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Extreme learning machine (ELM) has attracted attentions in pattern classification problems due to its preferences in low computations and high generalization. To overcome its drawbacks, caused by the randomness of input weights and biases, the ensemble of ELMs was proposed. The diversity of ELMs forming the ensemble was studied broadly in the literature, via using different activation functions and/or different number of hidden neurons. However, less attention was paid to aggregation mechanism in ensemble of ELMs. To speed up this aggregation process, we propose an ensemble framework for ELMs, called extreme ensemble of ELMs (EEoELMs) because of its extreme speed in ensemble process. In this framework, the input weights of each ELM are randomly pre‐assigned as usual. The ELMs make use of the same/distinct activation functions to increase the diversity of classifiers and so the generalization of ensemble. The output weights of each ELM are set using Moore–Penrose inverse method. However, the aggregation mechanism in EEoELM is novel. Instead of using majority/weighted voting on the prediction results of ELMs, their output neurons are combined in a new decision/ensemble layer. The output of this layer determines the ensemble output. As the weights of this decision layer are also computed using Moore–Penrose inverse method, the ensemble is extremely fast. Experimental results on synthetic and real‐world datasets indicate the acceptable classification performance of EEoELM in much less computational efforts. [ABSTRACT FROM AUTHOR]

In traditional fuzzy classification systems, learning is done from a stationary data distribution. In online rule learning, however, data are non-stationary and change dynamically over time. It confronts the learning process with some new challenges including concept drift. Evolving fuzzy schemes are common solutions in this field which try to handle these issues by in-time modification of their structures. In this regard, a basic challenge is how to apply a fast and simple scheme to modify the rule-base regarding each new sample. This paper introduces an efficient adaptive mechanism named adaptive fuzzy classifier based on gradient descent (AFCGD) for online learning of an evolving fuzzy model. We derive online rule update formulas for modification of the classifier's structure regarding the concept of data to minimize the misclassification error through gradient descent. The updating formulas, which are computationally cheap, allow AFCGD to adjust the rule-base after emergence of new incoming sample. Therefore, it always remains up-to-date and can handle any alteration in the concept of data. AFCGD has simple structure to build; thus, it is so effective in memory usage and computational time. The efficacy of our proposed algorithm has been assessed by some synthetic data and several real-world benchmark problems while comparing with some recent evolving and state-of-the-art classifiers. The proposed method achieves comparable and even better results against other fuzzy and non-fuzzy classifiers in terms of accuracy and run-time. [ABSTRACT FROM AUTHOR]

Edge detection is one of the most important preprocessing operations needed for detection and extraction of objects in scene, especially in the field of machine vision. Since the nature of image data is indeterminate and the edges of an object in an image are not very clear and occasionally transition from scene pixels to object ones occurs moderately, so fuzzy reasoning is able to extract useful attributes from approximate and incomplete data and improve the task of edge detection. In this paper a heuristic fuzzy rule-based algorithm for detecting the edge patterns in an image is presented. The Heuristic Fuzzy Edge Detector, HFED, uses three features from a 3 by 3 window size for each central pixel surrounded by its eight neighbors, to classify that pixel as part of an edge or as non-edge patterns. The fuzzy inference system use these features for classification and because of interpolative operation of fuzzy reasoning, the results are comparable with other well-known edge detector, especially in degraded images. [ABSTRACT FROM AUTHOR]