General Fuzzy Min-max Neural Network Research Articles

An online learning algorithm for a neuro-fuzzy classifier with mixed-attribute data

General fuzzy min–max neural network (GFMMNN) is one of the efficient neuro-fuzzy systems for data classification. However, one of the downsides of its original learning algorithms is the inability to handle and learn directly from mixed-attribute data without using encoding techniques. While categorical feature encoding methods can be used with the GFMMNN learning algorithms, they exhibit many shortcomings. Other improved approaches proposed in the literature are not suitable for online learning algorithms working in the dynamically changing environments without ability to retrain or access full historical data, which are usually required for many real world applications. This paper proposes an extended online learning algorithm for the GFMMNN. The proposed method can handle the datasets with both continuous and categorical features. It uses the change in the entropy values of categorical features of the samples contained in a hyperbox to determine if the current hyperbox can be expanded to include the categorical values of a new training instance. An extended architecture of the original GFMMNN and its new membership function are introduced for mixed-attribute data. Important mathematical properties of the proposed learning algorithms are also presented and proved in this paper. The extensive experiments confirmed superior and stable classification performance of the proposed approach in comparison to other relevant learning algorithms for the GFMM model.

An in-depth comparison of methods handling mixed-attribute data for general fuzzy min–max neural network

A general fuzzy min–max (GFMM) neural network is one of the efficient neuro-fuzzy systems for classification problems. However, a disadvantage of most of the current learning algorithms for GFMM is that they can handle effectively numerical valued features only. Therefore, this paper provides some potential approaches to adapting GFMM learning algorithms for classification problems with mixed-type or only categorical features as they are very common in practical applications and often carry very useful information. We will compare and assess three main methods of handling datasets with mixed features, including the use of encoding methods, the combination of the GFMM model with other classifiers, and employing the specific learning algorithms for both types of features. The experimental results showed that the target and James–Stein are appropriate categorical encoding methods for learning algorithms of GFMM models, while the combination of GFMM neural networks and decision trees is a flexible way to enhance the classification performance of GFMM models on datasets with the mixed features. The learning algorithms with the mixed-type feature abilities are potential approaches to deal with mixed-attribute data in a natural way, but they need further improvement to achieve a better classification accuracy. Based on the analysis, we also identify the strong and weak points of different methods and propose potential research directions.

Accelerated learning algorithms of general fuzzy min-max neural network using a novel hyperbox selection rule

This paper proposes a method to accelerate the training process of general fuzzy min-max neural network. The purpose is to reduce the unsuitable hyperboxes selected as the potential candidates of the expansion step of existing hyperboxes to cover a new input pattern in the online learning algorithms or candidates of the hyperbox aggregation process in the agglomerative learning algorithms. Our proposed approach is based on the mathematical formulas to form a new solution aiming to remove the hyperboxes which are certain not to satisfy expansion or aggregation conditions, and in turn decreasing the training time of learning algorithms. The efficiency of the proposed method is assessed over a number of widely used data sets. The experimental results indicated the significant decrease in training time of proposed approach for both online and agglomerative learning algorithms. Notably, the training time of the online learning algorithms is reduced from 1.2 to 12 times when using the proposed method, while the agglomerative learning algorithms are accelerated from 7 to 37 times on average.

A comparative study of general fuzzy min-max neural networks for pattern classification problems

General fuzzy min-max (GFMM) neural network is a generalization of fuzzy neural networks formed by hyperbox fuzzy sets for classification and clustering problems. Two principle algorithms are deployed to train this type of neural network, i.e., incremental learning and agglomerative learning. This paper presents a comprehensive empirical study of performance influencing factors, advantages, and drawbacks of the general fuzzy min-max neural network on pattern classification problems. The subjects of this study include (1) the impact of maximum hyperbox size, (2) the influence of the similarity threshold and measures on the agglomerative learning algorithm, (3) the effect of data presentation order, (4) comparative performance evaluation of the GFMM with other types of fuzzy min-max neural networks and prevalent machine learning algorithms. The experimental results on benchmark datasets widely used in machine learning showed overall strong and weak points of the GFMM classifier. These outcomes also informed potential research directions for this class of machine learning algorithms in the future.

Extracting the Classification Rules from General Fuzzy Min-Max Neural Network

The general fuzzy min-max neural network (GFMMN) is capable to perform the classification as well as clustering of the data. In addition to this it has the ability of learning in a very few passes with a very short training time. But like other artificial neural networks, GFMMN is also like a black box and expressed in terms of min-max values and associated class label. So the justification of classification results given by GFMMN is required to be obtained to make it more adaptive to the real world applications. This paper proposes the model to extract classification rules from trained GFMMN. These rules justify the classification decision given by GFMMN. For this GFMMN is trained for the appropriate value of . The min-max values of all the hyperboxes are quantized and these are expresses in the form of rules. Each rule represent the the kind of patteres falling in that hyperbox. These rules are readable and represents the trained network. Experiments are conducted on eight different benchmark datasets obtained from UCI machine learning repository. These results prove the applicability of the proposed method.

Data Mining using Modified GFMM Neural Network

The fuzzy neural networks are adaptive, learns quickly and are highly suitable in decision making where uncertainty is involved. In this paper the Modified General Fuzzy Min-Max Neural Network (MGFMMNN) is described which is experimented for the data mining tasks such as classification and clustering. The MGFMMNN utilizes fuzzy sets as pattern classes in which each fuzzy set is a union of fuzzy set hyperboxes. It is an extension of the general fuzzy min-max (GFMM) neural network proposed by Gabrys and Bargiala. The data mining tasks such as classification and clustering have been studied using MGFMMNN and Fisher Iris data set. Further, MGFMMNN is trained using Hepatitis Data Set to verify its classification and recognition ability. The results obtained are awfully persuading and confirms the effectiveness of the proposed system. The technique proposed is quick and reliably deployable in the applications that need classification and clustering. General Terms Data Mining, Fuzzy Systems, Neural Networks, Pattern Recognition.

Decision support system for water distribution systems based on neural networks and graphs theory for leakage detection

This paper presents an efficient and effective decision support system (DSS) for operational monitoring and control of water distribution systems based on a three layer General Fuzzy Min–Max Neural Network (GFMMNN) and graph theory. The operational monitoring and control involves detection of pipe leakages. The training data for the GFMMNN is obtained through simulation of leakages in a water network for a 24h operational period. The training data generation scheme includes a simulator algorithm based on loop corrective flows equations, a Least Squares (LS) loop flows state estimator and a Confidence Limit Analysis (CLA) algorithm for uncertainty quantification entitled Error Maximization (EM) algorithm. These three numerical algorithms for modeling and simulation of water networks are based on loop corrective flows equations and graph theory. It is shown that the detection of leakages based on the training and testing of the GFMMNN with patterns of variation of nodal consumptions with or without confidence limits produces better recognition rates in comparison to the training based on patterns of nodal heads and pipe flows state estimates with or without confidence limits. It produces also comparable recognition rates to the original recognition system trained with patterns of data obtained with the LS nodal heads state estimator while being computationally superior by requiring a single architecture of the GFMMNN type and using a small number of pattern recognition hyperbox fuzzy sets built by the same GFMMNN architecture. In this case the GFMMNN relies on the ability of the LS loop flows state estimator of making full use of the pressure/nodal heads measurements existent in a water network.

Data-Core-Based Fuzzy Min–Max Neural Network for Pattern Classification

A fuzzy min-max neural network based on data core (DCFMN) is proposed for pattern classification. A new membership function for classifying the neuron of DCFMN is defined in which the noise, the geometric center of the hyperbox, and the data core are considered. Instead of using the contraction process of the FMNN described by Simpson, a kind of overlapped neuron with new membership function based on the data core is proposed and added to neural network to represent the overlapping area of hyperboxes belonging to different classes. Furthermore, some algorithms of online learning and classification are presented according to the structure of DCFMN. DCFMN has strong robustness and high accuracy in classification taking onto account the effect of data core and noise. The performance of DCFMN is checked by some benchmark datasets and compared with some traditional fuzzy neural networks, such as the fuzzy min-max neural network (FMNN), the general FMNN, and the FMNN with compensatory neuron. Finally the pattern classification of a pipeline is evaluated using DCFMN and other classifiers. All the results indicate that the performance of DCFMN is excellent.

A Granular Reflex Fuzzy Min–Max Neural Network for Classification

Granular data classification and clustering is an upcoming and important issue in the field of pattern recognition. Conventionally, computing is thought to be manipulation of numbers or symbols. However, human recognition capabilities are based on ability to process nonnumeric clumps of information (information granules) in addition to individual numeric values. This paper proposes a granular neural network (GNN) called granular reflex fuzzy min-max neural network (GrRFMN) which can learn and classify granular data. GrRFMN uses hyperbox fuzzy set to represent granular data. Its architecture consists of a reflex mechanism inspired from human brain to handle class overlaps. The network can be trained online using granular or point data. The neuron activation functions in GrRFMN are designed to tackle data of different granularity (size). This paper also addresses an issue to granulate the training data and learn from it. It is observed that such a preprocessing of data can improve performance of a classifier. Experimental results on real data sets show that the proposed GrRFMN can classify granules of different granularity more correctly. Results are compared with general fuzzy min-max neural network (GFMN) proposed by Gabrys and Bargiela and with some classical methods.

A Fuzzy Min-Max Neural Network Classifier With Compensatory Neuron Architecture

This paper proposes a fuzzy min-max neural network classifier with compensatory neurons (FMCNs). FMCN uses hyperbox fuzzy sets to represent the pattern classes. It is a supervised classification technique with new compensatory neuron architecture. The concept of compensatory neuron is inspired from the reflex system of human brain which takes over the control in hazardous conditions. Compensatory neurons (CNs) imitate this behavior by getting activated whenever a test sample falls in the overlapped regions amongst different classes. These neurons are capable to handle the hyperbox overlap and containment more efficiently. Simpson used contraction process based on the principle of minimal disturbance, to solve the problem of hyperbox overlaps. FMCN eliminates use of this process since it is found to be erroneous. FMCN is capable to learn the data online in a single pass through with reduced classification and gradation errors. One of the good features of FMCN is that its performance is less dependent on the initialization of expansion coefficient, i.e., maximum hyperbox size. The paper demonstrates the performance of FMCN by comparing it with fuzzy min-max neural network (FMNN) classifier and general fuzzy min-max neural network (GFMN) classifier, using several examples.

Learning hybrid neuro-fuzzy classifier models from data: to combine or not to combine?

To combine or not to combine? This very important question is examined in this paper in the context of a hybrid neuro-fuzzy pattern classifier design process. A general fuzzy min–max neural network with its basic learning procedure is used within five different algorithm-independent learning schemes. Various versions of cross-validation and resampling techniques, leading to generation of a single classifier or a multiple classifier system, are scrutinised and compared. The classification performance on unseen data, commonly used as a criterion for comparing different competing designs, is augmented by further four criteria attempting to capture various additional characteristics of classifier generation schemes. These include: the ability to estimate the true classification error rate, the classifier transparency, the computational complexity of the learning scheme and the potential for adaptation to changing environments and new classes of data. One of the main questions examined is whether and when to use a single classifier or a combination of a number of component classifiers within a multiple classifier system.

Neuro-fuzzy approach to processing inputs with missing values in pattern recognition problems

An approach to dealing with missing data, both during the design and normal operation of a neuro-fuzzy classifier is presented in this paper. Missing values are processed within a general fuzzy min–max neural network architecture utilising hyperbox fuzzy sets as input data cluster prototypes. An emphasis is put on ways of quantifying the uncertainty which missing data might have caused. This takes a form of classification procedure whose primary objective is the reduction of a number of viable alternatives rather than attempting to produce one winning class without supporting evidence. If required, the ways of selecting the most probable class among the viable alternatives found during the primary classification step, which are based on utilising the data frequency information, are also proposed. The reliability of the classification and the completeness of information is communicated by producing upper and lower classification membership values similar in essence to plausibility and belief measures to be found in the theory of evidence or possibility and necessity values to be found in the fuzzy sets theory. Similarities and differences between the proposed method and various fuzzy, neuro-fuzzy and probabilistic algorithms are also discussed. A number of simulation results for well-known data sets are provided in order to illustrate the properties and performance of the proposed approach.

Speech Recognition using Modular General Fuzzy Min-Max Neural Network

In this paper, we propose the Modular General Fuzzy, Min-Max Neural Network (MMGFMM). MMGFMM contains number of modules of Modified General Fuzzy Min-Max Neural Network (MGFMM). In MGFMM, the transfer function of output layer of General Fuzzy Min-Max Neural Network (GFMM) is modified. The performance of GFMM, MGFMM and MMGFMM to recognition of spoken Marathi (Language spoken in the state of Maharashtra, India) digits is reported. MMGFMM has shown better average recognition accuracy compared to GFMM by 15.1% in speaker dependent mode and by 11.9% in speaker independent mode.

Agglomerative Learning Algorithms for General Fuzzy Min-Max Neural Network

In this paper two agglomerative learning algorithms based on new similarity measures defined for hyperbox fuzzy sets are proposed. They are presented in a context of clustering and classification problems tackled using a general fuzzy min-max (GFMM) neural network. The proposed agglomerative schemes have shown robust behaviour in presence of noise and outliers and insensitivity to the order of training patterns presentation. The emphasis is also put on the complimentary features to the previously presented incremental learning scheme more suitable for on-line adaptation and dealing with large training data sets. The performance and other properties of the agglomerative schemes are illustrated using a number of artificial and real-world data sets.

General fuzzy min-max neural network for clustering and classification

This paper describes a general fuzzy min-max (GFMM) neural network which is a generalization and extension of the fuzzy min-max clustering and classification algorithms developed by Simpson. The GFMM method combines the supervised and unsupervised learning within a single training algorithm. The fusion of clustering and classification resulted in an algorithm that can be used as pure clustering, pure classification, or hybrid clustering classification. This hybrid system exhibits an interesting property of finding decision boundaries between classes while clustering patterns that cannot be said to belong to any of existing classes. Similarly to the original algorithms, the hyperbox fuzzy sets are used as a representation of clusters and classes. Learning is usually completed in a few passes through the data and consists of placing and adjusting the hyperboxes in the pattern space which is referred to as an expansion-contraction process. The classification results can be crisp or fuzzy. New data can be included without the need for retraining. While retaining all the interesting features of the original algorithms, a number of modifications to their definition have been made in order to accommodate fuzzy input patterns in the form of lower and upper bounds, combine the supervised and unsupervised learning, and improve the effectiveness of operations. A detailed account of the GFMM neural network, its comparison with the Simpson's fuzzy min-max neural networks, a set of examples, and an application to the leakage detection and identification in water distribution systems are given.

Neural Networks Based Decision Support in Presence of Uncertainties

This paper addresses the problem of efficient and effective interpretation of water distribution network state estimates that are typically calculated on the basis of measurements and pseudomeasurements (consumption estimates) that have significant uncertainties associated with them. The task of the system state interpretation is particularly relevant to the diagnosis of leakages and other operational faults occurring in water distribution networks. A new approach, based on the examination of patterns of state estimates by a general fuzzy min-max neural network (GFMM) has been proposed and evaluated. The GFMM classification and clustering has been incorporated into a two-level fault diagnosis system. The proposed diagnostic procedure builds on the concept of confidence limit analysis of state estimates and estimation residuals. An extensive leakage detection and identification study in a small test system for a complete 24-h period of operation has been carried out. An analogy between the information processing by the GFMM and by human operators has been identified and highlighted in this context.