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     

A general framework for designing a fuzzy rule-based classifier

This paper presents a general framework for designing a fuzzy rule-based classifier. Structure and parameters of the classifier are evolved through a two-stage genetic search. To reduce the search space, the classifier structure is constrained by a tree created using the evolving SOM tree algorithm. Salient input variables are specific for each fuzzy rule and are found during the genetic search process. It is shown through computer simulations of four real world problems that a large number of rules and input variables can be eliminated from the model without deteriorating the classification accuracy. By contrast, the classification accuracy of unseen data is increased due to the elimination.     

Face recognition using a fuzzy fisherface classifier

In this study, we are concerned with face recognition using fuzzy fisherface approach and its fuzzy set based augmentation. The well-known fisherface method is relatively insensitive to substantial variations in light direction, face pose, and facial expression. This is accomplished by using both principal component analysis and Fisher's linear discriminant analysis. What makes most of the methods of face recognition (including the fisherface approach) similar is an assumption about the same level of typicality (relevance) of each face to the corresponding class (category). We propose to incorporate a gradual level of assignment to class being regarded as a membership grade with anticipation that such discrimination helps improve classification results. More specifically, when operating on feature vectors resulting from the PCA transformation we complete a Fuzzy K-nearest neighbor class assignment that produces the corresponding degrees of class membership. The comprehensive experiments completed on ORL, Yale, and CNU (Chungbuk National University) face databases show improved classification rates and reduced sensitivity to variations between face images caused by changes in illumination and viewing directions. The performance is compared vis-à-vis other commonly used methods, such as eigenface and fisherface.     

An initial comparison of a fuzzy neural classifier and a decision tree based classifier

At the present time a large number of AI methods have been developed in the field of pattern classification. In this paper, we will compare the performance of a well-known algorithm in machine learning (C4.5) with a recently proposed algorithm in the fuzzy set community (NEFCLASS). We will compare the algorithms both on the accuracy attained and on the size of the induced rule base. Additionally, we will investigate how the selected algorithms perform after they have been pre-processed by discretization and feature selection.     

Characterisation of ecotones using membership degrees computed with a fuzzy classifier

Ecotones zones lie between homogeneous ecological systems. They are characterised on images by heterogeneous pixels in a specific neighbourhood. Fuzzy classifiers output membership degrees that better represent the heterogeneity within a pixel and can be further processed within the context of a local neighbourhood. This Letter formalises these notations. Two coral reef systems examples are presented. They illustrate the use of possibility measurement to characterise ecotones, and the use of information on well-known ecotones to increase the accuracy of image classification.     

Evolutionary design of a fuzzy classifier from data

Genetic algorithms show powerful capabilities for automatically designing fuzzy systems from data, but many proposed methods must be subjected to some minimal structure assumptions, such as rule base size. In this paper, we also address the design of fuzzy systems from data. A new evolutionary approach is proposed for deriving a compact fuzzy classification system directly from data without any a priori knowledge or assumptions on the distribution of the data. At the beginning of the algorithm, the fuzzy classifier is empty with no rules in the rule base and no membership functions assigned to fuzzy variables. Then, rules and membership functions are automatically created and optimized in an evolutionary process. To accomplish this, parameters of the variable input spread inference training (VISIT) algorithm are used to code fuzzy systems on the training data set. Therefore, we can derive each individual fuzzy system via the VISIT algorithm, and then search the best one via genetic operations. To evaluate the fuzzy classifier, a fuzzy expert system acts as the fitness function. This fuzzy expert system can effectively evaluate the accuracy and compactness at the same time. In the application section, we consider four benchmark classification problems: the iris data, wine data, Wisconsin breast cancer data, and Pima Indian diabetes data. Comparisons of our method with others in the literature show the effectiveness of the proposed method.     

Compact fuzzy association rule-based classifier

Classification is one of the most popular data mining techniques applied to many scientific and industrial problems. The efficiency of a classification model is evaluated by two parameters, namely the accuracy and the interpretability of the model. While most of the existing methods claim their accurate superiority over others, their models are usually complex and hardly understandable for the users. In this paper, we propose a novel classification model that is based on easily interpretable fuzzy association rules and fulfils both efficiency criteria. Since the accuracy of a classification model can be largely affected by the partitioning of numerical attributes, this paper discusses several fuzzy and crisp partitioning techniques. The proposed classification method is compared to 15 previously published association rule-based classifiers by testing them on five benchmark data sets. The results show that the fuzzy association rule-based classifier presented in this paper, offers a compact, understandable and accurate classification model.     

A subspace decision cluster classifier for text classification

In this paper, a new classification method (SDCC) for high dimensional text data with multiple classes is proposed. In this method, a subspace decision cluster classification (SDCC) model consists of a set of disjoint subspace decision clusters, each labeled with a dominant class to determine the class of new objects falling in the cluster. A cluster tree is first generated from a training data set by recursively calling a subspace clustering algorithm Entropy Weighting k-Means algorithm. Then, the SDCC model is extracted from the subspace decision cluster tree. Various tests including Anderson–Darling test are used to determine the stopping condition of the tree growing. A series of experiments on real text data sets have been conducted. Their results show that the new classification method (SDCC) outperforms the existing methods like decision tree and SVM. SDCC is particularly suitable for large, high dimensional sparse text data with many classes.     

Fusion of images interpreted by a new fuzzy classifier

This paper presents a global system for the fusion of images segmented by various methods and interpreted by a fuzzy classifier. A set of complementary segmentation operators is applied to the image. Each region of the segmented images is interpreted by the fuzzy classifier, through membership degrees to classes. The fuzzy classifier builds the classes automatically from examples, even in the case of complex data sets. Interpreted images are then merged by a fusion operator from the fuzzy set theory. Several fusion operators are compared. They trust more high membership degrees to classes, which are considered as reliability degrees. The fusion of the interpreted images improves the segmentation, and gives solutions to segmentation and interpretation evaluation.     

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.     

Dynamic selection approaches for multiple classifier systems

In this paper we propose a new approach for dynamic selection of ensembles of classifiers. Based on the concept named multistage organizations, the main objective of which is to define a multi-layer fusion function adapted to each recognition problem, we propose dynamic multistage organization (DMO), which defines the best multistage structure for each test sample. By extending Dos Santos et al.’s approach, we propose two implementations for DMO, namely DSA ^m and DSA ^c . While the former considers a set of dynamic selection functions to generalize a DMO structure, the latter considers contextual information, represented by the output profiles computed from the validation dataset, to conduct this task. The experimental evaluation, considering both small and large datasets, demonstrated that DSA ^c dominated DSA ^m on most problems, showing that the use of contextual information can reach better performance than other existing methods. In addition, the performance of DSA ^c can also be enhanced in incremental learning. However, the most important observation, supported by additional experiments, is that dynamic selection is generally preferred over static approaches when the recognition problem presents a high level of uncertainty.     

An efficient fuzzy classifier with feature selection based on fuzzyentropy

This paper presents an efficient fuzzy classifier with the ability of feature selection based on a fuzzy entropy measure. Fuzzy entropy is employed to evaluate the information of pattern distribution in the pattern space. With this information, we can partition the pattern space into nonoverlapping decision regions for pattern classification. Since the decision regions do not overlap, both the complexity and computational load of the classifier are reduced and thus the training time and classification time are extremely short. Although the decision regions are partitioned into nonoverlapping subspaces, we can achieve good classification performance since the decision regions can be correctly determined via our proposed fuzzy entropy measure. In addition, we also investigate the use of fuzzy entropy to select relevant features. The feature selection procedure not only reduces the dimensionality of a problem but also discards noise-corrupted, redundant and unimportant features. Finally, we apply the proposed classifier to the Iris database and Wisconsin breast cancer database to evaluate the classification performance. Both of the results show that the proposed classifier can work well for the pattern classification application.     

Particle swarm optimization for ensembling generation for evidential k-nearest-neighbour classifier

The problem addressed in this paper concerns the ensembling generation for evidential k-nearest-neighbour classifier. An efficient method based on particle swarm optimization (PSO) is here proposed. We improve the performance of the evidential k-nearest-neighbour (EkNN) classifier using a random subspace based ensembling method. Given a set of random subspace EkNN classifier, a PSO is used for obtaining the best parameters of the set of evidential k-nearest-neighbour classifiers, finally these classifiers are combined by the “vote rule”. The performance improvement with respect to the state-of-the-art approaches is validated through experiments with several benchmark datasets.

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.     

Type-2 fuzzy logic-based classifier fusion for support vector machines

As a machine-learning tool, support vector machines (SVMs) have been gaining popularity due to their promising performance. However, the generalization abilities of SVMs often rely on whether the selected kernel functions are suitable for real classification data. To lessen the sensitivity of different kernels in SVMs classification and improve SVMs generalization ability, this paper proposes a fuzzy fusion model to combine multiple SVMs classifiers. To better handle uncertainties existing in real classification data and in the membership functions (MFs) in the traditional type-1 fuzzy logic system (FLS), we apply interval type-2 fuzzy sets to construct a type-2 SVMs fusion FLS. This type-2 fusion architecture takes considerations of the classification results from individual SVMs classifiers and generates the combined classification decision as the output. Besides the distances of data examples to SVMs hyperplanes, the type-2 fuzzy SVMs fusion system also considers the accuracy information of individual SVMs. Our experiments show that the type-2 based SVM fusion classifiers outperform individual SVM classifiers in most cases. The experiments also show that the type-2 fuzzy logic-based SVMs fusion model is better than the type-1 based SVM fusion model in general.     

A new nonlinear classifier with a penalized signed fuzzy measure using effective genetic algorithm

This paper proposes a new nonlinear classifier based on a generalized Choquet integral with signed fuzzy measures to enhance the classification accuracy and power by capturing all possible interactions among two or more attributes. This generalized approach was developed to address unsolved Choquet-integral classification issues such as allowing for flexible location of projection lines in n-dimensional space, automatic search for the least misclassification rate based on Choquet distance, and penalty on misclassified points. A special genetic algorithm is designed to implement this classification optimization with fast convergence. Both the numerical experiment and empirical case studies show that this generalized approach improves and extends the functionality of this Choquet nonlinear classification in more real-world multi-class multi-dimensional situations.     

The cluster assessment of facial attractiveness using fuzzy neural network classifier based on 3D Moiré features

Facial attractiveness has long been argued upon varied emphases by philosophers, artists, psychologists and biologists. A number of studies empirically investigated how facial attractiveness was influenced by 2D facial characteristics, such as symmetry, averageness and golden ratio. However, few implementations of facial beauty assessment were based on 3D facial features. The purpose of this paper is to propose a novel cluster assessment system for facial attractiveness that is characterized by the incorporation of 3D geometric Moiré features with an adjusted fuzzy neural network (FNN). We first extract 3D facial features from images acquired by a 3dMD scanner. Seven Moiré features are employed to represent a 3D facial image. The FNN classifier, taking the Moiré features as the parameters, is then trained and validated against independently conducted attractiveness ratings. A number of diverse referees were invited and offered their attractiveness ratings over a five-item Likert scale for 100 female facial images. The proposed assessment presents a high accuracy rate of 90%, and the area under curve (AUC) computed from the receiver operating characteristic (ROC) curve is 0.95. The results show that the perceptions of facial attractiveness are essentially consensus among raters, and can be mathematically modeled through supervised learning techniques. The high accuracy achieved proves that the proposed FNN classifier can serve as a general, automated and human-like judgment tool for objective classification of female facial attractiveness, and thus has potential applications to the entertainment industry, cosmetic industry, virtual media, and plastic surgery.     

A cluster validity index for fuzzy clustering

A new cluster validity index is proposed for the validation of partitions of object data produced by the fuzzy c-means algorithm. The proposed validity index uses a variation measure and a separation measure between two fuzzy clusters. A good fuzzy partition is expected to have a low degree of variation and a large separation distance. Testing of the proposed index and nine previously formulated indices on well-known data sets shows the superior effectiveness and reliability of the proposed index in comparison to other indices and the robustness of the proposed index in noisy environments.     

Rules discovery in fuzzy classifier systems with PSO for scheduling in grid computational infrastructures

Particle swarm optimization (PSO) is a bio-inspired optimization strategy founded on the movement of particles within swarms. PSO can be encoded in a few lines in most programming languages, it uses only elementary mathematical operations, and it is not costly as regards memory demand and running time. This paper discusses the application of PSO to rules discovery in fuzzy classifier systems (FCSs) instead of the classical genetic approach and it proposes a new strategy, Knowledge Acquisition with Rules as Particles (KARP). In KARP approach every rule is encoded as a particle that moves in the space in order to cooperate in obtaining high quality rule bases and in this way, improving the knowledge and performance of the FCS. The proposed swarm-based strategy is evaluated in a well-known problem of practical importance nowadays where the integration of fuzzy systems is increasingly emerging due to the inherent uncertainty and dynamism of the environment: scheduling in grid distributed computational infrastructures. Simulation results are compared to those of classical genetic learning for fuzzy classifier systems and the greater accuracy and convergence speed of classifier discovery systems using KARP is shown.     

A novel fuzzy classifier with Choquet integral-based grey relational analysis for pattern classification problems

This paper aims to propose a fuzzy classifier, which is a one-class-in-one-network structure consisting of multiple novel single-layer perceptrons. Since the output value of each single-layer perceptron can be interpreted as the overall grade of the relationship between the input pattern and one class, the degree of relationship between an attribute of the input pattern and that of this class can be taken into account by establishing a representative pattern for each class. A feature of this paper is that it employs the grey relational analysis to compute the grades of relationship for individual attributes. In particular, instead of using the sigmoid function as the activation function, a non-additive technique, the Choquet integral, is used as an activation function to synthesize the performance values, since an assumption of noninteraction among attributes may not be reasonable. Thus, a single-layer perceptron in the proposed structure performs the synthetic evaluation of the Choquet integral-based grey relational analysis for a pattern. Each connection weight is interpreted as a degree of importance of an attribute and can be determined by a genetic algorithm-based method. The experimental results further demonstrate that the test results of the proposed fuzzy classifier are better than or comparable to those of other fuzzy or non-fuzzy classification methods.