I. Gath and A. B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on pattern Analysis and Machine Intelligence, 11(7):773-- 781, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....yielding a single set of features weights. Unfortunately, class dependent feature selection weighting cannot be applied when the data set is unlabeled. In this case, one possible solution is to perform clustering using a covariance matrix based distance. Examples of such algorithms can be found in [3, 7, 6]. When the dimensionality of the feature space is large, it is common in practice to assume diagonal covariance matrices. Each diagonal element of the matrix (i.e. estimated variance) can be used to assign a degree of relevance to the corresponding feature. Another recently introduced clustering ....

I. Gath and A. B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7):773--781, July 1989.

....and leads to worse and instable results in case of noisy real life data. However, like RLVQ, GRLVQ has the advantage of an intuitive update rule and allows efficient input pruning compared to other approaches which adapt the metric to the data involving additional transformations as proposed in [8, 13, 34] or depend on less intuitive differentiable approximations of the original dynamics [21] Moreover, it is based on a gradient dynamics compared to heuristic methods like DSLVQ [26] We will verify our method on various small data sets. Moreover, we will apply GRLVQ to classify a real life ....

I. Gath and A. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:773--791, 1989.

....topology preservation [33] 35] 3.4 Further Approaches Beside the above introduced methods further approaches of neural inspired algorithms are well known. In this context we have to refer to the family of Fuzzy clustering algorithms as for instance FUzzy SOM [36] 37] 38] Fuzzy c means [39] [40] or other (neural) vector quantizers based on minimization of an energy function [41] 42] 20] For an overview of resepective approaches we refer to [43] neural network approaches) 44] 45] pattern classification) 4 Application in Remote Sensing Image Analysis 4.1 Low Dimensional Data: ....

I. Gath, A. Geva, Unsupervised optimal fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence ll (1989) 773-781.

....and leads to worse and instable results in case of noisy real life data. However, like RLVQ, GRLVQ has the advantage of an intuitive update rule and allows efficient input pruning compared to other approaches which adapt the metric to the data involving additional transformations as proposed in [7,9,22] or depend on less intuitive differentiable approximations of the original dynamics [15] We will apply GRLVQ to classify a real life satellite image with approx. 3 mio. data points. Apart from the above mentioned methods, dimensionality reduction is possible via standard methods like principal ....

I. Gath and A. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11:773--791, 1989.

.... Other validity indices for crisp clustering have been proposed in [9] and [10] The implementation of most of these measures is very expensive computationally, especially when the number of clusters and number of objects in the data set grow very large [11] Other validity measures are proposed in [12], 13] We should mention that the evaluation of proposed measures and the analysis of their reliability have been quite limited. In the following, we define a goodness index for evaluating clustering schemes based on the validity index defined for the fuzzy c means method (FCM) in [13] We use ....

Gath, Geva, B.: Unsupervised Optimal Fuzzy Clustering. IEEE Transactions on Pattern Analysis and machine Intelligence, Vol.11, No.7, July (1989)

....Davies and Bouldin offer some guidance for selecting appropriate values) The criterion value should be minimised over the solution space. Further discussion of criteria for determining the number of clusters can be found in [63, 15] Criteria for use with fuzzy clustering methods is described in [5, 22, 42]. 4.1.2 Adaptions for the General Clustering Problem It is possible to adapt the group number GCAs we developed in Chapter 2 by simply exchanging the fitness function for a criterion appropriate for the general clustering problem. The k parameter now becomes an upper limit on the number of ....

....Secondly, better clustering criteria may give the GCA an advantage over other clustering methods. Certainly, work in the area of fuzzy clustering suggests that genetic clustering may benefit from the clustering criteria in this field (the matrix representation is suitable for fuzzy clustering) [22, 42]. GCAs may perform better when there are large numbers of sub optimal minima that trap other search techniques. Thirdly, parallel implementations of GAs [66, 50] divide the algorithm between a number of computers by creating a number of small populations rather than a single larger population. ....

I. Gath and A. B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7):773--81, 1989.

....each cluster. Many algorithms have been proposed for such analysis and for the estimation of the optimal number of partitions. The majority of popular and computationally feasible techniques rely on assuming that clusters are hyper ellipsoidal in shape. In the case of Gaussian mixture modelling [18, 6, 7] this is explicit; in the case of dendogram linkage methods (which typically rely on the L 2 norm) it is implicit [11] For some data sets this leads to an over partitioning. Alternative methods, based on valley seeking [6] or maxima tracking in scale space [15] for example, have the advantage ....

I. Gath and B. Geva. Unsupervised Optimal Fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7):773--781, 1989.

....the corpus, it can have a degree of membership to the other clusters in the search space. Therefore fuzzy membership can be used for determining the biagram statistics of a cluster. Researchers working on fuzzy clustering present a framework for defining fuzzy membership of elements. Gath and Geva[9] describe such an unsupervised optimal fuzzy clustering. They present the K means algorithm based on minimization of an objective function. For the purpose of this research only the membership function of the presented algorithm is used. The memberhip function u ij that is the degree of membership ....

Gath I, Geva A.B. Unsupervised Optimal Fuzzy Clustering. IEEE Transactions on pattern analysis and machine intelligence, Vol. 11, No. 7, July 1989.

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I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7:773--781, 1989.

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I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7:773--781, 1989.

....di#erent distance measures. Often, the Gustafson Kessel clustering algorithm, with hyper elipsoid prototypes, is applied for fuzzy model identification [31] However, a drawback of this algorithm is that mainly clusters with equal volumes are found. We apply the method introduced by Gath and Geva [32] who interpret the data as normally distributed random variables and assume a normal (Gaussian) distribution with excepted value v i and covariance matrix F i to be chosen for generating the datum with a priori probability p(# i ) Hence, the Gath Geva clustering algorithm is identical to the ....

I. Gath, A. Geva, Unsupervised optimal fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence 7 (1989) 773--781.

....be reduced by using eigenvector projection [2] 19] and or by fine tuning the parameterized membership functions. This fine tuning, however, can result in overfitting and thus poor generalization of the identified model. In this paper, we propose to use the Gath Geva (GG) clustering algorithm [7] instead of the widely used GustafsonKessel method [9] because with the GG method, the parameters of the univariate membership functions can directly be derived from the parameters of the clusters. Through a linear transformation of the input variables, the antecedent partition can be accurately ....

....The main drawbacks of this algorithm are that only clusters with approximately equal volumes can be properly identified and that the resulted clusters cannot be directly described by univariate parametric membership functions. To circumvent these problems, in this paper Gath Geva algorithm [7] is applied (see also the Appendix) Since the cluster volumes are not restricted in this algorithm, lower approximation error and more relevant consequent parameters can be obtained than with Gustafson Kessel (GK) clustering. An example can be found in [2] p. 91. The clusters obtained by GG ....

I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7:773-- 781, 1989.

....sampled functions. Keywords: fuzzy clustering, function clustering, sets of features analysis, continuous piecewise linear function approximation, aggregated data, linear features 1 Introduction Fuzzy clustering algorithms like the algorithm by Gustafson and Kessel (GK) 6] Gath and Geva (GG) [5], or the fuzzy c varieties (FCV) algorithm [1] are capable of detecting linear substructures (clusters) in a set of feature attribute vectors (see [9] for a detailed discussion) These algorithms therefore have been used intensively to construct fuzzy models automatically from data, see [10] for ....

I. Gath and A. B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7):773-781, July 1989.

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I. Gath and A. B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on pattern Analysis and Machine Intelligence, 11(7):773-- 781, 1989.

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I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 11:773-781, 1989.

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I. Gath and A. B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on pattern Analysis and Machine Intelligence, 11(7):773-- 781, 1989.

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I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 7:773--781, 1989. 30

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I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 11:773-781, 1989.

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I. Gath and A. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7):773--780, 1989.

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I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 11:773-781, 1989.

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I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, pages 773--781, July 1989.

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I. Gath and A. B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-11(7):773--781, July 1989.

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I. Gath and A.B. Geva. Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 11:773-781, 1989.

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I. Gath, A. B. Geva, Unsupervised optimal fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence 7 (1989), pp 773-781.

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I. Gath, A. B. Geva, Unsupervised optimal fuzzy clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence PAMI-11 (7) (1989) 773--781.

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