decision. At the same time the upper bound of convergence complexity is determined. The experiments in this paper indicate that maintaining comparable accuracy, BTS is much faster to be trained than other methods. Especially in classification, due to its Log complexity, it is much faster than directed acyclic graph SVM (DAGSVM) and ECOC in problems that have big class number.     

Parallelizing multiclass support vector machines for scalable image annotation

Machine learning techniques have facilitated image retrieval by automatically classifying and annotating images with keywords. Among them, Support Vector Machines (SVMs) are used extensively due to their generalization properties. SVM was initially designed for binary classifications. However, most classification problems arising in domains such as image annotation usually involve more than two classes. Notably, SVM training is a computationally intensive process especially when the training dataset is large. This paper presents a resource aware parallel multiclass SVM algorithm (named RAMSMO) for large-scale image annotation which partitions the training dataset into smaller binary chunks and optimizes SVM training in parallel using a cluster of computers. A genetic algorithm-based load balancing scheme is designed to optimize the performance of RAMSMO in balancing the computation of multiclass data chunks in heterogeneous computing environments. RAMSMO is evaluated in both experimental and simulation environments, and the results show that it reduces the training time significantly while maintaining a high level of accuracy in classifications.     

基于二叉树的多分类SVM算法在电子邮件过滤中的应用

目前性能较好的多分类算法有1-v-r支持向量机（SVM）、1-1-1SVM、DDAG SVM等，但存在大量不可分区域且训练时间较长的问题。提出一种基于二叉树的多分类SVM算法用于电子邮件的分类与过滤，通过构建二叉树将多分类转化为二值分类，算法采用先聚类再分类的思想，计算测试样本与子类中心的最大相似度和子类间的分离度，以构造决策节点的最优分类超平面。对于C类分类只需C-1个决策函数，从而可节省训练时间。实验表明，该算法得到了较高的查全率、查准率。     

一种新的二叉树多类支持向量机算法

采用二叉树结构对多个二值支持向量机(SVM)子分类器组合,可实现多类问题的分类,并且还可克服传统多类SVM算法存在的不可分区域的情况。针对现有二叉树多类SVM方法未采用有效的二叉树生成算法,该文采用聚类分析中的类距离思想,提出了一种新的基于二叉树的多类SVM分类方法。实验结果表明,新算法具有较高的推广性能。     

Direct estimation of class membership probabilities for multiclass classification using multiple scores

Accurate estimation of class membership probability is needed for many applications in data mining and decision-making, to which multiclass classification is often applied. Since existing methods for estimation of class membership probability are designed for binary classification, in which only a single score outputted from a classifier can be used, an approach for multiclass classification requires both a decomposition of a multiclass classifier into binary classifiers and a combination of estimates obtained from each binary classifier to a target estimate. We propose a simple and general method for directly estimating class membership probability for any class in multiclass classification without decomposition and combination, using multiple scores not only for a predicted class but also for other proper classes. To make it possible to use multiple scores, we propose to modify or extend representative existing methods. As a non-parametric method, which refers to the idea of a binning method as proposed by Zadrozny et al., we create an “accuracy table” by a different method. Moreover we smooth accuracies on the table with methods such as the moving average to yield reliable probabilities (accuracies). As a parametric method, we extend Platt’s method to apply a multiple logistic regression. On two different datasets (open-ended data from Japanese social surveys and the 20 Newsgroups) both with Support Vector Machines and naive Bayes classifiers, we empirically show that the use of multiple scores is effective in the estimation of class membership probabilities in multiclass classification in terms of cross entropy, the reliability diagram, the ROC curve and AUC (area under the ROC curve), and that the proposed smoothing method for the accuracy table works quite well. Finally, we show empirically that in terms of MSE (mean squared error), our best proposed method is superior to an expansion for multiclass classification of a PAV method proposed by Zadrozny et al., in both the 20 Newsgroups dataset and the Pendigits dataset, but is slightly worse than the state-of-the-art method, which is an expansion for multiclass classification of a combination of boosting and a PAV method, on the Pendigits dataset.