A hybrid discretization method for naïve Bayesian classifiers

Since naïve Bayesian classifiers are suitable for processing discrete attributes, many methods have been proposed for discretizing continuous ones. However, none of the previous studies apply more than one discretization method to the continuous attributes in a data set for naïve Bayesian classifiers. Different approaches employ different information embedded in continuous attributes to determine the boundaries for discretization. It is likely that discretizing the continuous attributes in a data set using different methods can utilize the information embedded in the attributes more thoroughly and thus improve the performance of naïve Bayesian classifiers. In this study, we propose a nonparametric measure to evaluate the dependence level between a continuous attribute and the class. The nonparametric measure is then used to develop a hybrid method for discretizing continuous attributes so that the accuracy of the naïve Bayesian classifier can be enhanced. This hybrid method is tested on 20 data sets, and the results demonstrate that discretizing the continuous attributes in a data set by various methods can generally have a higher prediction accuracy.     

Bayesian network classifiers based on Gaussian kernel density

For learning a Bayesian network classifier, continuous attributes usually need to be discretized. But the discretization of continuous attributes may bring information missing, noise and less sensitivity to the changing of the attributes towards class variables. In this paper, we use the Gaussian kernel function with smoothing parameter to estimate the density of attributes. Bayesian network classifier with continuous attributes is established by the dependency extension of Naive Bayes classifiers. We also analyze the information provided to a class for each attributes as a basis for the dependency extension of Naive Bayes classifiers. Experimental studies on UCI data sets show that Bayesian network classifiers using Gaussian kernel function provide good classification accuracy comparing to other approaches when dealing with continuous attributes.     

Discretization for naive-Bayes learning: managing discretization bias and variance

Quantitative attributes are usually discretized in Naive-Bayes learning. We establish simple conditions under which discretization is equivalent to use of the true probability density function during naive-Bayes learning. The use of different discretization techniques can be expected to affect the classification bias and variance of generated naive-Bayes classifiers, effects we name discretization bias and variance. We argue that by properly managing discretization bias and variance, we can effectively reduce naive-Bayes classification error. In particular, we supply insights into managing discretization bias and variance by adjusting the number of intervals and the number of training instances contained in each interval. We accordingly propose proportional discretization and fixed frequency discretization, two efficient unsupervised discretization methods that are able to effectively manage discretization bias and variance. We evaluate our new techniques against four key discretization methods for naive-Bayes classifiers. The experimental results support our theoretical analyses by showing that with statistically significant frequency, naive-Bayes classifiers trained on data discretized by our new methods are able to achieve lower classification error than those trained on data discretized by current established discretization methods.     

Handling numeric attributes when comparing Bayesian network classifiers: does the discretization method matter?

Within the framework of Bayesian networks (BNs), most classifiers assume that the variables involved are of a discrete nature, but this assumption rarely holds in real problems. Despite the loss of information discretization entails, it is a direct easy-to-use mechanism that can offer some benefits: sometimes discretization improves the run time for certain algorithms; it provides a reduction in the value set and then a reduction in the noise which might be present in the data; in other cases, there are some Bayesian methods that can only deal with discrete variables. Hence, even though there are many ways to deal with continuous variables other than discretization, it is still commonly used. This paper presents a study of the impact of using different discretization strategies on a set of representative BN classifiers, with a significant sample consisting of 26 datasets. For this comparison, we have chosen Naive Bayes (NB) together with several other semi-Naive Bayes classifiers: Tree-Augmented Naive Bayes (TAN), k-Dependence Bayesian (KDB), Aggregating One-Dependence Estimators (AODE) and Hybrid AODE (HAODE). Also, we have included an augmented Bayesian network created by using a hill climbing algorithm (BNHC). With this comparison we analyse to what extent the type of discretization method affects classifier performance in terms of accuracy and bias-variance discretization. Our main conclusion is that even if a discretization method produces different results for a particular dataset, it does not really have an effect when classifiers are being compared. That is, given a set of datasets, accuracy values might vary but the classifier ranking is generally maintained. This is a very useful outcome, assuming that the type of discretization applied is not decisive future experiments can be d times faster, d being the number of discretization methods considered.     

Machine learning: a review of classification and combining techniques

Supervised classification is one of the tasks most frequently carried out by so-called Intelligent Systems. Thus, a large number of techniques have been developed based on Artificial Intelligence (Logic-based techniques, Perceptron-based techniques) and Statistics (Bayesian Networks, Instance-based techniques). The goal of supervised learning is to build a concise model of the distribution of class labels in terms of predictor features. The resulting classifier is then used to assign class labels to the testing instances where the values of the predictor features are known, but the value of the class label is unknown. This paper describes various classification algorithms and the recent attempt for improving classification accuracy—ensembles of classifiers.     

Maximum margin Bayesian network classifiers

We present a maximum margin parameter learning algorithm for Bayesian network classifiers using a conjugate gradient (CG) method for optimization. In contrast to previous approaches, we maintain the normalization constraints on the parameters of the Bayesian network during optimization, i.e., the probabilistic interpretation of the model is not lost. This enables us to handle missing features in discriminatively optimized Bayesian networks. In experiments, we compare the classification performance of maximum margin parameter learning to conditional likelihood and maximum likelihood learning approaches. Discriminative parameter learning significantly outperforms generative maximum likelihood estimation for naive Bayes and tree augmented naive Bayes structures on all considered data sets. Furthermore, maximizing the margin dominates the conditional likelihood approach in terms of classification performance in most cases. We provide results for a recently proposed maximum margin optimization approach based on convex relaxation. While the classification results are highly similar, our CG-based optimization is computationally up to orders of magnitude faster. Margin-optimized Bayesian network classifiers achieve classification performance comparable to support vector machines (SVMs) using fewer parameters. Moreover, we show that unanticipated missing feature values during classification can be easily processed by discriminatively optimized Bayesian network classifiers, a case where discriminative classifiers usually require mechanisms to complete unknown feature values in the data first.     

A Bayesian approach to joint feature selection and classifier design

This paper adopts a Bayesian approach to simultaneously learn both an optimal nonlinear classifier and a subset of predictor variables (or features) that are most relevant to the classification task. The approach uses heavy-tailed priors to promote sparsity in the utilization of both basis functions and features; these priors act as regularizers for the likelihood function that rewards good classification on the training data. We derive an expectation- maximization (EM) algorithm to efficiently compute a maximum a posteriori (MAP) point estimate of the various parameters. The algorithm is an extension of recent state-of-the-art sparse Bayesian classifiers, which in turn can be seen as Bayesian counterparts of support vector machines. Experimental comparisons using kernel classifiers demonstrate both parsimonious feature selection and excellent classification accuracy on a range of synthetic and benchmark data sets.     

Fast recognition of musical genres using RBF networks

This paper explores the automatic classification of audio tracks into musical genres. Our goal is to achieve human-level accuracy with fast training and classification. This goal is achieved with radial basis function (RBF) networks by using a combination of unsupervised and supervised initialization methods. These initialization methods yield classifiers that are as accurate as RBF networks trained with gradient descent (which is hundreds of times slower). In addition, feature subset selection further reduces training and classification time while preserving classification accuracy. Combined, our methods succeed in creating an RBF network that matches the musical classification accuracy of humans. The general algorithmic contribution of this paper is to show experimentally that RBF networks initialized with a combination of methods can yield good classification performance without relying on gradient descent. The simplicity and computational efficiency of our initialization methods produce classifiers that are fast to train as well as fast to apply to novel data. We also present an improved method for initializing the k-means clustering algorithm, which is useful for both unsupervised and supervised initialization methods.     

Hand-Geometry Recognition Using Entropy-Based Discretization

The hand-geometry-based recognition systems proposed in the literature have not yet exploited user-specific dependencies in the feature-level representation. We investigate the possibilities to improve the performance of the existing hand-geometry systems using the discretization of extracted features. This paper proposes employing discretization of hand-geometry features, using entropy-based heuristics, to achieve the performance improvement. The performance improvement due to the unsupervised and supervised discretization schemes is compared on a variety of classifiers: k-NN, naive Bayes, SVM, and FFN. Our experimental results on the database of 100 users achieve significant improvement in the recognition accuracy and confirm the usefulness of discretization in hand-geometry-based systems     

动态朴素贝叶斯网络分类器的特征子集选择

分类准确性是分类器最重要的性能指标,特征子集选择是提高分类器分类准确性的一种有效方法。现有的特征子集选择方法主要针对静态分类器,缺少动态分类器特征子集选择方面的研究。首先给出具有连续属性的动态朴素贝叶斯网络分类器和动态分类准确性评价标准,在此基础上建立动态朴素贝叶斯网络分类器的特征子集选择方法,并使用真实宏观经济时序数据进行实验与分析。     

Bad:基于最小描述长度的均衡离散化方法

连续数据离散化是数据挖掘分类方法中的重要预处理过程。本文提出一种基于最小描述长度原理的均衡离散化方法,该方法基于最小描述长度理论提出一种均衡的离散化函数,很好地衡量了离散区间与分类错误之间的关系。同时,基于均衡函数提出一种有效的启发式算法,寻找最佳的断点序列。仿真结果表明,在C5.0决策树和Naive贝叶斯分类器上,提出的算法有较好的分类学习能力。     

朴素贝叶斯小样本金融客户分类方法与分类偏好研究

对金融客户进行准确分类是向其提供个性化服务的前提.针对某金融产品的销售需求,通过在线推销测试收集客户样本数据,并根据用户反馈标注样本.通过构造概率分布函数、离散化连续型数据两种方式构建贝叶斯分类器.利用交叉检验训练和测试分类算法,发现朴素贝叶斯分类算法性能优于高斯贝叶斯算法和逻辑回归算法.离散化连续型数据过程中结合分类偏好进行数据过滤,实验证明,异常数据滤除率参数对客户分类算法的准确性有显著影响,通过恰当设置该参数的取值,可以调节分类算法的分类偏好.方法对于提升金融产品销售效率,降低营销成本有参考价值.     

贝叶斯网络分类模型研究及其在信用评估中的应用

基于概率估计的贝叶斯及贝叶斯网络分类模型,拥有其它数据挖掘工具所不具备的优势。在分析贝叶斯及贝叶斯网络分类模型基础上,结合最小风险决策准则,提出了一种新的信用评估模型。在实际数据集上采用交叉验证方式进行了测试。实验结果表明基于最小风险决策准则的贝叶斯及贝叶斯网络分类模型可以有效地减少信用评估风险。     

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.     

基于显露模式的数据流贝叶斯分类算法

基于模式的贝叶斯分类模型是解决数据挖掘领域分类问题的一种有效方法.然而,大多数基于模式的贝叶斯分类器只考虑模式在目标类数据集中的支持度,而忽略了模式在对立类数据集合中的支持度.此外,对于高速动态变化的无限数据流环境,在静态数据集下的基于模式的贝叶斯分类器就不能适用.为了解决这些问题,提出了基于显露模式的数据流贝叶斯分类模型EPDS（Bayesian classifier algorithm based on emerging pattern for data stream）.该模型使用一个简单的混合森林结构来维护内存中事务的项集,并采用一种快速的模式抽取机制来提高算法速度.EPDS采用半懒惰式学习策略持续更新显露模式,并为待分类事务在每个类下建立局部分类模型.大量实验结果表明,该算法比其他数据流分类模型有较高的准确度.     

Boosted Bayesian network classifiers

The use of Bayesian networks for classification problems has received a significant amount of recent attention. Although computationally efficient, the standard maximum likelihood learning method tends to be suboptimal due to the mismatch between its optimization criteria (data likelihood) and the actual goal of classification (label prediction accuracy). Recent approaches to optimizing classification performance during parameter or structure learning show promise, but lack the favorable computational properties of maximum likelihood learning. In this paper we present boosted Bayesian network classifiers, a framework to combine discriminative data-weighting with generative training of intermediate models. We show that boosted Bayesian network classifiers encompass the basic generative models in isolation, but improve their classification performance when the model structure is suboptimal. We also demonstrate that structure learning is beneficial in the construction of boosted Bayesian network classifiers. On a large suite of benchmark data-sets, this approach outperforms generative graphical models such as naive Bayes and TAN in classification accuracy. Boosted Bayesian network classifiers have comparable or better performance in comparison to other discriminatively trained graphical models including ELR and BNC. Furthermore, boosted Bayesian networks require significantly less training time than the ELR and BNC algorithms.     

基于Copula的贝叶斯分类器

利用Copula的理论提出了基于Copula贝叶斯分类算法,克服了一般的朴素贝叶斯分类器要求属性独立性假设的不足,进一步扩展了朴素贝叶斯分类器,实验结果表明,基于Copula贝叶斯算法取得了较好的分类效果。     

Using class-based feature selection for the classification of hyperspectral data

The rapid advances in hyperspectral sensing technology have made it possible to collect remote-sensing data in hundreds of bands. However, the data-analysis methods that have been successfully applied to multispectral data are often limited in achieving satisfactory results for hyperspectral data. The major problem is the high dimensionality, which deteriorates the classification due to the Hughes Phenomenon. In order to avoid this problem, a large number of algorithms have been proposed, so far, for feature reduction. Based on the concept of multiple classifiers, we propose a new schema for the feature selection procedure. In this framework, instead of using feature selection for whole classes, we adopt feature selection for each class separately. Thus different subsets of features are selected at the first step. Once the feature subsets are selected, a Bayesian classifier is trained on each of these feature subsets. Finally, a combination mechanism is used to combine the outputs of these classifiers. Experiments are carried out on an Airborne Visible/Infrared Imaging Spectroradiometer (AVIRIS) data set. Encouraging results have been obtained in terms of classification accuracy, suggesting the effectiveness of the proposed algorithms.     

A hybrid method for learning multi-dimensional Bayesian network classifiers based on an optimization model

Bayesian networks, which have a solid mathematical basis as classifiers, take the prior information of samples into consideration. They have gained considerable popularity for solving classification problems. However, many real-world applications can be viewed as classification problems in which instances have to be assigned to a set of different classes at the same time. To address this problem, multi-dimensional Bayesian network classifiers (MBCs), which organize class and feature variables as three subgraphs, have recently been proposed. Because each subgraph has different structural restrictions, three different learning algorithms are needed. In this paper, we present for the first time an MBC learning algorithm based on an optimization model (MBC-OM) that is inspired by the constraint-based Bayesian network structure learning method. MBC-OM uses the chi-squared statistic and mutual information to estimate the dependence coefficients among variables, and these are used to construct an objective function as an overall measure of the dependence for a classifier structure. Therefore, the problem of searching for an optimal classifier becomes one of finding the maximum value of the objective function in feasible fields. We prove the existence and uniqueness of the numerical solution. Moreover, we validate our method on five benchmark data sets. Experimental results are competitive, and outperform state-of-the-art algorithms for multi-dimensional classification.