J.C. Bezdek and S.K Pal, Fuzzy Models for Pattern Recognition, IEEE Press, New York, 1992. 29  Home/Search   Document Not in Database   Summary   Related Articles   Check

....used in the generation of a decision tree classifier. This approach is well suited to distributed learning, since the entire dataset is never required to be loaded in memory at one time. Examples can be randomly chosen and distributed across a set of processors. Fuzzy c means (FCM) clustering [1] is used to examine the effects of intelligent partitioning of a dataset. A clustersplitting FCM algorithm is applied to the dataset in order to create meaningful partitions of the data. The algorithm begins with two clusters ( and clusters until the fuzzy membership values are stable. The ....

J. C. Bezdek and S. K. Pal, editors. Fuzzy Models For Pattern Recognition. IEEE Press, New Jersey, 1991.

....of the image can be done with little a priori knowledge of the image characteristics. A c means clustering algorithm attempts to separate the data into c distinct clusters. The method for partitioning data is generally a minimization of square error of distance from the cluster center to example [1]. The fuzzy c means (FCM) algorithm broadens the notion of cluster membership. Each example in the dataset is assigned a membership value in [0, 1] for each cluster. The use of FCM has been shown to be effective in image segmentation, including medical imaging [3] However, large image sizes ....

....data into c distinct clusters. The method for partitioning data is generally a minimization of square error of distance from the cluster center to example [1] The fuzzy c means (FCM) algorithm broadens the notion of cluster membership. Each example in the dataset is assigned a membership value in [0, 1] for each cluster. The use of FCM has been shown to be effective in image segmentation, including medical imaging [3] However, large image sizes require significant amounts of computation. In [6] a clustering method called 2rFCM is introduced. This algorithm reduces the image precision in order ....

J. C. Bezdek and S. K. Pal, editors. Fuzzy Models For Pattern Recognition. IEEE Press, New Jersey, 1991.

....on neural networks and fuzzy logic. These topics will not be discussed in detail in this chapter; however, related references will be introduced throughout the dissertation as the methodology is presented. Several good references can be used for a general introduction to the topics, including [6, 7, 77] for fuzzy logic and [20] for neural networks. Also, 36] provides insights on using both neural networks and fuzzy logic. A. Understanding and Using Force Signals The use of force signals dates back to the 1950 s and 1960 s with force feedback for remote manipulators and artificial arm control ....

J. Bezdek and S. Pal, Fuzzy Models for Pattern Recognition, IEEE Press, New York, NY, 1992.

....FUZZY ADAPTIVE SYSTEM ART BASED Fuzzy sets theory based on pioneer work by Zadeh [30] introduces an alternative to cope with vague information through a formulation close to that used in natural language. It has been used in different areas including pattern recognition and classification [3]. In the past few years two criteria have been followed for the definition of fuzzy logic systems: on one hand heuristic methods usually based on ideas coming from statistical classification [1] on the other, embedding of fuzzy logic into neural networks in order to have fuzzy systems with ....

J. Bezdek and S. Pal, Fuzzy Models for Pattern Recognition, IEEE Press, Los Alamitos, CA, USA, 1992.

....in the class definition. Similarly in the high level vision there may occur ambiguities in the interpretation of a scene. We will present a summary of the research being done in both fields. In the low level vision ambiguities can be eradicated with the help of fuzzy object functional methods [2][3] which try to minimize the within group sum of squared errors. This has been successfully used for detecting edges from the images[51] 21] 6] There are other techniques used in the low level vision, histogram equalization [41] 16] and measuring geometrical features[46] 27] The high level vision ....

....algorithms exist[48] 35] e.g. dynamic programming, piecewise linear polygonal approximation of a connected edge list, Hough transform[48] A number of clustering techniques have been used for edge detection. Amongst these the fuzzy clustering techniques are proved to be highly successful[2][3][6 7] 51] not only for edge detection but for region segmentation as well. These techniques are mostly based on the minimization of objective functional[2] where the objective functional is the weighted sum of square (WGSS) of the distances (euclidean for linear clusters) from a measured pixel ....

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J.C. Bezdek and S.K. Pal, Fuzzy models for pattern recognition, IEEE Press, 1992.

....of Gaussian membership functions are set equal to a prespecified positive value. The problem of estimation initial values of membership functions for antecedent of if then rules may also be solved by means of preliminary clustering the input part of the training set using the fuzzy c means method [2], 6] 50] 51] Indeed, in our case we have I clusters. So, the name fuzzy I means method will be a better. In this method each input vector x 0 (n) n = 1, 2, N is assigned to clusters represented by prototypes v i ; i = 1, I measured by grade of membership u in [0, 1] The (I ....

.... in (1, #) The quantity d in is the inner product induced norm (72) d in = #x = x 0 (n) v i ) # (x 0 (n) v i ) It can be proved that a local minimum of criterion (71) may be obtained by an iterative method of commutative modification of partition matrix and prototypes [1] [2]: 73) u in = j=1 d in d jn m 1 (74) # 1#i#I v i = The optimal partition is a fixed point of (73) and (74) and the solution is obtained from the Picard iteration. This algorithm is called fuzzy ISODATA or Fuzzy I Means and can be described in the following steps: 1 # ....

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J.C. Bezdek and S.K. Pal, Fuzzy Models for Pattern Recognition. New York: IEEE Press, 1992.

....combining rules The fixed combining rules make use of the fact that the outputs of the base classifiers are not just numbers, but that they have a clear interpretation: class labels, distances, or confidences. The confidence is sometimes interpreted or generated by fuzzy class membership functions[1,17] sometimes by class posterior probabilities [4] In the following discussion we will use the latter concept. The confidence P i (x) of object x with respect to class w i (i = 1, c) is defined as P i (x) Prob(w i x) 1) In relation with classifier C j (x) however, it depends just on the ....

....x ( i x ( max i x ( min i x ( median same classifier outcome belong to class w i . So, if C ij (x)is based on some discriminant S ij (x) then C ij (x) f(S ij (x) 12) with f( such that (13) In general, f( has to map distances to a discriminant to probabilities, so f: [0,1]. An example is the logistic function f(z) 1 (1 exp( az) The free parameter a has to be optimized on the training set such that (13) holds. 4.2 Global selection and weighting of base classifiers The base classifiers may differ in performance as well as in the amount of overtraining. Both can ....

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J.C. Bezdek, S.K. Pal, Fuzzy models for Pattern Recognition, IEEE Press, Piscataway, 1992.

....in [19] the concept of fuzzy clusters stands in the assignation to each data element of a partial or distributed membership to each cluster. In the fuzzy c means algorithm, these memberships are used as weights in the computation of the distances between data elements and centroids (see [2]) Distributed memberships are assigned to the data elements until the process reaches convergence (i.e. improvement in the cost function smaller than a threshold) eventually the final memberships are exclusive (for the purpose of classification) and correspond to the highest memberships. For ....

Bezdek J and Pal S.K., Fuzzy models for pattern recognition, 1EEE Press, New York 1992.

.... theory in pattern recognition and cluster analysis was also recognized in the mid 1960 s [91] and the literature dealing with pattern recognition and fuzzy clustering is now quite extensive [12, 14] Fuzzy pattern recognition ranges from fuzzy image processing to control and modeling applications [15]. Another relatively common approach is fuzzy equivalence relation based hierarchical clustering [56] The aforementioned scientific results and practical applications have proven the relevance of fuzzy set theory to cluster analysis [13] Because our specific interest lies in fuzzy clustering ....

J. C.Bezdek and S. Pal, Fuzzy Models for Pattern recognition, IEEE Press, New York, 1992.

....or the Mexican Hat, but also many other locally operating filter masks [10] cannot distinguish sufficiently if deviations are chaotic or anisotropic. Another possibility we also took into consideration was to use wavelet transforms [3, 13] or more sophisticated image segmentation methods [2, 10]. Since we had to cope with serious restrictions in terms of computation speed, such highly advanced methods, although they are efficient, would require too much time. Finally, we found a fairly good alternative which is based on the discrepancy norm. This approach uses only, like the simplest ....

J. C. Bezdek and S. K. Pal, editors. Fuzzy Models for Pattern Recognition. IEEE Press, New York, 1992.

....of the jth cluster increases. Also, it is desired that the associations be non negative, and that P j a i;j = 1; 8i. The jth cluster center is simply P i a i;j x i . Depending on how the associations are formed and updated, a variety of powerful fuzzy clustering approaches have been obtained [18]. A critical issue in clustering is the choice of an appropriate scale, which determines the number of clusters obtained and hence the amount of segmentation obtained. For a given image, there are some natural scales for which the clusters are relatively well de ned and stable in the sense that ....

J. C. Bezdek and S.K. Pal. Fuzzy Models for Pattern Recognition. IEEE Press, Piscataway, NJ, 1992.

....are chaotic or anisotropic. Homogeneous Edge Halftone Picture Figure 1: Magnifications of typical representatives of the four types Another possibility we also took into consideration was to use wavelet transforms or more sophisticated image segmentation methods (see for instance [7] or [3]) Since we had to cope with serious restrictions in terms of computation speed, such highly advanced methods, although they are efficient, would require too much time. Finally, we found a fairly good alternative which is based on the discrepancy norm. This approach uses only, like the simpliest ....

J. C. Bezdek, S. K. Pal. Fuzzy Models for Pattern Recognition. IEEE Press, New York, 1992.

....other locally operating filter masks (see e.g. 7] cannot distinguish sufficiently if deviations are chaotic or anisotropic. Another possibility we also took into consideration was to use wavelet transforms (see [5] or [8] or sophisticated image segmentation methods (see for instance [7] or [3]) Since we have to cope with serious restrictions in terms of computation speed, such highly advanced methods would require too much time. Finally, we found a fairly good alternative which is based on the discrepancy norm. This approach uses only, as ordinary filter masks also do, the closest ....

J. C. Bezdek and S. K. Pal. Fuzzy Models for Pattern Recognition. IEEE Press, New York, 1992.

....sy stems converge. Still, due to the large amount of data available from good engines, the decision boundary between good and faulty can be learnt by examples. Therefore, a fuzzy rule based approach was selected as it allows both the incorporation of a priori knowledge and learning by examples [1,2]. The membership functions of the linguistic terms describing the good class are tuned by a learning algorithm using appropriate training examples [3] Faults that occur in various levels (e.g. the different levels of leakage in the exhaust pipe) should be treated as one fault class. Hence, fault ....

Bezdek J. C. and Pal S. K. (eds.), Fuzzy Models for Pattern Recognition, Prentice Hall, 1992

....of the system s structure based only in experts description can be very poor. If the information is wrong then the model will be bad. It s need to complement operator subjectivity with a more objective knowledge using available numerical data from the system in question. Both for fuzzy model (Bezdek and Pal, 1992) and fuzzy control, the number of fuzzy sets attributed for each variable and its localization in the universe of discourse is responsible for the acquired performance. In this paper the autonomous mountain clustering method (Costa Branco, Lori and Dente, 1995) is applied to fuzzy systems ....

Bezdek, J. C. and Pal, S. K., (1992) "Fuzzy Models for Pattern Recognition", Eds. New York: IEEE Press.

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J.C. Bezdek and S.K Pal, Fuzzy Models for Pattern Recognition, IEEE Press, New York, 1992. 29

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J.C. Bezdek and S.K. Pal, Eds., Fuzzy Models for Pattern Recognition, IEEE Press, New York, 1992.

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BEZDEK, J. C. and PAL, S. K., (editors) : `Fuzzy models for pattern recognition', (IEEE Press, New York, 1992).

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J.C. Bezdek and S.K. Pal. Fuzzy models for pattern recognition. IEEE Press, Piscataway. N.Y., 1992.

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J. C. Bezdek and S. K. Pal (eds.) Fuzzy models for pattern recognition, IEEE Press, N.Y., 1992.

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J. C. Bezdek and S. K. Pal, Fuzzy Models for Pattern Recognition.New York: IEEE Press, 1992.

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J. Bezdek and S. Pal, Fuzzy Models For Pattern Recognition, IEEE Press Inc., New York, 1992.

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James C. Bezdek and Sankar K. Pal, editors. Fuzzy Models For Pattern Recognition. IEEE Press, New Jersey, 1991.

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J. C. Bezdek and S. K. Pal, Fuzzy Models for Pattern Recognition. IEEE, New York (1992).

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James C. Bezdek and Sankar K. Pal. Fuzzy Models for Pattern Recognition. IEEE Press, 1992.

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