A fuzzy classifier with ellipsoidal regions

In this paper, we discuss a fuzzy classifier with ellipsoidal regions which has a learning capability. First, we divide the training data for each class into several clusters. Then, for each cluster, we define a fuzzy rule with an ellipsoidal region around a cluster center. Using the training data for each cluster, we calculate the center and the covariance matrix of the ellipsoidal region for the cluster. Then we tune the fuzzy rules, i.e., the slopes of the membership functions, successively until there is no improvement in the recognition rate of the training data. We evaluate our method using the Fisher iris data, numeral data of vehicle license plates, thyroid data, and blood cell data. The recognition rates (except for the thyroid data) of our classifier are comparable to the maximum recognition rates of the multilayered neural network classifier and the training times (except for the iris data) are two to three orders of magnitude shorter     

一种基于动态聚类的模糊分类规则的生成方法

介绍了一种基于动态聚类的模糊分类规则的生成方法，这种方法能决定规则数目，隶属函数的位置及形状．首先，介绍了基于超圆雏体隶属函数的模糊分类规则的基本形式；然后，介绍动态聚类算法，该算法能将每一类训练模式动态的分为成簇，对于每簇，则建立一个模糊规则；通过调整隶属函数的斜度，来提高对训练模式分类识别率，达到对模糊分类规则进行优化调整的目的；用两个典型的数据集评测了这篇文章研究的方法，这种方法构成的分类系统在识别率与多层神经网络分类器相当，但训练时间远少于多层神经网络分类器的训练时间．     

Fuzzy function approximation with ellipsoidal rules

A fuzzy rule can have the shape of an ellipsoid in the input-output state spare of a system. Then an additive fuzzy system approximates a function by covering its graph with ellipsoidal rule patches. It averages rule patches that overlap. The best fuzzy rules cover the extrema or bumps in the function. Neural or statistical clustering systems can approximate the unknown fuzzy rules from training data. Neural systems can then both tune these rules and add rules to improve the function approximation. We use a hybrid neural system that combines unsupervised and supervised learning to find and tune the rules in the form of ellipsoids. Unsupervised competitive learning finds the first-order and second-order statistics of clusters in the training data. The covariance matrix of each cluster gives an ellipsoid centered at the vector or centroid of the data cluster. The supervised neural system learns with gradient descent. It locally minimizes the mean-squared error of the fuzzy function approximation. In the hybrid system unsupervised learning initializes the gradient descent. The hybrid system tends to give a more accurate function approximation than does the lone unsupervised or supervised system. We found a closed-form model for the optimal rules when only the centroids of the ellipsoids change. We used numerical techniques to find the optimal rules in the general case.     

AUTOMATICALLY CONSTRUCTING MEMBERSHIP FUNCTIONS AND GENERATING FUZZY RULES USING GENETIC ALGORITHMS

The most important task in designing a fuzzy classification system is to find a set of fuzzy rules from training data to deal with a specific classification problem. In recent years, many methods have been proposed to construct membership functions and generate fuzzy rules from training data for handling fuzzy classification problems. We propose a new method to generate fuzzy rules from training data by using genetic algorithms (GAs). First, we divide the training data into several clusters by using the weighted distance clustering method and generate a fuzzy rule for each cluster. Then, we use GAs to tune the membership functions of the generated fuzzy rules. The proposed method attains a higher average classification accuracy rate than the existing methods.     

Intrusion detection by integrating boosting genetic fuzzy classifier and data mining criteria for rule pre-screening

The purpose of the work described in this paper is to provide an intelligent intrusion detection system (IIDS) that uses two of the most popular data mining tasks, namely classification and association rules mining together for predicting different behaviors in networked computers. To achieve this, we propose a method based on iterative rule learning using a fuzzy rule-based genetic classifier. Our approach is mainly composed of two phases. First, a large number of candidate rules are generated for each class using fuzzy association rules mining, and they are pre-screened using two rule evaluation criteria in order to reduce the fuzzy rule search space. Candidate rules obtained after pre-screening are used in genetic fuzzy classifier to generate rules for the classes specified in IIDS: namely Normal, PRB-probe, DOS-denial of service, U2R-user to root and R2L-remote to local. During the next stage, boosting genetic algorithm is employed for each class to find its fuzzy rules required to classify data each time a fuzzy rule is extracted and included in the system. Boosting mechanism evaluates the weight of each data item to help the rule extraction mechanism focus more on data having relatively more weight, i.e., uncovered less by the rules extracted until the current iteration. Each extracted fuzzy rule is assigned a weight. Weighted fuzzy rules in each class are aggregated to find the vote of each class label for each data item.     

Constructing L2-SVM-Based Fuzzy Classifiers in High-Dimensional Space With Automatic Model Selection and Fuzzy Rule Ranking

In this paper, a new scheme for constructing parsimonious fuzzy classifiers is proposed based on the L2-support vector machine (L2-SVM) technique with model selection and feature ranking performed simultaneously in an integrated manner, in which fuzzy rules are optimally generated from data by L2-SVM learning. In order to identify the most influential fuzzy rules induced from the SVM learning, two novel indexes for fuzzy rule ranking are proposed and named as alpha-values and omega-values of fuzzy rules in this paper. The alpha-values are defined as the Lagrangian multipliers of the L2-SVM and adopted to evaluate the output contribution of fuzzy rules, while the omega-values are developed by considering both the rule base structure and the output contribution of fuzzy rules. As a prototype-based classifier, the L2-SVM-based fuzzy classifier evades the curse of dimensionality in high-dimensional space in the sense that the number of support vectors, which equals the number of induced fuzzy rules, is not related to the dimensionality. Experimental results on high-dimensional benchmark problems have shown that by using the proposed scheme the most influential fuzzy rules can be effectively induced and selected, and at the same time feature ranking results can also be obtained to construct parsimonious fuzzy classifiers with better generalization performance than the well-known algorithms in literature.     

Classification based on specific rules and inexact coverage

Association rule mining and classification are important tasks in data mining. Using association rules has proved to be a good approach for classification. In this paper, we propose an accurate classifier based on class association rules (CARs), called CAR-IC, which introduces a new pruning strategy for mining CARs, which allows building specific rules with high confidence. Moreover, we propose and prove three propositions that support the use of a confidence threshold for computing rules that avoids ambiguity at the classification stage. This paper also presents a new way for ordering the set of CARs based on rule size and confidence. Finally, we define a new coverage strategy, which reduces the number of non-covered unseen-transactions during the classification stage. Results over several datasets show that CAR-IC beats the best classifiers based on CARs reported in the literature.     

Cluster‐based ensemble of classifiers

This paper presents cluster‐based ensemble classifier – an approach toward generating ensemble of classifiers using multiple clusters within classified data. Clustering is incorporated to partition data set into multiple clusters of highly correlated data that are difficult to separate otherwise and different base classifiers are used to learn class boundaries within the clusters. As the different base classifiers engage on different difficult‐to‐classify subsets of the data, the learning of the base classifiers is more focussed and accurate. A selection rather than fusion approach achieves the final verdict on patterns of unknown classes. The impact of clustering on the learning parameters and accuracy of a number of learning algorithms including neural network, support vector machine, decision tree and k‐NN classifier is investigated. A number of benchmark data sets from the UCI machine learning repository were used to evaluate the cluster‐based ensemble classifier and the experimental results demonstrate its superiority over bagging and boosting.     

Neutrosophic classifier: An extension of fuzzy classifer

Fuzzy classification has become of great interest because of its ability to utilize simple linguistically interpretable rules and has overcome the limitations of symbolic or crisp rule based classifiers. This paper introduces an extension to fuzzy classifier: a neutrosophic classifier, which would utilize neutrosophic logic for its working. Neutrosophic logic is a generalized logic that is capable of effectively handling indeterminacy, stochasticity acquisition errors that fuzzy logic cannot handle. The proposed neutrosophic classifier employs neutrosophic logic for its working and is an extension of commonly used fuzzy classifier. It is compared with the commonly used fuzzy classifiers on the following parameters: nature of membership functions, number of rules and indeterminacy in the results generated. It is proved in the paper that extended fuzzy classifier: neutrosophic classifier; optimizes the said parameters in comparison to the fuzzy counterpart. Finally the paper is concluded with justifying that neutrosophic logic though in its nascent stage still holds the potential to be experimented for further exploration in different domains.     

A design of granular fuzzy classifier

In this paper, we propose a new design methodology of granular fuzzy classifiers based on a concept of information granularity and information granules. The classifier uses the mechanism of information granulation with the aid of which the entire input space is split into a collection of subspaces. When designing the proposed fuzzy classifier, these information granules are constructed in a way they are made reflective of the geometry of patterns belonging to individual classes. Although the elements involved in the generated information granules (clusters) seem to be homogeneous with respect to the distribution of patterns in the input (feature) space, they still could exhibit a significant level of heterogeneity when it comes to the class distribution within the individual clusters. To build an efficient classifier, we improve the class homogeneity of the originally constructed information granules (by adjusting the prototypes of the clusters) and use a weighting scheme as an aggregation mechanism.     

Using multiple and negative target rules to make classifiers more understandable

One major goal for data mining is to understand data. Rule based methods are better than other methods in making mining results comprehensible. However, current rule based classifiers make use of a small number of rules and a default prediction to build a concise predictive model. This reduces the explanatory ability of the rule based classifier. In this paper, we propose to use multiple and negative target rules to improve explanatory ability of rule based classifiers. We show experimentally that this understandability is not at the cost of accuracy of rule based classifiers.     

Support vector learning for fuzzy rule-based classification systems

To design a fuzzy rule-based classification system (fuzzy classifier) with good generalization ability in a high dimensional feature space has been an active research topic for a long time. As a powerful machine learning approach for pattern recognition problems, the support vector machine (SVM) is known to have good generalization ability. More importantly, an SVM can work very well on a high- (or even infinite) dimensional feature space. This paper investigates the connection between fuzzy classifiers and kernel machines, establishes a link between fuzzy rules and kernels, and proposes a learning algorithm for fuzzy classifiers. We first show that a fuzzy classifier implicitly defines a translation invariant kernel under the assumption that all membership functions associated with the same input variable are generated from location transformation of a reference function. Fuzzy inference on the IF-part of a fuzzy rule can be viewed as evaluating the kernel function. The kernel function is then proven to be a Mercer kernel if the reference functions meet a certain spectral requirement. The corresponding fuzzy classifier is named positive definite fuzzy classifier (PDFC). A PDFC can be built from the given training samples based on a support vector learning approach with the IF-part fuzzy rules given by the support vectors. Since the learning process minimizes an upper bound on the expected risk (expected prediction error) instead of the empirical risk (training error), the resulting PDFC usually has good generalization. Moreover, because of the sparsity properties of the SVMs, the number of fuzzy rules is irrelevant to the dimension of input space. In this sense, we avoid the "curse of dimensionality." Finally, PDFCs with different reference functions are constructed using the support vector learning approach. The performance of the PDFCs is illustrated by extensive experimental results. Comparisons with other methods are also provided.     

Hierarchical classification of protein function with ensembles of rules and particle swarm optimisation

This paper focuses on hierarchical classification problems where the classes to be predicted are organized in the form of a tree. The standard top-down divide and conquer approach for hierarchical classification consists of building a hierarchy of classifiers where a classifier is built for each internal (non-leaf) node in the class tree. Each classifier discriminates only between its child classes. After the tree of classifiers is built, the system uses them to classify test examples one class level at a time, so that when the example is assigned a class at a given level, only the child classes need to be considered at the next level. This approach has the drawback that, if a test example is misclassified at a certain class level, it will be misclassified at deeper levels too. In this paper we propose hierarchical classification methods to mitigate this drawback. More precisely, we propose a method called hierarchical ensemble of hierarchical rule sets (HEHRS), where different ensembles are built at different levels in the class tree and each ensemble consists of different rule sets built from training examples at different levels of the class tree. We also use a particle swarm optimisation (PSO) algorithm to optimise the rule weights used by HEHRS to combine the predictions of different rules into a class to be assigned to a given test example. In addition, we propose a variant of a method to mitigate the aforementioned drawback of top-down classification. These three types of methods are compared against the standard top-down hierarchical classification method in six challenging bioinformatics datasets, involving the prediction of protein function. Overall HEHRS with the rule weights optimised by the PSO algorithm obtains the best predictive accuracy out of the four types of hierarchical classification method.     

Fuzzy relational classifier trained by fuzzy clustering

A novel approach to nonlinear classification is presented, in the training phase of the classifier, the training data is first clustered in an unsupervised way by fuzzy c-means or a similar algorithm. The class labels are not used in this step. Then, a fuzzy relation between the clusters and the class identifiers is computed. This approach allows the number of prototypes to be independent of the number of actual classes. For the classification of unseen patterns, the membership degrees of the feature vector in the clusters are first computed by using the distance measure of the clustering algorithm. Then, the output fuzzy set is obtained by relational composition. This fuzzy set contains the membership degrees of the pattern in the given classes. A crisp decision is obtained by defuzzification, which gives either a single class or a "reject" decision, when a unique class cannot be selected based on the available information. The principle of the proposed method is demonstrated on an artificial data set and the applicability of the method is shown on the identification of live-stock from recorded sound sequences. The obtained results are compared with two other classifiers.     

受限模糊规则进化的入侵检测

基于生物进化机理,提出了模糊规则进化的推理方法,并对初始群体产生加以控制,实现受限的模糊规则进化的入侵检测“LEFRIDS”。该方法可以有效控制规则数,加速检测过程,并且由于变异会产生新的规则,使检测规则不断“新陈代谢”,楗高了对未知攻击的检测能力。     

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.     

ID3-derived fuzzy rules and optimized defuzzification forhandwritten numeral recognition

Presents a technique to produce fuzzy rules based on the ID3 approach and to optimize defuzzification parameters by using a two-layer perceptron. The technique overcomes the difficulties in a conventional syntactic approach to handwritten character recognition, including problems of choosing a starting or reference point, scaling, and learning by machines. The authors' technique provides: a way to produce meaningful and simple fuzzy rules; a method to fuzzify ID3-derived rules to deal with uncertain, noisy, or fuzzy data; and a framework to incorporate fuzzy rules learned from the training data and those extracted from human recognition experience. The authors' experimental results on NIST Special Database 3 show that the technique out-performs the straight forward ID3 approach. Moreover, ID3-derived fuzzy rules can be combined with an optimized nearest neighbor classifier, which uses intensity features only, to achieve a better classification performance than either of the classifiers. The combined classifier achieves a correct classification rate of 98.6% on the test set     

BRACID: a comprehensive approach to learning rules from imbalanced data

In this paper we consider induction of rule-based classifiers from imbalanced data, where one class (a minority class) is under-represented in comparison to the remaining majority classes. The minority class is usually of primary interest. However, most rule-based classifiers are biased towards the majority classes and they have difficulties with correct recognition of the minority class. In this paper we discuss sources of these difficulties related to data characteristics or to an algorithm itself. Among the problems related to the data distribution we focus on the role of small disjuncts, overlapping of classes and presence of noisy examples. Then, we show that standard techniques for induction of rule-based classifiers, such as sequential covering, top-down induction of rules or classification strategies, were created with the assumption of balanced data distribution, and we explain why they are biased towards the majority classes. Some modifications of rule-based classifiers have been already introduced, but they usually concentrate on individual problems. Therefore, we propose a novel algorithm, BRACID, which more comprehensively addresses the issues associated with imbalanced data. Its main characteristics includes a hybrid representation of rules and single examples, bottom-up learning of rules and a local classification strategy using nearest rules. The usefulness of BRACID has been evaluated in experiments on several imbalanced datasets. The results show that BRACID significantly outperforms the well known rule-based classifiers C4.5rules, RIPPER, PART, CN2, MODLEM as well as other related classifiers as RISE or K-NN. Moreover, it is comparable or better than the studied approaches specialized for imbalanced data such as generalizations of rule algorithms or combinations of SMOTE + ENN preprocessing with PART. Finally, it improves the support of minority class rules, leading to better recognition of the minority class examples.     

基于选择性集成分类器的面部表情识别研究*

为了提高面部表情的分类识别性能,基于集成学习理论,提出了一种二次优化选择性(Quadratic Optimization Choice, QOC)集成分类模型。首先,对于9个基分类器,依据性能进行排序,选择前30%的基分类器作为集成模型的候选基分类器。其次,依据组合规则产生集成模型簇。最后,对集成模型簇进行二次优化选择,选择具有最小泛化误差的集成分类器的子集,从而确定最优集成分类模型。为了验证QOC集成分类模型的性能,选择采用最大值、最小值和均值规则的集成模型作为对比模型,实验结果表明：相对基分类器,QOC集成分类模型取得了较好的分类效果,尤其是对于识别率较差的悲伤表情类,平均识别率提升了21.11%。相对于非选择性集成模型,QOC集成分类模型识别性能也有显著提高。     

基于模糊集合的汉语主观句识别

主观句识别的工作在诸如情感分类和意见摘要等意见挖掘系统中占有很重要的地位。在该文中,我们提出一种基于情感密度的模糊集合分类器以识别汉语主观句。首先,我们利用优势率方法从训练语料中抽取主观性线索词;然后,为了能更好的表达一个句子的主观性,我们利用抽取出的主观性线索词计算出每个句子的情感密度;最后,我们结合情感密度的特点实现了一个三角形隶属度函数的模糊集合分类器以识别主观句。我们在NTCIR-6中文数据中做了两组实验。实验结果表明我们的方法具有一定的可行性。