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 of Simpson (1992, 1993). The GFMM method combines supervised and unsupervised learning in 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. It exhibits a 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 and consists of placing and adjusting the hyperboxes in the pattern space; this is 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

Combining Neuro-Fuzzy Classifiers for Improved Generalisation and Reliability

In this paper a combination of neuro-fuzzy classifiers for improved classification performance and reliability is considered. A general fuzzy min-max (GFMM) classifier with agglomerative learning algorithm is used as a main building block. An alternative approach to combining individual classifier decisions involving the combination at the classifier model level is proposed. The resulting classifier complexity and transparency is comparable with classifiers generated during a single crossvalidation procedure while the improved classification performance and reduced variance is comparable to the ensemble of classifiers with combined (averaged/voted) decisions. We also illustrate how combining at the model level can be used for speeding up the training of GFMM classifiers for large data sets

Learning Hybrid Neuro-Fuzzy Classifier Models From Data: To Combine or Not to Combine?

To combine or not to combine? Though not a question of the same gravity as the Shakespeare’s to be or not to be, it 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 six different algorithm independent learning schemes. Various versions of cross-validation, resampling techniques and data editing approaches, leading to a 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

A Survey of Adaptive Resonance Theory Neural Network Models for Engineering Applications

This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a general picture of the architectures developed by researchers over the past 30 years. The learning dynamics of these ART models are briefly described, and their distinctive characteristics such as code representation, long-term memory and corresponding geometric interpretation are discussed. Useful engineering properties of ART (speed, configurability, explainability, parallelization and hardware implementation) are examined along with current challenges. Finally, a compilation of online software libraries is provided. It is expected that this overview will be helpful to new and seasoned ART researchers

Enabling Explainable Fusion in Deep Learning with Fuzzy Integral Neural Networks

Information fusion is an essential part of numerous engineering systems and biological functions, e.g., human cognition. Fusion occurs at many levels, ranging from the low-level combination of signals to the high-level aggregation of heterogeneous decision-making processes. While the last decade has witnessed an explosion of research in deep learning, fusion in neural networks has not observed the same revolution. Specifically, most neural fusion approaches are ad hoc, are not understood, are distributed versus localized, and/or explainability is low (if present at all). Herein, we prove that the fuzzy Choquet integral (ChI), a powerful nonlinear aggregation function, can be represented as a multi-layer network, referred to hereafter as ChIMP. We also put forth an improved ChIMP (iChIMP) that leads to a stochastic gradient descent-based optimization in light of the exponential number of ChI inequality constraints. An additional benefit of ChIMP/iChIMP is that it enables eXplainable AI (XAI). Synthetic validation experiments are provided and iChIMP is applied to the fusion of a set of heterogeneous architecture deep models in remote sensing. We show an improvement in model accuracy and our previously established XAI indices shed light on the quality of our data, model, and its decisions.Comment: IEEE Transactions on Fuzzy System

Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

A new neural network architecture is introduced for incremental supervised learning of recognition categories and multidimensional maps in response to arbitrary sequences of analog or binary input vectors. The architecture, called Fuzzy ARTMAP, achieves a synthesis of fuzzy logic and Adaptive Resonance Theory (ART) neural networks by exploiting a close formal similarity between the computations of fuzzy subsethood and ART category choice, resonance, and learning. Fuzzy ARTMAP also realizes a new Minimax Learning Rule that conjointly minimizes predictive error and maximizes code compression, or generalization. This is achieved by a match tracking process that increases the ART vigilance parameter by the minimum amount needed to correct a predictive error. As a result, the system automatically learns a minimal number of recognition categories, or "hidden units", to met accuracy criteria. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy logic play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Improved prediction is achieved by training the system several times using different orderings of the input set. This voting strategy can also be used to assign probability estimates to competing predictions given small, noisy, or incomplete training sets. Four classes of simulations illustrate Fuzzy ARTMAP performance as compared to benchmark back propagation and genetic algorithm systems. These simulations include (i) finding points inside vs. outside a circle; (ii) learning to tell two spirals apart; (iii) incremental approximation of a piecewise continuous function; and (iv) a letter recognition database. The Fuzzy ARTMAP system is also compared to Salzberg's NGE system and to Simpson's FMMC system.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI 90-00530); Office of Naval Research (N00014-91-J-4100); Air Force Office of Scientific Research (90-0175

ARTMAP Neural Networks for Information Fusion and Data Mining: Map Production and Target Recognition Methodologies

The Sensor Exploitation Group of MIT Lincoln Laboratory incorporated an early version of the ARTMAP neural network as the recognition engine of a hierarchical system for fusion and data mining of registered geospatial images. The Lincoln Lab system has been successfully fielded, but is limited to target I non-target identifications and does not produce whole maps. Procedures defined here extend these capabilities by means of a mapping method that learns to identify and distribute arbitrarily many target classes. This new spatial data mining system is designed particularly to cope with the highly skewed class distributions of typical mapping problems. Specification of canonical algorithms and a benchmark testbed has enabled the evaluation of candidate recognition networks as well as pre- and post-processing and feature selection options. The resulting mapping methodology sets a standard for a variety of spatial data mining tasks. In particular, training pixels are drawn from a region that is spatially distinct from the mapped region, which could feature an output class mix that is substantially different from that of the training set. The system recognition component, default ARTMAP, with its fully specified set of canonical parameter values, has become the a priori system of choice among this family of neural networks for a wide variety of applications.Air Force Office of Scientific Research (F49620-01-1-0397, F49620-01-1-0423); Office of Naval Research (N00014-01-1-0624

Fuzzy ART: Fast Stable Learning and Categorization of Analog Patterns by an Adaptive Resonance System

A Fuzzy ART model capable of rapid stable learning of recognition categories in response to arbitrary sequences of analog or binary input patterns is described. Fuzzy ART incorporates computations from fuzzy set theory into the ART 1 neural network, which learns to categorize only binary input patterns. The generalization to learning both analog and binary input patterns is achieved by replacing appearances of the intersection operator (n) in AHT 1 by the MIN operator (Λ) of fuzzy set theory. The MIN operator reduces to the intersection operator in the binary case. Category proliferation is prevented by normalizing input vectors at a preprocessing stage. A normalization procedure called complement coding leads to a symmetric theory in which the MIN operator (Λ) and the MAX operator (v) of fuzzy set theory play complementary roles. Complement coding uses on-cells and off-cells to represent the input pattern, and preserves individual feature amplitudes while normalizing the total on-cell/off-cell vector. Learning is stable because all adaptive weights can only decrease in time. Decreasing weights correspond to increasing sizes of category "boxes". Smaller vigilance values lead to larger category boxes. Learning stops when the input space is covered by boxes. With fast learning and a finite input set of arbitrary size and composition, learning stabilizes after just one presentation of each input pattern. A fast-commit slow-recode option combines fast learning with a forgetting rule that buffers system memory against noise. Using this option, rare events can be rapidly learned, yet previously learned memories are not rapidly erased in response to statistically unreliable input fluctuations.British Petroleum (89-A-1204); Defense Advanced Research Projects Agency (90-0083); National Science Foundation (IRI-90-00530); Air Force Office of Scientific Research (90-0175