Max Neural Network Research Articles

Deep Fuzzy Min-Max Neural Network: Analysis and Design.

Fuzzy min-max neural network (FMNN) is one kind of three-layer models based on hyperboxes that are constructed in a sequential way. Such a sequential mechanism inevitably leads to the input order and overlap region problem. In this study, we propose a deep FMNN (DFMNN) based on initialization and optimization operation to overcome these limitations. Initialization operation that can solve the input order problem is to design hyperboxes in a simultaneous way, and side parameters have been proposed to control the size of hyperboxes. Optimization operation that can eliminate overlap region problem is realized by means of deep layers, where the number of layers is immediately determined when the overlap among hyperboxes is eliminated. In the optimization process, each layer consists of three sections, namely, the partition section, combination section, and union section. The partition section aims to divide the hyperboxes into a nonoverlapping hyperbox set and an overlapping hyperbox set. The combination section eliminates the overlap problem of overlapping hyperbox set. The union section obtains the optimized hyperbox set in the current layer. DFMNN is evaluated based on a series of benchmark datasets. A comparative analysis illustrates that the proposed DFMNN model outperforms several models previously reported in the literature.

A flexible enhanced fuzzy min-max neural network for pattern classification

In this paper, the existing enhanced fuzzy min–max (EFMM) neural network is improved with a flexible learning procedure for undertaking pattern classification tasks. Four new contributions are introduced. Firstly, a new training strategy is proposed for avoiding the generation of unnecessary overlapped regions between hyperboxes of different classes. The learning phase is simplified by eliminating the contraction procedure. Secondly, a new flexible expansion procedure is introduced. It eliminates the use of a user-defined parameter (expansion coefficient) to determine the hyperbox sizes. Thirdly, a new overlap test rule is applied during the test phase to identify the containment cases and activate the contraction procedure (if necessary). Fourthly, a new contraction procedure is formulated to overcome the containment cases and avoid the data distortion problem. Both the third and fourth contributions are important for preventing the catastrophic forgetting issue and supporting the stability-plasticity principle pertaining to online learning. The performance of the proposed model is evaluated with benchmark data sets. The results demonstrate its efficiency in handling pattern classification tasks, outperforming other related models in online learning environments.

Accelerated fuzzy min–max neural network and arithmetic optimization algorithm for optimizing hyper-boxes and feature selection

Accelerated fuzzy min–max neural network and arithmetic optimization algorithm for optimizing hyper-boxes and feature selection

Lung cancer subtyping from gene expression data using general and enhanced Fuzzy min–max neural networks

AbstractIn this article, we address the problem of lung cancer diagnosis from gene expression data, which is now recognized as an effective means for early treatment and prevention of cancer. Specifically, we employ Fuzzy min–max (FMM) classifier for the task which is a well‐known neuro‐fuzzy neural network. The idea is to take advantage of the fuzzy class definitions whose boundaries are set using the min–max hyperbox constructed for each class. We implement two advanced FMM neural network architectures: general Fuzzy min–max (GFMM) and enhanced Fuzzy min–max (EFMM) for the classification of lung cancer subtypes from gene expression data. The advantage of GFMM is that it involves very simple operations for hyperbox manipulation, and can handle both labeled and unlabeled data. On the other hand, EFMM proposes three heuristic rules related to hyperbox expansion, contraction and the overlap test, which enhances the learning algorithm. We perform the classification of gene expression data using these two models, and then we analyze the performance by visualizing the hyperboxes obtained after training, and compare the accuracies of these classifiers with the state of the art. Least absolute shrinkage and selection operator (LASSO) is used for selecting the informative genes from the high‐dimensional gene expression data. From the empirical results, we observe that GFMM with LASSO gives the best performance of all, with validation accuracy of 98.04% and cross‐validation accuracy of 94.06%.

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.

Fuzzy min–max neural networks: a bibliometric and social network analysis

Fuzzy min–max neural networks: a bibliometric and social network analysis

A hybrid approach based on mathematical modelling and improved online learning algorithm for data classification

This paper proposes a novel hybrid classifier method using a mixed-integer linear programming (MILP) model and an improved online learning algorithm for general fuzzy min–max neural networks (IOL_GFMM). IOL_GFMM is used to generate initial hyper-boxes for the MILP model in order to improve its efficiency. This paper is the first attempt that integrates the fuzzy min–max neural networks and the MILP model. The applicability of the proposed hybrid model is proven on both real and artificial datasets. Performance evaluation parameters of the novel hybrid classifier are classification accuracy, training time, number of iterations, and number of misclassified data. Results show that the proposed hybrid method provides satisfying improvements in performance evaluation parameters compared with the pure MILP model. Our proposed approach achieves to speed the training time up to 76 times and decreases the number of misclassified data by up to 17 times. Results of artificial datasets show another contribution that the proposed hybrid approach is very efficient in order to classify data samples not only when they belong to separate regions but also when there exists significant overlap.

A compact fuzzy min max network with novel trimming strategy for pattern classification

Hyperbox classifier has large contribution to the field of pattern classification, because of its efficiency and transparency. Hyperbox classifier is efficiently implemented by using fuzzy min–max (FMM) neural network. FMM was modified many times to improve the classification accuracy. Moreover, there still exists a space for increasing the accuracy of hyperbox based classifiers. In this paper, four modifications are proposed to FMM network for increasing the classification accuracy rate. First, centroid and K-highest (CCK) based criteria to select the expandable hyperbox. Second, a new set of overlap test cases to consider all types of overlapping regions. Third, a new set of contraction rules to settle the overlapped regions. Fourth, novel hyperbox trimming strategy to reduce the system complexity. The proposed method is compared with FMM, enhanced FMM (EFMM) and Kn_FMM using five datasets. Experimental results clearly reflect the improved efficiency of proposed method. Proposed FMM (PFMM) network is also used to classify the histopathological images for knowing the best magnifying factor.

Enhancing the scalability of fuzzy rough set approximate reduct computation through fuzzy min–max neural network and crisp discernibility relation formulation

Fuzzy rough sets (FRS) framework is proven to be useful in computing predictive features in the presence of incompleteness and uncertainty in hybrid systems. However, the existing FRS methods for feature subset selection (reduct computation) are not scalable to large datasets due to higher space and time complexities. Towards increasing the scalability of FRS reduct computation, FMNN-FRS approach is proposed earlier, utilizing fuzzy min–max neural network (FMNN) preprocessing to enable reduct computation in fuzzy hyperbox space instead of object space. FMNN-FRS approach considers fuzzy discernibility matrix (DM) for computation of an approximate reduct. However, it is observed that the space utilization of fuzzy DM limits the scalability of FMNN-FRS. To further increase the scalability of FMNN-FRS method by the reduction in the space complexity, in this work, a novel way of crisp DM construction is proposed from the knowledge derived from FMNN preprocessing (CDM-FMFRS). Extended overlapping criteria, with tolerance parameter, are also designed for arriving at the crisp discernibility relation through fuzzy hyperboxes. The proposed CDM-FMFRS approach computes an approximate reduct using SFS strategy on the generated crisp DM. Empirically, the experimental results established that the classifiability of the induced model from the proposed algorithm is similar or better than FMNN-FRS and other state-of-the-art FRS reduct approaches with a significant reduction in computational time. Results also established better scalability achieved by CDM-FMFRS than FMNN-FRS.

A semisupervised learning model based on fuzzy min–max neural networks for data classification

Semisupervised learning (SSL) models are useful for undertaking classification problems with a small set of labeled samples and a large number of unlabeled samples. In this regard, the family of fuzzy min–max (FMM) neural networks offers the capability of online learning for addressing both unsupervised and supervised problems. As such, this paper proposes a novel two-stage SSL model based on FMM networks, denoted SSL–FMM. The first stage employs the unlabeled samples to generate a number of hyperboxes using the unsupervised FMM algorithm, while the second stage uses the labeled samples to associate the generated hyperboxes with their target classes using the supervised FMM algorithm. In addition, a neighborhood-labeling mechanism based on the Euclidean distance and hyperbox centroids is formulated to associate the unlabeled hyperboxes with the most likely target classes. A number of benchmark problems and a real-world case study are employed to evaluate the effectiveness of the proposed SSL–FMM model. The outcome indicates that SSL–FMM is able to use unlabeled samples effectively and improve the FMM performance, producing promising results compared with other SSL methods in the literature.

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.

Improvement of grey wolf optimizer with adaptive middle filter to adjust support vector machine parameters to predict diabetes complications

In medical science, collecting and classifying data from various diseases is a vital task. The confused and large amounts of data are problems that prevent us from achieving acceptable results. One of the major problems for diabetic patients is a failure to properly diagnose the disease. As a result of this mistake in diagnosis or failure in early diagnosis, the patient may suffer from complications such as blindness, kidney failure, and cutting off the toes. Nowadays, doctors diagnose the disease by relying on their experience and knowledge and performing complex and time-consuming tests. One of the problems with current diabetic, diagnostic methods is the lack of appropriate features to diagnose the disease and consequently the weakness in its diagnosis, especially in its early stages. Since diabetes diagnosis relies on large amounts of data with many parameters, it is necessary to use machine learning methods such as support vector machine (SVM) to predict the complications of diabetes. One of the disadvantages of SVM is its parameter adjustment, which can be accomplished using metaheuristic algorithms such as particle swarm optimization algorithm (PSO), genetic algorithm, or grey wolf optimizer (GWO). In this paper, after preprocessing and preparing the dataset for data mining, we use SVM to predict complications of diabetes based on selected parameters of a patient acquired by laboratory test using improved GWO. We improve the selection process of GWO by employing dynamic adaptive middle filter, a nonlinear filter that assigns appropriate weight to each value based on the data value. Comparison of the final results of the proposed algorithm with classification methods such as a multilayer perceptron neural network, decision tree, simple Bayes, and temporal fuzzy min–max neural network (TFMM-PSO) shows the superiority of the proposed method over the comparable ones.

Class label altering fuzzy min-max network and its application to histopathology image database

Hyperbox classifier is efficiently implemented using fuzzy min max neural network, where the input patterns present in the training phase place a vital role. In the training phase, a set of hyperboxes are constructed which are used to classify a testing pattern. A better selection of input patterns of the training set will generate an efficient set of hyperboxes. Inappropriate selection of training samples leads to an erroneous set of hyperboxes, which will degrade the accuracy rate. Therefore, instead of using a single training set an extra training set, secondary training set, may be used to reshuffle the hyperboxes generated during the primary training set. In this paper, we have used a secondary training set to update the hyperboxes generated during the primary training phase. When a secondary training set is used, two cases are arised. First, change the class label of some inefficient hyperboxes created during the primary training phase. Second, fix the class label of efficient hyperboxes to the class allotted during the primary training set. By using the above secondary training set mechanism, a novel class label altering fuzzy min max (CLAFMM) network is proposed to alter the class labels depending on the secondary training set. Experimental results prove that the proposed approach provides more accuracy rate than the FMM, Enhanced FMM and K-nearest FMM. Simultaneously, the proposed approach reduces the complexity of the network by reducing the number of hyperboxes generated by the above said state-of-the-art methods. The proposed method is also applied to the breast cancer histopathological images to identify the best magnifying factor for classification.

A Refined Fuzzy Min–Max Neural Network With New Learning Procedures for Pattern Classification

The fuzzy min–max (FMM) neural network stands as a useful model for solving pattern classification problems. FMM has many important features, such as online learning and one-pass learning. It, however, has certain limitations, especially in its learning algorithm, which consists of the expansion, overlap test, and contraction procedures. This article proposes a refined fuzzy min–max (RFMM) neural network with new procedures for tackling the key limitations of FMM. RFMM has a number of contributions. First, a new expansion procedure for overcoming the problems of overlap leniency and irregularity of hyperbox expansion is introduced . It avoids the overlap cases between hyperboxes from different classes, reducing the number of overlap cases to one (containment case). Second, a new formula that simplifies the original rules in the overlap test is proposed. It has two important features: (i) identifying the overlap leniency problem during the expansion procedure; (ii) activating the contraction procedure to eliminate the containment case. Third, a new contraction procedure for overcoming the data distortion problem and providing more accurate decision boundaries for the contracted hyperboxes is proposed. Fourth, a new prediction strategy that combines both membership function and distance measure to prevent any possible random decision-making during the test stage is proposed. The performance of RFMM is evaluated with the UCI benchmark datasets. The results demonstrate the effectiveness of the proposed modifications in making RFMM a useful model for solving pattern classification problems, as compared with other existing FMM and non-FMM classifiers.

Hyperbox-based machine learning algorithms: a comprehensive survey

With the rapid development of digital information, the data volume generated by humans and machines is growing exponentially. Along with this trend, machine learning algorithms have been formed and evolved continuously to discover new information and knowledge from different data sources. Learning algorithms using hyperboxes as fundamental representational and building blocks are a branch of machine learning methods. These algorithms have enormous potential for high scalability and online adaptation of predictors built using hyperbox data representations to the dynamically changing environments and streaming data. This paper aims to give a comprehensive survey of the literature on hyperbox-based machine learning models. In general, according to the architecture and characteristic features of the resulting models, the existing hyperbox-based learning algorithms may be grouped into three major categories: fuzzy min–max neural networks, hyperbox-based hybrid models and other algorithms based on hyperbox representations. Within each of these groups, this paper shows a brief description of the structure of models, associated learning algorithms and an analysis of their advantages and drawbacks. Main applications of these hyperbox-based models to the real-world problems are also described in this paper. Finally, we discuss some open problems and identify potential future research directions in this field.

Scalable Fuzzy Rough Set Reduct Computation Using Fuzzy Min–Max Neural Network Preprocessing

A fuzzy rough set (FRS) is a hybridization of rough sets and fuzzy sets and provides a framework for reduct (feature subset selection) computation for hybrid decision systems. However, the existing FRS-based feature selection approaches are intractable for large decision systems due to the space complexity of the FRS methodology. We propose a novel fuzzy min–max neural network (FMNN)-FRS reduct computation approach utilizing the FMNN to enhance the scalability of FRS approaches. The FMNN provides a single pass epoch learning of arriving at granules of objects in the form of fuzzy hyperboxes for multiple decision classes. In the proposed approach, the FMNN model is used to reconstruct the object-based decision system into a fuzzy hyperbox-based interval-valued decision system. Then, a novel way of constructing the fuzzy discernibility matrix (FDM) from the interval-valued decision system is introduced. A fuzzy rough approximate reduct computation algorithm is developed with the induced FDM. The FMNN-FRS approach reduces the space complexity of FRS reduct computation significantly and results in enhanced scalability. Comparative experimental analysis has been done with the existing FRS reduct approaches on benchmark hybrid decision systems and established the relevance of the FMNN-FRS approach. The FMNN-FRS approach obtained the exact reduct in most of the datasets in much lesser computational time than existing FRS approaches while preserving similar classification accuracy. The FMNN-FRS method achieved enhanced scalability to such large decision systems, at which it is not possible to obtain reduct by existing FRS approaches.

Medical Data Classification using Fuzzy Main Max Neural Network Preceded by Feature Selection through Moth Flame Optimization

Prediction of the diseases are possible using medical diagnosis system. This type of health care model can be developed using soft computing techniques. Hybrid approaches of data classification and optimization algorithm increases data classification accuracy. This research proposed applications of Moth Flame optimization (MFO) and Fuzzy Min Max Neural Network (FMMNN) for the development of medical data classification system. Here MFO algorithm considers bulk of features from the disease dataset and produces optimized set of features based on fitness function. MFO is able to avoid local minima problem and this is the main cause behind production of optimal set of features. Optimized features are then passed to FMMNN for classification of malignant and benign cases. As classification is concerned, model experiment achieved 97.74% accuracy for Liver Disorders and 86.95 % accuracy for Pima Indian Diabetes dataset. Improving the medical data classification accuracy is directly related to attain good human health.

Breast cancer detection in mammogram image with segmentation of tumour region

In our proposed breast cancer malignant detection study are performed with the aid of fuzzy min max neural network technique. Majority of women's are affected in this breast cancer at a early stage...

Semi-supervised Fuzzy Min–Max Neural Network for Data Classification

Learning from the lack of labeled data is a challenging task which often limits the performance of the classifier. Since the unlabeled data is easy to obtain, using both of the labeled and unlabeled data in the training process provide a way to solve this problem. In this paper, a semi-supervised classification method based on fuzzy min–max neural network (SS-FMM) is proposed. In SS-FMM, the network has been modified for handling both of the labeled and unlabeled data. In addition, the staged feedback process is designed to modify the network structure of the traditional fuzzy min–max neural network. A staged-threshold function designed in SS-FMM, the hyperbox pruning process and the hyperbox relabeling process can be started dynamically. Moreover, the hyperboxes relabeling process and the hyperbox pruning process are designed to maximize using the unlabeled data and control the amount of the hyperboxes. In order to testify the effectiveness of SS-FMM, various experiments are carried out with several benchmark data sets. In addition, SS-FMM has been applied on the internal inspection data of our system. The results show that SS-FMMM has got good performance.

An Improved Fuzzy Min–Max Neural Network for Data Classification

Hyperbox classifier is an efficient tool for modern pattern classification problems due to its transparency and rigorous use of Euclidian geometry. Fuzzy min–max (FMM) network efficiently implements the hyperbox classifier, and has been modified several times to yield better classification accuracy. However, the obtained accuracy is not up to the mark. Therefore, in this paper, a new improved FMM (IFMM) network is proposed to increase the accuracy rate. In the proposed IFMM network, a modified constraint is employed to check the expandability of a hyperbox. It also uses semiperimeter of the hyperbox along with k -nearest mechanism to select the expandable hyperbox. In the proposed IFMM, the contraction rules of conventional FMM and enhanced FMM (EFMM) are also modified using semiperimeter of a hyperbox in order to balance the size of both overlapped hyperboxes. Experimental results show that the proposed IFMM network outperforms the FMM, k- nearest FMM, and EFMM by yielding more accuracy rate with less number of hyperboxes. The proposed methods are also applied to histopathological images to know the best magnification factor for classification.