F.L. Chung, T. Lee, Fuzzy competitive learning, Neural Netw. 7 (3) (1994) 539--551.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....all the neurones. With this general structure, various learning algorithms have been designed and developed such as Kohonen s self organizing feature mapping [10,13,18,33,52,70] competitive learning [1,54,55,65] frequency sensitive competitive learning [1,10] fuzzy competitive learning [11,31,32], general learning [25,49] and distortion equalized fuzzy competitive learning [7] and PVQ (predictive VQ) neural networks [46] Let W (t) be the weight vector of the ith neurone at the tth iteration, the basic competitive learning algorithm can be summarized as follows: z 1 d(x, ....

....= t) 0 otherwise, 2.18) t)##(x = t) z , 2.19) where d(x, # (t) is the distance in the metric between the input vector x and the coupling weight vector = # (t) #w ## #; K p#p; # is the learning rate, and z is its output. A so called under utilization problem [1,11] occurs in competitive learning which means some of the neurones are left out of the learning process and never win the competition. Various schemes are developed to tackle this problem. Kohonen selforganizing neural network [10,13,18] overcomes the problem by updating the winning neurone as well ....

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F.L. Chung, T. Lee, Fuzzy competitive learning, Neural Networks 7 (3) (1994) 539}551.

....processing structures that operate in together to reach an outcome, often they require the use of a learning phase to train the network prior to its use. Certain problems that are difficult or impractical to solve using traditional programming techniques can be easily tackled in a neural network [10]. A number of neural networks exist; Jiang [11] describes many Neural Network variants for image applications, among which the competitive learning model can be regarded as the most important foundations for all neural networks applied to image compression. The use of the network for image ....

....Networks, the competitive learning network contains neurones, interconnections and weights. The layout of the neural network used to solve the image indexing problem can be illustrated in Figure 1, loosely based on the classic general competitive learning algorithm as described by Chung and Lee [10]. The competitive learning network designed for indexing consists of two layers, the input and output. This particular design contains no interconnections to maximise calculation speed. This partially connected network runs un supervised, automatically train ing itself as it processes the image ....

F Chung and T Lee, "Fuzzy Competitive Learning", Neural Networks Volume 7 No 3, 1994.

....distribution [9] To this end the proposed system uses the coefficient information to describe the content of the complete image and form an indexing key. Certain problems that are difficult or impractical to solve using traditional programming techniques can be easily tackled in a neural network [10]. A number of neural networks exist; Jiang [11] describes many Neural Network variants for image applications, among which the competitive learning model can be regarded as the most important foundation for all neural networks applied to image compression. The use of the network for image indexing ....

F Chung and T Lee, "Fuzzy Competitive Learning", Neural

....voxels. After each iteration, if two sets belonging to the same neuron contains neighbor voxels, these sets are merged together. B. Network Convergence The energy function of the proposed CSSOFM is always convergent during the network evolution. The proof is similar to the one presented by Lee [56] for the traditional unsupervised competitive learning algorithm. The network minimizes an energy function F(W) given by N N N K kma 2 F(w) Z Z w )11 (4:3) x ly lz lk 1 j 1 where km,x is the number of sets associated with neuron k and Vj k is the binary state if Af(x,y,z) Qw b. ....

F. L. Lee and T. Lee "Fuzzy competitive learning," Neural Networks, vol. 7(3), pp. 539-551, 1994.

....that is introduced when using competitive learning is that of an initial overassignment of the larger clusters. This problem is solved by incorporating a frequency sensitive term. Hard clustering as well as fuzzy clustering versions exist of the k means [17 19] and competitive learning algorithm [20]. By simple extension, a fuzzy version of the ellipsoidal competitive learning technique will be introduced. 2 The problem of texture segmentation has been studied for many years [21] We choose to apply the proposed algorithm to the problem of texture segmentation, for the following reasons. On ....

.... #v k (t 1) #v k (t) #(t)u q ik (#x i #v k (t) 15) With this rule, a Fuzzy Competitive Learning algorithm (FCL) can be obtained, where a data point i is presented and u ik is calculated using (13) after which all cluster centers, having a non zero membership are updated using (15) [20]. 3.2 Fuzzy Frequency Sensitive Competitive Learning For the same reasons as in section 2.2, a frequency sensitive approach can be useful. The distance measure is then multiplied by k (t 1) k (t) u q ik (16) 8 which is the total of membership values of cluster k during all previous ....

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F.-L. Chung, T. Lee, Fuzzy competitive learning, Neural Networks 7 (3) (1994) 539--551.

.... J (q) w qk ,c (k) w qk = 0; w qk = 1 x (q) c (k) 2 (r=1,K) 1 x (q) c (r) 2 (9a,b) c n (k) c n (k) J q w qk = c n (k) w qk ) 2 [x n (q) c n (k) n = 1, N (10) The unsupervised fuzzy competitive learning (UFCL) algorithm (Chung and Lee [8], 1994 or see [14] extends the unsupervised competitive learning (UCL) algorithm. The constrained functional to beminimized and the resulting optimal weights and component adjustments are J(w qk ,c (k) q=1,Q) k=1,K) w qk ) p x (q) c (k) 2 , 0 w qk 1; k=1,K) w ....

F. L. Chung and T. Lee, "Fuzzy competitive learning," Neural Networks, vol. 7, no. 3, 539-552, 1994. -12-

....is treated as a fuzzy membership value of the current input sample in the class of each neuron. The membership values are computed with the fuzzy c means algorithm. Tsao et al. 60] have extended their ideas to a family of Kohonen s SOM algorithms. Similarly, Bedzek et al. 5] and Chung and Lee [12] have extended this approach to Kohonen s learning vector quantization algorithm. Similarly, Carpenter et al. 7, 8] have also developed fuzzy versions of their ART and ARTMAP models. 4.2 Neural fuzzy inference systems The basic idea in neural fuzzy inference systems is to incorporate parallel ....

F. L. Chung and T. Lee, "Fuzzy competitive learning," Neural Networks, vol. 7, no. 3, pp. 539--551, 1994.

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F.L. Chung, T. Lee, Fuzzy competitive learning, Neural Netw. 7 (3) (1994) 539--551.

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F.-L. Chung and T. Lee. Fuzzy competitive learning. Neural Networks, 7(3):539-- 551, 1994.

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