P. K. Simpson, "Fuzzy min--max neural networks---Part 2: Clustering," IEEE Trans. Fuzzy Syst., vol. 1, pp. 32--45, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... synergy of fuzzy sets and neural networks is multifaceted and center on the coherent treatment of data and knowledge processing: neural networks concentrate on detailed numeric processing [3,4] whereas fuzzy sets focus on granular computing thereby being positioned at the logic end of processing [2,5,13,14,17,18,19,20,21]. This point of view has resulted in a vast array of neumfuzzy systems topologies. There is also another stream of research of fuzzy neurocompufing that focuses on the synergy between (fuzzy) logic and geometry. In this combination, low end geometric constructs operate on numerical entities and ....

P.K. Simpson, "Fuzzy min-max neural networks - Part2: Clustering", IEEE Trans Neural Networks 4 32-45, 1993.

....rules from available data. In this sense, neural networks provide a means to automatic construction of the fuzzy rule set due to their self organizing properties. Several neuro fuzzy systems have been proposed in the literature, and successfully applied to different engineering problems [11] 14] [15]. Fuzzy ARTMAP [6] is a modification of ARTMAP architecture that introduces some basic principles of fuzzy logic. However, the main motivation of this change was to allow ARTMAP architecture to work with analog input patterns. In this sense, although Fuzzy ARTMAP could be used for the automatic ....

P. Simpson, "Fuzzy Min-Max neural networks, part 2: clustering," IEEE Trans. on Fuzzy Systems, Vol. 1, No. I, Feb. 1993, pp. 32-45.

.... G(x=a) x Gamma , in which case dG(x=a) dx Sigma = G(x=a) x . 2. 1 Other gradient descent techniques In the fuzzy neural research literature [ Buckley and Hayashi, 1994; Gupta and Rao, 1994; Ishibuchi et al. 1993; Keller et al. 1992; Mitra and Pal, 1994; Pedrycz, 1993; Simpson, 1992; Simpson, 1993 ] many ad hoc gradient descent techniques for max min functions have been proposed. Some suggested using simple intuition based heuristics. Yet others side stepped the differentiability problem by replacing a max min function with a differentiable one, for example by replacing the max and min ....

.... C 0 (x 0 ) 3 A Fuzzy Neural Network Model The synthesis of fuzzy logic and neural networks has been a popular theme in research in the past decade [ Buckley and Hayashi, 1994; Gupta and Rao, 1994; Ishibuchi et al. 1993; Keller et al. 1992; Mitra and Pal, 1994; Pedrycz, 1993; Simpson, 1992; Simpson, 1993 ] This is not surprising considering that neural networks and fuzzy logic complement each other. Neural networks are well known for their learning capabilities, which allow them to model accurately almost any input output relationship. Fuzzy logic, on the other hand, facilitates the encoding of ....

Simpson P.K. (1993) "Fuzzy Min Max Neural Networks - Part 2: Clustering". IEEE Transactions on Neural Networks, Vol.1, No.1, pp.32-45.

....executed is selected [10] The most widely used model of action selection network is the multilayer perceptron with stochastic output units. Other types of networks have also been proposed belonging to the neurofuzzy family like the fuzzy ART network [11] In [9] the fuzzy min max neural network [13, 14] has been proposed as a model for the action network in the case of reinforcement problems with discrete action space. The operation of the network was suitably adapted in order to be able to cope with the specific requirements imposed by the reinforcement learning framework. For this reason, the ....

P. K. Simpson, "Fuzzy Min-Max Neural Networks-Part 2: Clustering", IEEE Trans. on Fuzzy Systems, vol. 1, no. 1, pp. 32-45, 1993.

....spaces. Zadeh [16] points out that using a non grid oriented set of rules leads to a relatively small number of fuzzy rules to characterize a complex relationship between two or more variables. An approach that tries to find individual fuzzy hyperboxes via a growth process was proposed in [17] [18] but the generation of the rule set depends heavily on the order of training examples which has to be controlled carefully to achieve satisfactory performance. In this paper a constructive approach is presented that addresses the problem of deriving a fuzzy rule base directly from observations. ....

Patrick K. Simpson, "Fuzzy min-max neural networks -- part 2: Clustering", IEEE Transactions on Fuzzy Systems, vol. 1, no. 1, pp. 32--45, Jan. 1993.

....reported in the literature, each one demonstrating unique and interesting features. This paper presents a comparative study of four of them, all potentially suitable for solving very high throughput clustering problems. They are the Fuzzy Adaptive Resonance Theory [7] Fuzzy Min Max Clustering [8], Integrated Adaptive Fuzzy Clustering [9] and Self Organizing Feature Mapping [10] The performance of these four neural networks is examined from three points of view clustering quality, convergence time, and computational complexity. Indeed, in many practical applications, the accuracy of ....

....they can cluster patterns autonomously, in most cases without prior knowledge of the number of categories. Moreover, they do not require long term storage of the input patterns, and permit adaptive determination of the shape, size, number, and placement of categories, while operating in parallel [8]. Self organizing neuro fuzzy networks have recently been developed, where fuzzy logic concepts are integrated into the SONN framework. Categories are then modeled as fuzzy sets that allow encoding the input scene s vagueness [20] An important familly of SONNs is derived from the basic idea of ....

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P. Simpson, "Fuzzy Min-Max Neural Networks - Part2: Clustering", IEEE Transactions on Fuzzy Systems, Vol. 1, No. 1, pp. 32-45, 1993.

....data set on line; 2) they can create new output nodes (categories) incrementally; and (3) they do not suffer from the problem of forgetting previously learned categories if the environment changes. Usually, an unknown input scene is very complex and may exhibit a hierarchical structure [5 7]. If input data contain structural relationships, a single layer of output nodes in traditional self organizing neural networks [1,2,4,8] is definitely not sufficient to reveal their hierarchical characteristics. In order to make the scheme more flexible and powerful, Bartfai proposed a ....

P. K. Simpson, "Fuzzy Min-Max Neural Networks-Part 2: Clustering", IEEE Transactions on Fuzzy Systems, vol. 1, no. 1, pp. 32--45, Feb. 1993.

....visual stimuli (observations) into perceived objects which are separated from their background [16] For our purpose the problem of perceptual grouping can be described by considering the set of points shown in Fig. 1, hereafter referred to as Simpson s data set, consisting of 24 vectors [17]. Typically, different human observers would provide different partitions of the Simpson data set. This means that perceptual grouping is an ill posed problem which allows different (subjective) solutions depending on vi the state of (subjective) prior world knowledge. This view is consistent ....

P. Simpson, "Fuzzy min-max neural networks - Part 2: clustering," IEEE Trans. Fuzzy Systems, 1(1), pp. 32-45, 1993.

....to the class of ecological nets. 7 On fuzzy clustering algorithms A clustering algorithm performs unsupervised detection of statistical regularities in a random sequence of input patterns. Our attention is focused on fuzzification of clustering learning schemes. In the definition presented in [8], it is stated that an artificial Neural Network (NN) model performs fuzzy clustering when it allows a pattern to belong to multiple categories to different degrees depending on the neurons ability to recognize the input pattern. This approach is well known in the traditional field of coding ....

....the winning cluster but also affects all cluster centers depending on their proximity to the input pattern [9] In general, soft competitive learning decreases dependency on initialization and reduces the presence of dead units [27] We observe that: 1. The fuzzy clustering definition provided in [8] is equivalent to the definition of the soft competitive adaptation rule traditionally employed in the field of data compression [9] i.e. a clustering algorithm is termed fuzzy clustering algorithm iff it employs a soft competitive (non crisp) parameter adaptation strategy. 2. As a corollary of ....

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P. K. Simpson,"Fuzzy Min-Max neural network-Part 2: Clustering," IEEE Trans. on Fuzzy Systems, vol. 1, no. 1, pp. 32-45, 1993.

....the modification of its definition and operation in order to deal with the discrete dimensions. Experimental results using the modified model on a difficult pattern recognition problem establishes the strengths and weaknesses of the proposed approach. INTRODUCTION Fuzzy min max neural networks [2, 3] consitute one of the many models of computational intelligence that have been recently developed from research efforts aiming at synthesizing neural networks and fuzzy logic [1] The fuzzy min max classification neural network [2] is an on line supervised learning classifier that is based on ....

....maximum values v ji and w ji respectively (j = 1; K, i = 1; n) Let al..so c k denote the class label associated with hyperbox B k . When the h th input pattern A h = a h1 ; a hn ) is presented to the network, the corresponding membership function for hyperbox B j is ([3]) b j (A h ) 1 n n X i=1 [1 Gamma f(a hi Gamma w ji ; fl) Gamma f(v ji Gamma a hi ; fl) 1) where f(x; fl) xfl, if 0 xfl 1, f(x; fl) 1 if xfl 1 and f(x; fl) 0 if xfl 0. If the input pattern A h falls inside the hyperbox B j then b j (A h ) 1, otherwise the membership ....

P. K. Simpson, "Fuzzy Min-Max Neural Networks-Part 2: Clustering, " IEEE Trans. on Fuzzy Systems, vol. 1, No. 1, pp. 32-45, February 1993.

....r pred . If r Gamma r pred 0 then weights are modified to increase the probability p j , otherwise they are modified to decrease the probability p j . In this letter, we present an approach to reinforcement learning problems with discrete action space where the fuzzy min max neural network [1, 2] is employed as a model for the action network. The fuzzy min max network is suitably adapted in order to be able to cope with the specific requirements imposed by the reinforcement learning framework. The proposed method constitutes an attempt to use a local learning technique (based on ....

....against the approaches based on feedforward networks with Bernoulli output units. Of course, other on line supevised local learning techniques could also have been employed and adapted to fit to the reinforcement framework. 2 The Proposed Action Selection Network Fuzzy min max neural networks [1, 2] consitute one of the many models of computational intelligence that have been developed in recent years from research efforts aiming at synthesizing neural networks and fuzzy logic. The fuzzy min max classification neural network [1, 3] is an on line supervised learning classifier that is based ....

P. K. Simpson, "Fuzzy Min-Max Neural Networks-Part 2: Clustering", IEEE Trans. on Fuzzy Systems, vol. 1, no. 1, pp. 32-45, 1993.

....decision by which we can associate a pattern with more than one class. B. Clustering Simpson has also presented a related technique for clustering that uses groups of fuzzy hyperboxes to represent pattern clusters. The details are almost analogous to his classification scheme and can be found in [31]. Hyperboxes, defined by pairs of min max points, and their membership functions are used to define fuzzy subsets of the ndimensional pattern space. The pattern clusters are represented by these hyperboxes. The bulk of the processing of this algorithm involves the finding and fine tuning of the ....

P.K. Simpson, "Fuzzy Min-Max Neural Networks--Part 2: Clustering, " IEEE Transactions on Fuzzy Systems,, vol. vol.1, no. 1, pp. pp.32--45, 1993. 13

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P. K. Simpson, "Fuzzy min--max neural networks---Part 2: Clustering," IEEE Trans. Fuzzy Syst., vol. 1, pp. 32--45, 1993.

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P. K. Simpson, "Fuzzy min-max neural network---part 2: Clustering," IEEE Transactions on Fuzzy Systems, vol. 1, pp. 32--45, 1993.

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